Neutrino Oscillations and Their Origin

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The Fourth International Workshop on

Neutrino Oscillations and their Origin

This page intentionally left blank

The Fourth International Workshop on

Neutrino Oscillations and their Origin Kanazawa, Japan

10 - 14 February 2003

Edited by

Y. Suzuki, M. Nakahata,Y. Itow, M. Shiozawa & Y. Obayashi University of Tokyo, Japan

N E W JERSEY

-

r pWorld Scientific LONDON

SINGAPORE * BElJlNG

-

SHANGHAI

*

HONG KONG

*

TAIPEI * C H E N N A I

Published by

World Scientific Publishing Co. Re. Ltd.

5 Toh Tuck Link, Singapore 596224 LISA ofice: Suite 202, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-PublicationData A catalogue record for this book is available from the British Library.

Proceedings of the 4th International Workshop on NEUTRINO OSCILLATIONS AND THEIR ORIGIN Copyright 0 2004 by World Scientific Publishing Co. Pte. Ltd.

All rights reserved. This book, or parts thereof; may not be reproduced in any form or by any means, electronic or mechanical, includingphotocopying, recording or any informarion storage and reirieval sysiem now known or ro be invented, without written permissionfrom the Publisher.

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PREFACE NOON2003 (Neutrino Oscillations and their Origin) was held at Kanazawa between lO* and 14' February, 2003. This is the fourth of this series. The first was held at Fuji-Yoshida in March 2000, as a local workshop. Since the participants from abroad have been increasing gradually through the past workshops, we have therefore made this fourth workshop an international one and we have set up an international advisory committee. We would like to thank the members of the international advisory committee for all their suggestions and comments to the organizers. This workshop was very timely since the solar neutrino oscillation has been confirmed by KamLAND after the first indication of the solar neutrino oscillation by Super-Kamiokande and SNO in June 2001. Together with the discovery of atmospheric neutrino oscillations in 1998, we feel that we are now entering the new era for the neutrino oscillation study. We have therefore compiled a global summary of our current knowledge on the neutrino oscillations and conveyed a significant discussion on the future direction of neutrino oscillation studies and the related subjects for both theoretical and experimental works. The workshop has covered future researches on neutrino oscillations by accelerator based experiments, which may provide a better understanding of the yet-determined mixing angle OI3 and lead to the discovery on CP violation in lepton sector. Another important subject discussed was the searches for the Majorana mass term of neutrinos which will provide quantitatively different information other than the oscillation phenomena. The precision studies on atmospheric and solar neutrinos were extensively discussed, and the astrophysical roles of the neutrino mass were seen as interesting subjects. We had about 118 participants, 77 from Japan and 41 from 12 countries abroad. This workshop was supported by the Grant-in Aid of Scientific Research in the specific field for NEUTRINOS. May 2003 Yoichiro Suzulu Chairman of the Workshop

V

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International Advisory Committee J .N. Bahcall A. Bettini H. Ejiri E. Fiorini W. Haxton P. Lipari A. McDonald G. Raffelt S. Schoenert A.Y. Smirnov P. Vogel S. Wojicki T. Yanagida M. Yoshimura

Princeton GranSasso Osaka Milano Washington Roma Queens Max Plank Munich Max Plank Heidelberg Trieste Caltech Stanford Tokyo/CERN ICRR, Tokyo

Scientific Program Committee M.Bando T.Kajino T.Kajita H.Minakata T.Mori M .Nakahata M .Sakuda H .Shibahashi Y.Suzuki M.Tanimoto T.Yoshida

Aichi NAO ICRR, Tokyo Tokyo Metropolitan Univ. ICEPP, Tokyo ICRR, Tokyo KEK Tokyo ICRR, Tokyo Niigata KEK

Local Organizing Committee ICRR, Tokyo ICRR, Tokyo ICRR, Tokyo ICRR, Tokyo ICRR, Tokyo

Y.Itow Y.Obayashi M.Nakahata M.Shiozawa Y.Suzuki vi i

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Contents Preface Z Suzuki

V

International Advisory Committee, Scientific Program Committee and Local Organizing Committee

vii

Session 1 Solar and Reactor Neutrinos

1

KamLAND Results K. Inoue

3

Sudbury Neutrino Observatory: Physics Implications of Upcoming Data M. C. Chen

13

Solar Neutrino Precision Measurements using all 1496 Days of Super-Kamiokande-IData M. B. Smy

21

Solar Neutrino Spectroscopy with Borexino and Future Low Energy Solar Neutrino Experiments S. Schonert

29

Neutrino Oscillations and the Sunshine M. C. Gonzalez-Garcia

39

Supernova Relic Neutrino Search Results from Super-Kamiokande M. Malek

51

Supernova Relic Neutrinos and Neutrino Oscillation S. Ando & K. Sat0

57

Solar and Reactor Neutrino Analysis: Results and Desiderata G . L. Fogli, E. Lisi, A. Marrone, A. Palauo, A. M. Rotunno & D. Montanino

65

Can Four Neutrinos Explain Global Oscillation Data Including LSND and Cosmology? T Schwetz, M. Maltoni, M. A. Tortola & J. W E Valle IX

75

X

Universal Texture of Quark and Lepton Mass Matrices !l Koide, H . Nishiura, K. Matsuda, T. Kikuchi & T. Fukuyama

85

Neutrino Masses and Beyond from Supersymmetry 0. C. H! Kong

91

Neutrino Physics after KamLAND A. Smirnov

99

Session 2 Accelerated Neutrinos and Future Neutrino OscillationExperiments

113

Results in K2K and Future T. Kobayashi

115

BooNE at Six Months E. D. Zimmerman

123

Status of MINOS (contribution was not received) M . Messier Status of OPEWCNGS (Contribution was not received) M. Nakamura The ICARUS Project: An Underground Observatory for Astro-Particle Physics A. Ereditato

131

Off-Axis Experiment in the NuMI Beam at Fermilab S. Wojcicki

139

JHFNU (Phase I) Neutrino Oscillation Experiment A. K. Ichikawa

147

Precise Measurement of sin22OI3Using Japanese Reactors E Suekane, K. Inoue, T. Araki & K. Jongok

155

The HLMA Project in the Light of the First KamLAND Results Measurement of sin2(2813) with a New Short Baseline Reactor Neutrino Experiment T. Lasserre, S. Schonert & L. Oberauer

163

xi

Using Reactors to Measure M . H. Shaevitz & J. M. Link

171

Impact of Ue3 on Neutrino Models M . Tanimoto

179

CP Violation in JHF, (Phase-11) T. Nakaya

189

Long Baseline Neutrino Oscillations: Parameter Degeneracies and JHF/NuMI Complementarity H. Minakata, H. Nunokawa & S. Parke

196

Golden and Silver Channels at the Neutrino Factory A. Donini

202

Parameter Degeneracy and Reactor Experiments 0. Yasuda

208

Session 3 Atmospheric Neutrinos

217

Results from L3+C I? Le Coultre

219

A Measurement of Mu, P and He Energy Spectra at the Small Atmospheric Depth K. Abe The Calculation of Atmospheric Neutrino Flux M. Honh Progress in Analysis of High Energy Primary Cosmic-Ray Spectra Measured in BESS-02 S. Haino Atmospheric Neutrinos C. Yanagisawa

225

23 1

239 247

Initial Results from HARP (Contribution was not received) C. Wiebusch Study of Neutrino-Nucleus Interactions for Neutrino Oscillation Experiments M. Sakuda

253

xii

Session 4 Dark Matter and Double Beta Decay

261

Status of Evidence for Neutrinoless Double Beta Decay and the Future: Genius and Genius-TF H. V Klapdor-Kleingrothaus

263

CUORICINO and CUORE: Results and Prospects A. Giuliani, A. Fascilla, M. Pedretti, C. Arnaboldi, C. Broferio, S. Capelli, L. Carbone, 0. Cremonesi, E. Fiorini, A. Nucciotti, M. Puvan, G. Pessina, S. Pirro, E. Previtali, M. Sisti, L. Torres, D. R. Artusa, E 7:Avignone, Ill, I. Banduc, R. J. Creswick, H. A. Farach, C. Rosenfeld, M. Balata, C. Bucci, M. Pyle, M. Burucci, E. Pasca, E. Olivieri, L. Risegari, G. Ventura, J. Beeman, R. J. McDonald, E. E. Haller, E. B. Nonnan, A. R. Smith, S. Cebrian, P. Gorla, I. G. Irastorza, A. Morales, C. Pobes, G. Frossati, A. De Waard & V Palmieri

283

Initial Runs of the NEMO 3 Experiment: NEMO Collaboration S. Jullian

29 1

Neutrinoless Double Beta Decay Constraints H. Sugiyama

300

Neutrino Mixing and (PP)w - Decay S. 7: Petcov

308

The Majorana Experiment: A Straightforward Neutrino Mass Experiment using the Double-Beta Decay of 76Ge H. S. Miley MOON (Mo Observatory of Neutrinos) for Neutrino Studies by Double Beta Decays and Low Energy Solar Neutrinos H. Ejiri, T Itahashi, 7: Shima, R. Hazama, I: Ikegami, K. Mutsuoka, H. Nukamura, M. Nomachi, I: Shimada, I: Suguyu, S. Yoshida, K. Fushimi, K. Ichihara, I: Shichijo, M. Greenjield, t! J. Doe, R. G. H. Robertson, 0. E. Vilches, J. F. Wilkerson, D. I. Will, S. R. Elliott, J. Engel, A. Para, M. Finger, K. Kuroda, A, Gorin, L. Manouilov, A. Rjazantsev, V Kutsalo, V Vatulin, V Kekelidze, G. Shirkov, A. Sisakian, A. Titov & V Voronon

318

326

...

Xlll

EXO: A Next Generation Double Beta Decay Experiment C. Hall

332

Candles for the Study of pp Decay of 48Ca 'I: Kishimoto, I. Ogawa, R. Hazama, S. Yoshida, S. Umehara, S.Ajimura, K. Matsuoka, H. Sakai, D. Yokoyama, T. Miyawaki, K. Mukaida, K. Ichihara, !I Tatewuki, K. Fushimi & H . Ohsumi

338

CAMEO/GEM Projects and Discovery Potentiality of the Future 2p Decay Experiments Yu. G. Zdesenko, E A. Danevich & V I. Tretyak

350

XMASS Experiment S. Moriyama

364

Cosmological Constraints on Neutrino Masses and Mixings A. D. Dolgov

372

Supernova Neutrinos: Flavor-Dependent Fluxes and Spectra G. G. Raffelt, M. Th. Keil, R. Buras, H. -T. Janka & M. Rampp

380

Neutrino Flavor Conversion Inside and Outside a Supernova C.Lunardini

388

Future Detection of Supernovas M. R. Vagins

396

Session 5 Lepton Flavor Violation, Leptogenesis and Proton Decays Birth of Neutrino Astrophysics M. Koshiba

403

405

Lepton Flavor Violation and SUSY GUT (contribution was not received) E Shimizu (S) Fermion Masses and Lepton Flavor Violation - A Democratic Approach K. Hamaguchi, M. Kakizaki & M. Yamaguchi pe Gamma Experiment (MEG) (contribution was not received) D. Nicolo

418

xiv

Fe Conversion Experiments: Testing Charged Lepton Flavor Violation A. Van Der Schaaf

425

Neutrino Bi-Large Mixings and Family M. Bando & M. Obara

433

Leptogenesis and Neutrino Masses M. Pliimacher

439

Leptogenesis and CP Violation of Neutrino Oscillation T. Morozumi

447

Experimental Review of Proton Decays M. Shiozawa

455

Theoretical Review of Proton Decay (contribution was not received) J. Hisano Impact and Implication of Bi-Large Neutrino Mixings on GUTS T. Kugo

46 1

Scientific Programme

469

List of Participants

475

Session 1

Solar and Reactor Neutrinos

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KAMLAND RESULTS

K.INOUE Research Center for Neutrino Science, Tohoku University, Aramaki Aoba, Aoba, Sendai, Miyagi 980-8578, J A P A N E-mail: inoueaawa. tohoku. ac.jp The LMA solution of the solar neutrino problem has been explored with the 1,000 t,nn liqiiid srintillator detector, KamLAND. It utilizes nuclear power reactors distributing effectively -180 km from the experimental site. Comparing observed neutrino rate with the calculation of reactor operation histories, an evidence for reactor neutrino disappearance has been obtained from 162 ton.year exposure data. This deficit is only compatible with the LMA solution and the other solutions in the two neutrino oscillation hypothesis are excluded at 99.95% confidence level.

1. Reactor Neutrinos In spite of the deficits observed in all solar neutrino experiments and improvement of their precisions, the solar neutrino problem has lasted for more than 30 years. A recent revolutionary neutral-current-measurement by SNO experiment has provided an evidence of neutrino flavor transformation and proved that the problem is really on neutrino characteristic. We also know the evidence of atmospheric neutrino oscillation from SK, and it is natural to invest neutrino oscillation hypothesis to explain the solar neutrino problem. In the two neutrino oscillation hypothesis, the large mixing angle (LMA) solution is the most preferable solution. However, another solution also appears at 99% confidence level and even completely different models such as neutrino magnetic moment and neutrino decay can explain all the experimental data as well as the LMA solution. It is necessary to use a well-understood artificial neutrino source to meet a breakthrough in the solar neutrino study. Anti-electron-neutrinos from nuclear power plants are such candidates. Total power generation of worldwide reactors amounts to -1.1 TW and it corresponds to one third mole 0, creation per second. Fortunate characteristic of KamLAND site is that 70 GW (7% of world total) distributes at distances from 130 to 240 km and consists 80% of neutrino flux at Kamioka site, 5 x 106/cm2/sec. N

3

4

This long baseline, effectively 180 km, is sensitive to the LMA oscillation parameters as shown in Fig. 1.

1.2 2 1

=

0.8 0.6 j 0.4 p 0.2 0 50 100 150 200 250 300 350 400 450 500 Distance (km)

’5

0

Figure 1. Distribution of nuclear power reactors SLS a function of distance from KamLAND site. Solid histogram is the current operation and dashed histogram is an expected operation in 2006 (Shika at 88km increases by a factor 3). Height of the histogram shows thermal power flux contribution at Kamioka. Also shown as solid (Am’= 7 x 10-5eV2), lines are the survival probability of Ye as a funcdashes ( 3 x and dots (1.4 x tion of distance (all for sin2 29 = 0.84). The probability is calculated for events above 2.6 MeV in visible energy.

Thermal power output of rector cores directly relates to the neutrino flux. Those of all 54 Japanese commercial reactor cores are measured with strictly better than 2% accuracy. In more detail, contributions from 4 different fisile nuclei, 235Ul 238U, 239Pu and 241Pu, have to be known for 1% precision. Since the chemical composition of nuclear fuel changes in time as a burn-up effect, we have t o know the initial 235U enrichment and history of thermal power output for each relevant reactor cores. This history information is also important to estimate time lag (0.28% error) of beta decay from energy release and non-equilibrium effect of long-life nuclei (0.65% error). We have obtained these information from all 54 Japanese cores. The contribution of Korean reactors is 2.5% and we obtained history of their electric power output. Conversion of electric powers to thermal ones causes -10% error and, thus, Korean reactor makes 0.3%error on neutrino flux estimation. All the other reactors contribute by only 0.7% of total neutrino flux and error contribution from them won’t be larger than 0.35%. Measured and/or calculated neutrino spectra for 4 fissile nuclei make 2.48% error on neutrino event rate. Cross section of inverse beta decay is strongly related to free neutron life time. Recent precise measurement of its life time (0.1%) improved calculation of the cross section to better than 0.2% with 1st order radiative corrections.

5

2. KamLAND Detector

KamLAND is the KAMioka Liquid-scintillator Anti-Neutrino Detector located at the cavity for the former Kamiokande experiment. It contains 1,200 m3 liquid scintillator (LS: Pseudo-cumene 20%, dodecane 80% and PPO 1.5g/l) and 1,800 m3 buffer oil (BO) in 18 m diameter stainless steel tank. Free protons in the LS are the ge targets. A positron from the inverse beta decay reaction ( f i e + p -t e+ + n) and a 2.2 MeV gamma ray from the neutron capture on a proton (mean capture time is -210 psec) make clear two-fold-delayed-coincidence signal. The LS is suspended in the BO with an 135pm-thick-film balloon (EVOH-Nylon-Nylon-Nylon-EVOH) and Kevlar rope network controled at neutral buoyancy (0.04% heavier). Photons emitted in the detector are monitored by 1325 newly developed 17” tubes and 554 old Kamiokande 20” tubes. While the total photo-coverage is 34%, only the 17” tubes, corresponding to 22%, are used for this analysis. All these PMTs are isolated from inner region by a 3-mm-thick acrylic sphere preventing radon emanation from these materials. The outer detector (OD) is a water Cherenkov detector with 3.2 kton pure water and 225 old Kamiokande 20” tubes for purposes of external background absorption and cosmic-ray muon tag. Each photo-tubes are connected to two sets of three ranges analogtransient-waveform-digitizer recording whole pulse shape from one to thousands of photo-electrons for about 200 nsec. Global triggers are issued based on number of hit channels (each channels has about 0.3 p.e. threshold) and currently set at 200 hits (- 700 keV) as a prompt trigger and at 120 hits (-400 keV) as delayed trigger for 1 msec after each prompt triggers. Current trigger rate is -25 Hz and the data size amounts to 400 GB/day. This huge data size determines the lowest trigger threshold but it is sufficiently low for the reactor neutrino analysis (all phenomena have visible energies more than two electron mass). The OD trigger threshold is set to provide more than 99% muon tagging efficiency. The primary target, reactor neutrino measurements, requires radioactive impurity level of lower than 10-13g/g for Uranium and Thorium. These impurity level are measured by tagging 214,212Bi-214y212Po in their decay chain and found t o be 3.5f0.5 x g/g of Uranium and 5.2f0.8 x g/g of Thorium assuming radioactive equilibrium. These values are much better than the initial requirement and even better than that of the future

6

7Be solar neutrino measurement. However, an extra purification of 85Kr and 210Pb (daughter of 222Rn)contamination is necessary to start solar neutrino observation in the second stage. Vigorous efforts are being made to invent an efficient purification method and methods to measure their concentration. Requirements and achievements are listed in Table. 1. Table 1. Requirements and Achievements of Radioactive Impurities. Impurities ”‘Rn 2 3 8 ~

232Th 40 K

85Kr 210Pb

Achievements

Req.(solar)

3.5 f0.5 x 10-l8 g / g 5.2 f0.8 x

< 2.7 x

g/g g/g

~1 Bq/rn2 ~ 1 0 mBq/m2 0

equiv. mine dust

on the balloon 222Rn

Req. (reactor)

0.03 pBq/m3

4.0 x l o p 4 Bq

238u

3.1 x l o p 8 g

0.9 g

232Th

9.7 x 1 0 - ~g

0.1 g

3. Calibrations and Systematic errors Energy calibrations are performed suspending radioactive sources (68Ge, 65Zn, 6oCo and AmBe) along the z-axis. They covers energy range from 0.5 MeV to 7.6 MeV. Spallation products (neutron, 12B/12N and 8He/9Li) are also utilized to know the behavior at off z-axis and in higher energies up to -15 MeV. They distribute uniformly both in time and space and thus very useful to monitor space uniformity and time variation. Gamma rays (40K and ‘08T1) from external material also provided a good monitor of time variations. In addition to these wide energy range calibrations, alpha decays in Bi-Po chain provides wide variety of dE/dx and it helped detail study of quenching effect of LS (thus linearity study of energy scale). Observed uniformity of energy scale is better than 0.5% in 5-m-radius fiducial volume and time variation of the scale was controlled within 0.6%. The systematic error for the 2.6 MeV energy threshold is estimated as 2.13% in neutrino event rate. Observed photon yield is -300 p.e./MeV at the center only with 17” PMTs and it will become about 500 p.e./MeV when we start to use 20’’ PMTS. Current energy resolution is 7.5%/dE.

-

7 -15

;

E 210-

-10-15

-600

A Ge

0

Am/Be(Z.ZMeV)

'

'

j

j

j '

:

fiducial .

I

'

-400

.

'

I

'

'

-200

.

'

'

l

.

'

'

l

'

:

'

200 400 6 0 Z position (cm)

0

neutron data

n

fiducial

0.2

0.4

0.6

0.8

1.0

1.2 1.4 (R/6.5m)3

Figure 2. Vertex calibrations. Upper panel shows systematic bias of reconstructed positions along z-axis. Biases are less than 5 cm within fiducial region -500 cm to 500 cm for all energies. Lower panel is the R3 distribution of uniformly distributing spallation neutron events. Uniform distribution appears as flat distribution.

The LS density is 0.780 g/cm3 at 11.5 degree and, thus, the number of free protons in the 5-m-radius fiducial volume is 3.46 x The fiducia1 cut is applied based on the reconstructed vertices from the relative times of PMT hits (typical resolution is -25 cm for 2 MeV events). As shown in Fig. 2, observed systematic biases along z-axis are smaller than 5 cm in the entire fiducial range. It corresponds to less than 3% fiducial volume error under spherical symmetry of the detector. This systematic error was verified with uniformly distributing spallation events (gamma ray from neutron capture and "B beta decays). These spallation events covers energy range from 2.2 MeV to -15MeV where all relevant energies to the reactor neutrino analysis is included. Event rates in the fiducial and in the total volume are compared with the volume ratio and their precision is considered as the systematic error of the fiducial volume. Neutron data gave -1.48 f 2.58% and 12B data gave +0.16 f 3.34%. This verification is currently limited by statistics of spallation events. We employ the most conservative value 1.48% 2.58% + f4.1% and accounting for uncertainty in the LS total mass of 2.13%. we assign 4.6% as the systematic error of the number of target protons. Detection and tagging efficiencies of delayed coincidence signals are

+

8

measured by a LED pulser, intensity measurements of radioactive sources, AmBe delayed coincidence signals and so on. For the specific selection criteria applied in this analysis; (1) a 5-m-radius fiducial cut, (2) a time correlation cut (0.5 psec to 660 psec), (3) a vertex correlation cut (1.6 m), (4) a delayed energy cut (1.8 MeV to 2.6 MeV), and (5) a cylindrical cut around z-axis for delayed signal (1.2 m), we obtained 78.3f 1.6% efficiency for the reactor neutrino signals. Total systematic error we estimated is 6.42% for 2.6 MeV analysis threshold. And break down of the error is listed in Table. 2. Table 2.

Estimated systematic uncertainties in %.

Thermal power output (Japanese)

2.0

Cross section

Korean reactors

0.3

Total LS mass

2.13

Other reactors

0.35

Fiducial ratio

4.06

0.2

Burn up effect

1.0

Energy threshold

2.13

Long-life nuclei

0.65

Efficiency of Cuts

2.06

Time lag of beta decay

0.28

Live time

0.07

Neutrino spectra

2.48

Total

6.42%

4. Backgrounds

The most difficult background in reactor neutrino analysis is geo-neutrinos. The earth has 44 T W heat flow at the surface. Twenty T W of it is thought to come from radio-activities in the earth, 16 T W from Uranium and Thorium and 4 T W from 40K. In U and T h decay chains, there are beta decays emitting observable 0, with the inverse decay (1.806 MeV threshold). They have identical signature with reactor neutrinos. Thier sharp edges at the end-points will be useful t o distinguish them when statistics is sufficient. We currently cannot subtract their contributions blindly using inaccurate predictions. Then, the analysis threshold of visible energy, 2.6 MeV, is set above the geo-neutrino end-point energy, 2.49 MeV. On the other hand, we can separately obtain U and T h contributions from their characteristic energy spectra when sufficient statistics is acquired. Subtraction of nearby contributions with a radio-activity map will make possible to investigate interior of the earth with neutrinos. This is the start of the new field ”Neutrino Geophysics.’’ The lower threshold covering all v, events (0.9 MeV) is also used for a consistency check and geo-neutrino search.

9

Accidental backgrounds are expected to be only 1.81f0.08 and 0.0085f 0.0005 events in final data sets of 0.9 and 2.6 MeV thresholds, respectively. Main fakes are from 'loBi as prompt and '"Tl as delayed events. We also have two types of correlated backgrounds associated by energetic cosmic-ray muons. One is fast neutrons from outside and another is long-lived beta-decay-nuclei associating neutron emission in the detector. Contribution of fast neutrons are estimated by tagging muons in the OD and look for delayed coincidence signal in the ID. Vertices of such events are concentrated close to the wall, and there are no events entering the fiducial volume. We obtained upper limit of such events. Considering inefficiency of the OD tagging and estimating contribution of rock penetrating muons by simulation with restriction of this measurement] we obtained fast neutron backgrounds be smaller than 0.5 events. Long-lived neutron emitters are 'He and 'Li. Their half-lives are 0.12 and 0.18 sec and 16% and 50% of their beta decays they also emit neutrons] respectively. In order to eliminate these backgrounds] spallation cuts are employed. We apply 2 msec veto after any muons. For muons with extra energy losses from minimum ionization larger than lo6 p.e. (-3 GeV), two seconds veto is additionally applied. For smaller energy losses, 2 sec veto is applied only in 3-m-radius cylinder around muon track. These spallation cuts cause 11.4% dead time. After these cuts, we expect 1.1 f 1.0 and 0.94 f 0.85 events for two analysis thresholds. Summary of backgrounds is shown in Table. 3 together with a model prediction of geo-neutrino events.

Table 3. Summary of backgrounds 0.9 MeV threshold

2.6 MeV threshold

Accidental

1.81 f 0.08

0.0085 3z 0.0005

He/g Li

1.1 f 1.0

0.94 3z 0.85

< 0.5

< 0.5

2.91 f 1.12

0.95 f 0.99

9.1

0.044

Backgrounds

Fast neutron Total Geov, 16 TW

5 . Results

The data used for the analysis is from March 4th to October 6th1 2002. Total live time is 145.1days (after dead time subtraction) and it corresponds to 162 ton-year exposure. As seen in Fig. 3, observed rates are always

10

-

Mar

Apr

May

Jun

Jul

Aug

Sep

Figure 3. Reactor neutrino event rate. Plots and line are the observed and expected event rate, respectively, and gray hatches are their averages. Structure in expected rate reflects change of reactor operations.

smaller than the expected ones from no oscillation. While expected number of neutrino events above 2.6 MeV is 86.8 f 5.6, we observed only 54 events including 0.95 f 0.99 background events resulting neutrino disappesarance at 99.95% confidence level. The ratio (Observed-B.G.)/no-oscillation is 0.611 f 0.085(stat.) f 0.04l(syst.). In the 0.9 MeV threshold dataset, we expect 124.8f 7.5 reactor neutrino events, 2.91 f1.12 backgrounds and also -9 geo-neutrino events from a model. However, we observed only 86 events and low energy data is also consistent with the deficit above 2.6 MeV. This evidence of neutrino disappearance supports the LMA solution of the solar neutrino problem and all the other oscillation solutions are excluded at 99.95% C.L. under the CPT invariance. Also the other exotic models (RSFP, neutrino decay etc) can not be the leading phenomena of the solar neutrino problem. Adding the KamLAND results to the solar neutrino observations, we finally solved the solar neutrino problem and the LMA solution is the right solution. In order to claim the neutrino oscillation with KamLAND data alone, spectrum distortion has to be observed. Currently, the distortion (see Fig. 4) is not significant to claim it but helps to shrink the allowed region of the oscillation parameters. Fig. 5 shows the excluded region from the rate analysis and allowed region from rate shape analysis with two different threshold data. Only two bands overlap with the LMA region from solar observations. Two different thresholds give similar allowed region and it means data below and above 2.6 MeV are consistent with each

+

11

+

data

- no osci. Ireactor

-

15

0

1

He8, Li9

2 3 4 5 6 7 prompt energy [MeV1

Figure 4. Observed energy spectrum is shown together with the expected from no oscillation and best fit oscillation spectra. Best fit backgrounds are also shown.

other. When using data below 2.6 MeV, both Uranium and Thorium geoneutrino contributions are treated as free parameters. This is the reason that the allowed region doesn’t shrink with larger statistics in 0.9 MeV threshold. The best fit parameters are met a t (sin2 20,Am2)=(1.0,6.9 x 10-5eV2) with 2.6 MeV threshold and (0.91,6.9 x with 0.9 MeV threshold. The mass difference is stable but mixing angle changes easily. In the low threshold analysis, we obtained the best fit value for U and T h as 4 and 5 events. It corresponds to -40 T W heat flow from Uranium and Thorium. But 0 to 110 T W is allowed at 95% C.L. and statistics is yet insufficient to claim an observation of geo-neutrinos. KamLAND results shrank the allowed region of oscillation parameters to two bands, LMAl (Am2 7 x lop5 eV2) and LMA2 (Am2 1.4 x lop4 eV2). Chi-square of LMA2 is about 3 worse than that of LMAl with current statistics. If LMAl is the true answer, the LMA2 may be excluded in the next update in a year. In any cases, new Shika reactor starts in 2006 locates at a good distance to discriminate them. As shown in Fig. 1, Shika, distance is close to the first minimum of the LMAl and the LMA2 has the second maximum at the distance. Comparison before and after 2006 will give good separation of these two solutions. Our current efforts are focused on the purification of the LS aiming at observing ’Be solar neutrinos with neutrino-electron scattering. It will make a next milestone in the ”Neutrino Astrophysics” and also by combining with charged current observations, it will give a precise measurement

-

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Figure 5. Excluded region by rate analysis and allowed region by rate+shape analysis are shown. All region are shown for 95% confidence level. The LMA is obtained from combined analysis of solar neutrino observations.

of mixing angle. 6. Summary KamLAND observed an evidence of reactor neutrino disappearance at -180 km baseline. Only the LMA solution is compatible with this disappearance and the long standing solar neutrino problem is finally solved with a combination of KamLAND and solar neutrino observations. KamLAND will give a precise value of Am2 and the mixing angle with reactor and solar 7Be solar neutrino observations. Current hint of the geo-neutrino flux will soon become first observation of geo-neutrinos. This manuscript is based on the paper' and the KamLAND experiment is successfully operated and performed by efforts of the KamLAND collaboration from Japan, United States and China.

References 1. KamLAND collaboration, Phys. Rev. Lett. 90(2003)021802.

SUDBURY NEUTRINO OBSERVATORY: PHYSICS IMPLICATIONS OF UPCOMING DATA

M.C. CHEN, FOR THE SNO COLLABORATION Department of Physics Queen’s University Kingston, Ontario, K7L 3N6, Canada E-mail: [email protected]

The Sudbury Neutrino Observatory reported results from neutral-current and charged-current measurements in April 2002. The difference between those event rates was interpreted as the presence, at the 5 c level, of active, non-electron neutrinos coming from the Sun. A global solar neutrino analysis within the framework of matter-enhanced oscillations of two active flavors strongly favored the Large Mixing Angle (LMA) solution. With data from KamLAND confirming oscillation parameters in the LMA region, it is interesting to study the physics capabilities of upcoming SNO data, which will have enhanced neutral-current sensitivity due to the addition of salt to the heavy water. SNO data will constrain the mixing angle since the CC/NC ratio is a direct measure of the survival probability.

1. Introduction The Sudbury Neutrino Observatory (SNO) detects ‘B solar neutrinos using heavy water. Deuterons in heavy water allow SNO to separately measure the flux of all flavors of neutrinos and the flux and energy spectrum of just the electron neutrinos. The results from the pure DzO phase of the experiment were reported in April 2002 - measurements of the fluxes of electron and non-electron, active neutrinos,’ and the energy spectra for day and for night.’ An earlier publication3 compared the flux of electron neutrinos measured by the charged-current reaction (CC) in SNO to the rate of neutrino-electron elastic scattering (ES), as measured in Super-K and SNO. Those measurements conclusively demonstrated that there are other active flavors in the solar neutrino flux beyond electron neutrinos. For over thirty years solar neutrino experiment^^^^^^^^^'^^ have observed that the flux of electron neutrinos from several reactions within the Sun is significantly smaller than predicted by models of the Sun’s energy generation

13

14

rnechanism.l0>l1A natural explanation for all the observations is that u,’s from the Sun undergo matter-enhanced neutrino oscillations, while passing through the Sun, and are converted t o other active flavors. Those flavors have now been detected. SNO is a water Cerenkov detector which uses 1,000 tons of heavy water (DzO) as both the interaction and detection medium.12 SNO is located -2 km (6020 m.w.e.) underground in INCO’s Creighton Mine, deep enough that the rate of cosmic-ray muons passing through the entire active volume is just 3 per hour. A 12-m diameter transparent acrylic vessel (AV) holds the heavy water. Cerenkov light produced by neutrinos and radioactivity is detected by an array of 9,500 photomultiplier tubes (PMT’s) mounted on a geodesic support structure. Light water fills the detector, outside the AV, and acts as shielding against the surrounding radioactivity.

2. Reactions in SNO

SNO detects ‘B solar neutrinos with three different reactions: u,+d+p+p+eu, + d - + p + n + u , u, e- + u, e-

+

+

(CC) (NC)

(ES)

The deuterium in the heavy water makes the first process possible: the charged-current (CC) reaction which (at solar energies)‘ occurs only for u,’s. In addition to providing exclusive sensitivity to U,’S, this reaction has the advantage that the recoil electron energy is strongly correlated with the incident neutrino energy, and thus can provide a good measurement of the *B energy spectrum. The CC reaction also has an angular correlation with the solar direction of (1- 0.340 C O S I ~ ~ and ) , ~ has ~ a much larger cross section ( ~ 1 times 0 larger) than the ES reaction. The second reaction, also unique to heavy water, is a purely neutralcurrent process. This reaction has equal sensitivity to all neutrino flavors, and thus provides a direct, model-independent measurement of the total flux of neutrinos from the Sun. Neutrino-electron elastic scattering (ES) has been used to detect solar neutrinos in other water Cerenkov detectors. The recoil electron direction is strongly correlated with the direction of the incident neutrino (and hence, the direction of the Sun). This reaction has some sensitivity to neutrino flavors up and u,, but sees predominantly u, which has a cross section 6.5 times larger.

15

For both the ES and CC reactions, the recoil electrons are directly detected through their production of Cerenkov light. The data in this analysis have an analysis kinetic energy threshold of 5 MeV. For the NC reaction, the neutrons are not seen directly but are detected if they capture on a deuteron. A 6.25 MeV y ray is emitted following neutron capture; the y ray Compton scatters an electron and it is this secondary particle which is detected in SNO.

3. SNO Analysis and Pure D 2 0 Results Summary After run selection and data cleaning to remove events produced by instrumental sources of light in the detector, candidate neutrino (and radioactive background) events are histogrammed into three distributions: kinetic energy, reconstructed radial position, and direction angle with respect to the incident neutrino direction (i.e. from the Sun). Figure 1 shows the Monte Carlo of these distributions for each of the neutrino reactions.

cc

NC

ES 0.1

0.05

5

10

15

5

10 15 KE (MeV)

0.02 0.01 1

0

1

1

R' (AV radii)

Figure 1. The energy (top), radial (middle), and directional (bottom) distributions used to build pdfs to fit the SNO signal data.

The top row of Figure 1 plots the different energy distributions for the three signals; the middle row plots the radial positions as a function of R3, where R3 = 1 is the radius of the AV (600 cm). The CC reaction occurs only where there are deuterons (i.e. inside the AV) and has a uniform

16

distribution; the NC reaction does not have the same uniform distribution because, though NC neutrons are produced uniformly in the heavy water, neutrons wander far after being produced and can be captured by hydrogen in either the AV or the surrounding light water. Neutron capture on hydrogen produces 2.2 MeV y rays that are below the detection threshold. The bottom row plots the pdfs for the angular correlation to the solar direction. The angular correlation for the CC reaction and the strong forward peak seen for the ES reaction are distinguishing features. The pdfs are used t o perform a generalized maximum likelihood fit to the distributions in the data, in order to extract the number of events from the three reactions. When performing this fit, Cerenkov background events at low energy and neutron background events are included with fixed amplitude, since those amplitudes are estimated separately from in-situ and ex-situ analyses of radioactivity in the detector. Following maximum likelihood signal extraction, the resultant decomposition of events is: 1967.72:::; CC events, 2 6 3 . 6 ~ES ~ ~events, : ~ and 576.5-t:::: NC events, with statistical uncertainties coming from the fit, including 452:; events that are Cerenkov background at low energy and 78 f 12 background neutrons. Normalized t o the integrated rates above the kinetic energy threshold of T,tf 2 5 MeV, the flux of 8B neutrinos measured with each reaction in SNO, assuming the standard spectrum shape14 is (in units of lo6 cm-2 s-'): +0.06 +0.09 4:;' = 1.76~o.o,(stat.)~o,09 (syst.) +0.24 +0.12 4;;' = 2.39_o.,3(stat.)_o,,, (syst.) SNO +0.44 +0.46 ~ N C- 5.09-0.43(stat.)-0,,3 (syst.). Electron neutrino cross sections are used to calculate all fluxes. The CC and ES results reported here are consistent with the earlier SNO results3 for T,tf 2 6.75 MeV. The excess of the NC flux over the CC and ES fluxes implies neutrino flavor transformations. 4. Global Solar Neutrino Analysis SNO day and night energy spectra are shown in Figure 2. These plots show the summed spectra, including all signals and backgrounds. This data was used to produce MSW exclusion plots and limits on neutrino flavor mixing parameters. MSW oscillation models between two active flavors were considered. For simplicity, only the day and night energy spectra were used in the fit; radial and direction information used in SNO's null hypothesis test (described above) are not incorporated in the MSW fits. This procedure

17

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Figure 2. (a) Energy spectra for day and night. All signals and backgrounds contribute. The final bin extends from 13.0 to 20.0 MeV. (b) Difference, night - day, between the spectra. The integrated day rate was 9.23 5 0.27 events/day, and the integrated night rate was 9.79 f 0.24 events/day.

-12

-4

-3

-2

-1

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Figure 3. Allowed regions of the MSW plane determined by a x 2 fit to SNO day and night energy spectra and all solar neutrino experimental and solar model data. The star indicates the best fit.

preserves most of the ability t o discriminate between oscillation parameters. A model was constructed for the expected number of counts in each energy bin by combining the neutrino spectrum,14 the survival probability, and the cross sections15 with SNO's energy, background and efficiency response

18

functions.' Including flux information from the C14 and Ga e x p e r i m e n t ~ , ~the >~>~ day and night spectra from the Super-K experiment's 1258-day dataset,17 along with solar model predictions for the more robust p p , pep and 7Be neutrino fluxes,I0 the contours shown in Figure 3 were produced. The global analysis strongly favors the Large Mixing Angle (LMA) region with tan'd values < 1.

5. SNO Observables After KamLAND The KamLAND experiment reported their observation of the disappearance of reactor antineutrinos." The experiment measured (61 9)% of the expected flux. Fits to KamLAND rate and spectral data suggest oscillation parameters in the LMA region, consistent with the analysis from solar neutrinos. It is interesting to examine what the SNO LMA observables are, in light of the KamLAND results.

*

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9

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Figure 4. Spectral distortions for different values of tan2 0 for Am2 = 7 x lop5 eV2. Pure D 2 0 data are plotted; upcoming SNO salt data will reduce the statistical error bars on the data points and could provide some sensitivity to these distortions, especially at low energies.

Three observables from upcoming SNO data will be instructive: spectral shape, the CC/NC ratio and the day/night asymmetry. To illustrate the effect of spectral distortion from LMA neutrino oscillations, Figure 4 shows SNO spectral data from the pure D20 phase with curves superimposed for different values of the mixing angle tan' 8. The data points and the curves show the summed spectrum (CC+ES+NC); they have been normalized to the signal-extracted, best-fit signal rates; and they have had the background contribution subtracted (and error bars enlarged to account for

19

the subtraction, in the lowest two bins). The curves are for tan' 8 values of 0.3 and 0.9, from bottom to top, and for Am2 = 7 x lop5 eV2. All of the curves can translate up or down t o reflect the act of floating the 8B flux in the fit.

102 s.,Faa

.>I 1111

m

Delta mr [ev'l

Figure 5 . The curves plot the CC/NC ratio for an integrated SNO measurement above 5.0 MeV versus Am2. The curves are for tan' 6' values ranging from 0.3 at the bottom t o 0.9 at the top, in steps of 0.1. Upcoming SNO data with salt added to the heavy water will define a horizontal band on this plot, which helps to constrains the allowed mixing angle.

The key feature to note in this plot is that the CC/NC ratio is embodied in the spectral shape. Neutrons, in both the pure D2O phase and the salt phase of SNO, are detected at Teff values below 6 MeV. The different curvature seen in Figure 4 at low energy comes from different CC/NC ratios dependant upon the mixing angle. Illustrated another way, Figure 5 shows the CC/NC ratio as a function of Am2,for various values of tan2 0. Upcoming SNO data with salt added to the heavy water will have improved neutral-current sensitivity. The neutron detection efficiency with C1 added to the detector is higher by a factor of -4. Improved precision, coming from rate and spectrum, will enable SNO to define a horizontal band across Figure 5. Future KamLAND measurements could pin down Am2,defining a vertical band across the plot. This combination should tightly constrain the oscillation parameters. Day/night asymmetry for SNO's CC measurement is illustrated in Figure 6. This last LMA observable is seen t o be small, if the KamLAND allowed LMA regions are correct. Upcoming SNO day/night data will shrink statistical and systematic uncertainties; however, getting precision to detect a few percent asymmetry could be very difficult.

20 I

DayR4lghtAsymmetry

1

2" 0 05

0 04

0 03

0 02

0 01

0 WF.b

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Figure 6. The curves plot the day/night asymmetry for a SNO CC measurement versus Am2. The curves are for tan2 0 values ranging from 0.3 at the top to 0.9 at the bottom, in steps of 0.1. The allowed LMA parameters from KamLAND do not predict large values for A N D .

References 1. 2. 3. 4. 5.

6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

16. 17. 18.

Q.R. Ahmad et al., Phys. Rev. Lett. 89,011301 (2002). Q.R. Ahmad et al., Phys. Rev. Lett. 89,011302 (2002). Q.R. Ahmad et al., Phys. Rev. Lett. 87,071301 (2001). B.T. Cleveland et al., Astrophys. J . 496,505 (1998). K.S. Hirata et al., Phys. Rev. Lett. 65,1297 (1990); K.S. Hirata et al., Phys. Rev. D 44,2241 (1991); K.S. Hirata et al., Phys. Rev. D 45,2170 (1992); Y.Fukuda et al., Phys. Rev. Lett. 77,1683 (1996). J.N. Abdurashitov et al., Phys. Rev. C 60,055801(1999); J.N. Abdurashitov et al., J. Ezp. Theor. Phys. 95,181 (2002). W. Hampel et al., Phys. Lett. B 447,127 (1999). S. Fukuda et al., Phys. Rev. Lett. 86,5651 (2001). M. Altmann et al., Phys. Lett. B 490,16 (2000). J.N. Bahcall, M. H. Pinsonneault and S. Basu, Astrophys. J . 555,990 (2001). A.S. Brun, S. Turck-Chikze and J.P. Zahn, Astrophys. J . 525,1032 (1999). The SNO Collaboration, NIM A 449,172 (2000). J.F. Beacom and P. Vogel, Phys. Rev. Lett. 83, 5222 (1999). C.E. Ortiz et al., Phys. Rev. Lett. 85,2909 (2000). S. Nakamura, T. Sato, V. Gudkov and K. Kubodera, Phys. Rev. C63,034617 (2001); M. Butler, J.-W. Chen and X. Kong, Phys. Rev. (763,035501 (2001); G. 't Hooft, Phys. Lett. B 37,195 (1971). The BCK cross section with L ~ , = A 5.6 fm3 was used, with correction factors to update it to NSGK. Details of SNO response functions are available from the SNO web site: http://sno.phy.queensu.ca. S. Fukuda et al., Phys. Rev. Lett. 86,5651 (2001). K. Eguchi et al., Phys. Rev. Lett. 90,021802 (2003).

SOLAR NEUTRINO PRECISION MEASUREMENTS USING ALL 1496 DAYS OF SUPER-KAMIOKANDE-I DATA

M. B. SMY (FOR THE SUPER-KAMIOKANDE COLLABORATION) Department of Physics and Astronomy, University of California, Irvine, Irvine, California 92697, USA E-mail: [email protected] The results of the entire Super-Kamiokande-I solar neutrino data are presented. The measured interaction rate is 47*2% of the rate expected by the standard solar model and 133 It 5% of the rate implied by the SNO charged-current interaction rate. There is no evidence for spectral distortion or a time dependent neutrino flux. Together with the rates of other experiments, the Super-Kamiokande results imply active solar neutrino oscillations and restrict neutrino mixing and mass square difference to lie within the LMA solution area.

1. Introduction Between May 31st, 1996 and July 15th, 2001 Super-Kamiokande (SK) exposed 22,500 tons of purified water for 1496 days to solar neutrinos. The detector is described elsewhere '. Solar neutrinos are detected using the Cherenkov light emitted by the recoiling electron from neutrino-electron elastic scattering which offers four advantages: (i) the reconstructed direction of the recoiling electron is strongly correlated with the neutrino direction, (ii) the time of each neutrino interaction is recorded, (iii) the neutrino spectrum can be inferred from the recoil electron spectrum, and (iv) neutrino-elastic scattering is sensitive t o all neutrino flavors (the cross section for Y~ and Y, is about six to seven times less than for Y J . Unfortunately, only high energy solar neutrinos can be observed in this fashion: the SK total (recoil electron) energy threshold is 5 MeV. Only extremely few solar neutrinos have an energy that high; they arise from the ,l3+ decay of 8B ('B neutrinos) and 3He-proton fusion (hep neutrinos) in the sun. The standard solar model (SSM) prediction of the flux of those rare neutrinos (f#8B = 5.05'::;: x 106/cm2sand f#hep = 9 . 3 103/cm2s ~ with no uncertainty given 2 , is therefore difficult and beset by large uncertainties.

21

22 CI

p

x (d

:2

P

W

1

Figure 1. Angular Distribution of Solar Neutrino Event Candidates.

2. Solar Neutrino Flux

SK uses the known position of the sun (at the time of a solar neutrino event candidate) to statistically separate solar neutrino interactions from background events. During 1496 effective days 22,400&800 solar neutrino interactions were found in the gray shaded forward peak of Figure 1. From Monte Carlo calculations based on the SSM, 48,200';;6,:0, are expected. In spite of the large neutrino flux uncertainty, the observed rate is significantly less than expected. The suppression factor Data/SSM MC is about 3a less than one: 0.465f0.005(stat.)~~:~~~(sy~t.)~~:~~(SSM). All solar neutrinos are born as v, in the sun; if all solar neutrinos detected by SK are ye's as well then a v, flux of 2.35~0.02(stat.)f0.08(syst.)x106/cm2s leads to the observed interaction rate. SNO has measured the interaction rate of solar v, with deuterium (above a threshold neutrino energy of about 7 MeV) implying a v, flux of 1.76~~:~6,(stat.)fO.lO(syst.) x106/cm2s (assuming an undistorted 'B neutrino spectrum) and consequently 16,8002:;;:: v, interactions in SK. SK has observed 1.334+0.013(stat.)~~~~~~(syst.)~ more events which is about 4 . 5 above ~ one. Beyond the 'B endpoint of M 15 MeV, h e p neutrinos dominate the solar neutrino flux. From the observation of 4.9 f 2.7 events in an energy window (optimized by Monte Carlo: 18 to 21 MeV) where one hep neutrino interaction is expected, the hep flux is limited to less than 73 x 103/cm2s (or less than 7.9 times the SSM flux) at 90% C.L.

23

45-Day Time Bins

I

I

Figure 2. Time Variation of the SK Elastic Scattering Flux. The gray data points are measured every 10 days, the black data points every 1.5 months. The SSM prediction is indicated by the gray band; also shown are the SNO charged-current and neutral-current measurements. The dark gray line indicates the expected annual 7% rate variation. The right-hand panel shows the frequency spectrum of the 10-day time variation data.

3. Time Variations and Spectrum Figure 2 shows the time variation of the neutrino flux inferred from the SK rate in bins of ten days and 1.5 months. A 7% yearly variation is expected due to the 3.5% change in distance between sun and earth (assuming the neutrino flux is proportional to the inverse square of this distance, that is, the sun is a neutrino point source). The data favor such a 7% variation over no variation by about 2.50. No significant time variation is seen after subtraction of this effect. Recently, a frequency analysis of the SK ten-day time variation data reported a possible signal at O.O72/day '. The time values used in this analysis were assumed to be the arithmetic mean of the reported start and stop time of each bin. Repeating the analysis, we find a similarly strong peak in the frequency spectrum. Replacing the arithmetic mean by a live-time average, the peak decreases in significance to 81.7% C.L. suggesting that this peak might be an artifact of the precise choice of time bins. The frequency spectrum is shown in the right panel of Figure 2. The analysis method will only yield significant frequency peaks, if the variation amplitude is at least of the same order as the statistical uncertainty of one data point (about 10%). Therefore the 7% yearly variation doesn't produce a significant peak at 0.0027/day.

24

Figure 3. Elastic Scattering Flux as a Function of Solar Zenith Angle (Left), Rate Suppression (Upper Right Panel) and Day/Night Asymmetry (Lower Right Panel) as a Function of Energy. The error bars in the left and the smaller error bars in the right panels represent only statistical uncertainty, the larger error bars the combined uncorrelated uncertainty. The gray lines are the *la correlated uncertainty due to the uncertainty in the ‘B v spectrum and the SK energy scale and resolution. All uncertainties are statistically dominated except for the combined rate uncertainty.

To search for daily variation, the data. was binned according to solar zenith angle d,. The left panel of Figure 3 displays the resulting distribution. No significant daily variation is found. The result can be summarized by forming the “day/night asymmetry” ADN = 0 , 5D(-DN+ N ) (with D meaning “day rate” and N meaning “night rate”): ADN = -0.021 k O.O20(stat.)?:::~~(syst.) is consistent with zero within 0.90. For precision measurements of the spectrum it is necessary to calibrate the absolute energy scale (and determine the energy resolution) of SK with an outside source. We employed an electron linear accelerator to determine the energy scale within 0.64% and the resolution within 2.5% In Figure 3 the observed recoil electron spectrum is compared to the expected spectrum: the ratio Data/SSM effectively plots spectral distortion. There is no significant spectral distortion; the fit to the no-distortion hypothesis results in x2 = 20.2/20 d.0.f. corresponding to 44.3% C.L. The x2 includes three systematic effects which will shift all bins of the distribution in a correlated way (correlated uncertainties): the uncertainty in (i) the sB v spectrum, (ii) the absolute SK energy calibration, and (iii) the SK energy resolution. The gray lines of Figure 3 show the size of the sum (in quadrature) of (i), (ii) and (iii). The same figure also plots the day/night asymmetry as a function of recoil electron energy. It is consistent with zero over the entire energy range. Here, the correlated uncertainty is the sum of only (ii) and (iii), since (i) is the same for the day and the night.

25

4. Solar Neutrino Oscillations

Solar neutrino oscillations explain both the observed SK rate reduction compared to the SSM prediction and the observed SK rate enhancement relative to the SNO-based expectation (mentioned in section 2) as conversion of u, into other active flavors, that is up or u,. They also explain the rates observed by various radio-chemical solar neutrino experiments 5,6,7. Solar neutrinos are always born as u,; their conversion probability into up or u, in vacuum is determined by their energy, the distance of flight and the oscillation parameters Am2 and 0”. The presence of matter strongly influences this conversion probability. In particular, the matter density in the sun is high enough to induce resonant conversion at solar neutrino energies for a wide range of Am2 (lo-* to 10W4eV2).In that case, the conversion probability is large or even maximal, even if the mixing angle is small: the famous small mixing angle solutionb (SMA) has an angle of a few l o p 2 . The two other solutions with matter-dominated conversion probabilities, the large mixing angle (LMA; Am2 > 10W5eV2)and the low Am2 solution (LOW; Am2 M 10W7eV2)have a large mixing angle close to 7r/4 like the vacuum solutions (VAC), which match the first oscillation phase maximum to the solar neutrino energy range (Am2Ma fewx10-l1eV2). SMA and VAC solutions predict spectral distortions within the SK range, LMA and LOW do not. The matter density in the earth also affects the conversion probability leading t o apparent daily variations of the solar neutrino flux. In particular, the LMA and LOW solution predict such daily variations. SK may therefore observe distortions of the recoil electron spectrum or daily variations. We simultaneously search the SK data for both with the “zenith angle spectrum”: eight energy bins between 5 and 20 MeV where each energy bin between 5.5 and 16 MeV is subdivided into seven solar zenith angle bins. The x2 for a flat shape hypothesis of this distribution is x2 = 40.5/43 d.0.f. (58.1% C.L.) excluding VAC and SMA (absence of spectral distortion) as well as the LOW solution (absence of daily variations). Above Am2 > 3 . 10-5eV2, the still allowed LMA solutions predict small daily variation amplitudes and a rapidly oscillating phase washed out in SK due to energy resolution and the size of the zenith angle bins.

”We assume just two massive neutrinos; in that case the oscillation parameters are the mixing angle 0 (controlling the relationship between flavor and mass eigenstates) and the differences of the squared masses between the two neutrinos Am’. bA region of oscillation parameters capable of explaining all (or most) of the solar neutrino observations is referred to as a “solution”.

26

N

2

Ni

10 -3

lo -4 10

10

=

10

-7

10 10 -O

l o 4 10”

I

10

lo2

10’~

10”

I

10

lo2

10-I

I

10 lo2 tan2(@)

Figure 4. SK Excluded (Left) and Allowed (Middle) Regions as well as Regions Allowed by All Solar Data (Right) at 95% C.L. The cross hatched areas use only the SK spectrum, the shaded areas the zenith angle spectrum. To get the allowed regions in the middle, the shape is combined with the SK rate and the SSM constraint on the ‘B flux. The right panel shows the results of a fit t o all solar neutrino data using the SSM v flux predictions except for the ‘B and hep fluxes.

Figure 4 shows the strong constraints on solar neutrino oscillation parameters which are imposed by the SK spectral distortion data (cross hatched areas) and the SK zenith angle spectrum (gray areas). The analysis is further described in the definition of the x2 employed to extract those constraints can be found in lo. The areas in the left panel of Figure 4 are excluded and use only the (zenith angle) spectrum shape while the right panel shows allowed areas based on this shape and the SK rate (and the SSM ‘B flux). SK rate and spectrum allow only large mixing angles. The large daily variation predicted between = lop5 and x 10p7eV2 splits this “large mixing band” into two distinct allowed areas (SK LMA and SK LOW/quasi-VAC). The SK LOW/quasi-VAC region conflicts with data from other solar neutrino experiments (Homestake 5 , Gallex 6 , SAGE and most recently SNO 3 ) . Even stronger constraints on neutrino oscillation parameters can be obtained when the SK results are combined with other solar neutrino data. In particular, a unique solution was obtained for the first time in l o : the LMA solutions are strongly favored (see right panel of Figure 4). Figure 5 compares the x2 difference Ax2 as a function of only one parameter‘ (the other ~

cAx2 has the statistics of a x 2 with one degree of freedom.

27

10

1 0 ~ ~ 1 0 - ~ 11 0 ~1'0 " tan%

Am'

x2

Figure 5 . Difference in as a Function of tan' 0 (left) and Am' (right). The black lines show only the fit to the SK data and the SSM, the gray lines are the fit to all solar

data.

parameter is chosen as to minimize x 2 ) of a fit to SK data alone (black line) and to all solar data (gray line). SK data by itself strongly disfavors small mixing. LMA solutions are favored, however quasi-VAC solutions (between LOW and VAC) provide reasonable fits as well with small "pockets" of parameter space that fit even better than LMA solutions. The combined fit favors the LMA by almost 3a with small allowed ranges in tan2 0 and Am2. The best-fit Am2 (6.6.1OV5eV2)was recently confirmed by the KamLAND reactor neutrino oscillation experiement" . The accuracy of the agreement (< 5%) is remarkable and much better than expected from the statistical uncertainties. 5 . Super-Kamiokande-I1

Due to the destruction of more than half of its photomultiplier tubes (PMTs) in November 2002, Super-Kamiokande had to be rebuilt. The initial schedule called for the end of February 2003 as the date of completion. The work was actually finished in early December 2002 and data taking resumed. The rebuilt detector, Super-Kamiokande-I1 has a fullyequipped outer detector and 5,183 20"PMTs in the inner detector. Each 20" PMT is now enclosed by an acrylic-fiberglass shell to prevent implosion chain reactions. Due to the reduction in PMTs (46.5% of SK-I), the low energy threshold is higher than before (at present around 7 MeV), and the detector has to be calibrated again. The first calibration data was taken in January 2003 (see Figure 6). Even though event reconstruction was not optimized, electrons in the energy range relevant for 'B solar neutrinos can still be successfully reconstructed.

28

LINAC Deviation Radius Iremnstlucted-In

Figure 6. Vertex Resolution, Angular Resolution and Distribution of the Number of Hit PMTs Within 50 ns (after time-of-flight subtraction) from 8.7MeV LINAC calibration events in SK-11.

6. Conclusion

Super-Kamiokande solar neutrino precision measurements provided the first hint of solar neutrino flavor conversion due to oscillation in a unique parameter region, the LMA solution.

Acknowledgment We gratefully acknowledge the cooperation of the Kamioka Mining and Smelting Company. The Super-Kamiokande detector has been built and operated from funding by the Japanese Ministry of Education, Culture, Sports, Science and Technology, the U.S. Department of Energy, and the U.S. National Science Foundation.

References M. Nakahata et al., Nucl. Instrum. Methods A421, 113 (1999). J.N. Bahcall, M.H. Pinsonneault, S. Basu, Astrophys. J . 555, 990 (2001). Q.R. Ahmad et al., Phys. Rev. Lett. 89, 011301 (2002). A. Milsztajn, hep-ex/0301252 (2003). B.T. Cleveland et al., Astrophys. J . 496, 505 (1998). T. Kirsten, Nucl. Phys. B(Proc.Supp1.) 118, 33 (2003) V.N. Gavrin, Nucl. Phys. B(Proc.Supp1.) 118, 39 (2003). S.P. Mikheyev and A.Y. Smirnov, Sow. Jour. Nucl. Phys. 42, 913 (1985); L. Wolfenstein, Phys. Rev. D17, 2369 (1978). 9. S. f i k u d a et al., Phys. Rev. Lett. 86, 5656 (2001). 10. M.B. Smy, hep-ex/0202020 (2002). 11. K. Eguchi et al., Phys. Rev. Lett. 90, 021802 (2003).

1. 2. 3. 4. 5. 6. 7. 8.

SOLAR NEUTRINO SPECTROSCOPY WITH BOREXINO AND FUTURE LOW ENERGY SOLAR NEUTRINO EXPERIMENTS

s. SCHONERT Max-Planck-Institut fur Kernphysik Heidelberg, Saupfercheckweg 1 , 6911 7 Heidelberg, G e r m a n y E-mail: [email protected] The physics goals of BOREXINO and of future low energy solar neutrino projects are summarized and experimental challenges discussed. In the near future, 7Be and conceivably pep neutrinos will be measured via neutrino electron scattering. On the long term, direct measurements of the primary pp neutrino flux appears feasible.

1. Introduction With the observation of flavor conversion by the combined analysis of SNO' (CC) and Super-Kamiokande2 (ES), and by SN03 (NC+CC) on its own, the scientific goals of upcoming experiments and future projects have shifted from discovery and identification of the solar neutrino flux deficit to a comprehensive study of the phenomena. The central challenge now is t o measure, with high accuracy, neutrino oscillation parameters and to determine accurately the neutrino fluxes of the primary solar pp-, pep- and 7Be branches as well as the CNO cycle. Beyond this clear cut goal, and despite the apparent consistency of observations with solar model predictions and oscillation scenarios, unexpected results might await and lead to further new physics. Details of stellar evolution theory can be tested by comparing experimental neutrino fluxes with theoretical prediction^^>^. Most suited for such tests are the low energy pp-, pep- and 7Be fluxes, since they are predicted with rather small theoretical uncertainties compared with the high energy 'B: the pp- and pep-branch errors are estimated with 1%and 1.5% uncertainty, and the 7Be line with 10% to be compared with 18% for the 'B branch6. Oscillation solutions derived from solar neutrino data alone, allow two

29

30

distinct parameter ranges, named LMA, and at a lower confidence level, the LOW/VAC MSW-solutions. Including the recent results from the KamLAND experiment7 into the global analysis’ which reported evidence for the disappearance for Ye from nuclear reactors, and provided that CPT symmetry is not violated, all but the LMA solution are excluded. This solution makes clear predictions for the spectral deformation at sub-MeV range of the solar neutrino spectrum, ie. for pp-, pep- and 7Be neutrinos as displayed in Figure 1. Any deviation from this oscillation prediction, as time variations or different spectral suppression probabilities would ask for new physics. Less speculative, but of fundamental importance is to improve the accuracy of 0 1 2 . This could be achieved by a high precision measurement of the pp neutrino branch and taking the flux uncertainties of solar model predictions at its face value, or in principle at least, combine electron scattering and charged current measurements . To address these fundamental issues of particle- and astrophysics, pp-, pep- and 7Be neutrinos which are emitted in the predominant terminations of the solar fusion processes, need to be studied with new detectors that provide information about the energy and time of the neutrino interaction.

2. Real-time detection of low-energy solar neutrinos

Rigorous tests of particle properties, and simultaneously of solar model predictions, require t o measure the neutrino spectra flavour specific. The electron neutrino (ve) flux can be probed by the charged current inverse electron-capture reaction v, ( A ,2 ) + e- + ( A ,2 + 1)*(CC). Solar neutrinos, converted to muon ( v p ) and tau ( v T ) neutrinos can not produce their charged lepton partners, because their restmasses are large compared to the energy available. However, the vp,Tflux component can be derived from the combined analysis of inverse electron-capture detection with elastic electron scattering v , , ~ , ~e- -+ v , , ~ ,(ES), ~ as shown by SNO and Super-Kamiokande. The ES detection involves both charged and neutral current interactions, albeit the contribution of the latter to the cross section is only about 1/6. Therefore, high precision measurements are needed, in particular if only a fraction of the flux is converted to V ~ , ~ ’ S . The total flux of all active flavors - the quantity to be compared with solar model predictions - can only be derived by a combined analysis of CC and ES experiments. An exclusive neutral current detection technique, as for the high energy ‘B flux, is not at hand to be realized experimentally.

+

+

3f

0.8

0.3 0.2

0.2

J 0.2

0

0.2

0.4

0.6

0.8

1

E” (MeV) Figure 1. Energy dependent survival probabilities for solar neutrinos for various oscillation scenarios. The distinct differences at energies below 1 MeV should be noted. The dashed, solid and dashed lines correspond to night, average and day spectra respectivelyg. The LMA solution is preferred including the KamLAND reactor neutrino results.

The Cherenkov technique for measuring solar neutrinos has been successfully used for 8B neutrinos. However, at energies at 1 MeV or below, the Cherenkov photon yield is insufficient to perform spectroscopic measurements. For this reason, scintillation techniques will be used for the upcoming low-energy neutrino experiments. A primary photon yield of up to 1 x 104/MeV can be achieved for organic liquid scintillators and up t o 4 x 104/MeV in liquid noble gases. Ultra pure liquid scintillators will be used for ES detection, while metal loaded organic scintillators for CC detection. Alternative t o ES scintillation detection, the use of a T P C is under study with the goal t o reconstruct the full kinematics of the ES reaction. Only a few promising candidate nuclei exist for CC real time detection.

32

Either the transition must populate an isomeric excited state with a subsequent electromagnetic de-excitation, or the final state needs to be unstable in order to provide a coincidence tag t o discriminate against background events such as ES signals and radioactive decays. Moreover, the energy threshold of the transition needs to be sufficiently low to have sensitivity to sub-MeV neutrinos. Only a few isotope meet these requirements of which '151n, loOMo,82Se, 16'Gd, 176Ybare under careful consideartion. The SSM interaction rates (without flavor conversion) for ES experiments amounts to about 0.5/ton/day for 7Be-v's (860 keV branch), to 2/ton/day for pp-v's and 0.04/ton/day for pep-v's. Hence target masses of about 100 ton are required for 7Be- and pep-measurements, while a few 10 ton are sufficient for pp-neutrinos in order to acquire a rate of a few ten events per day. The interaction rates for CC detection via inverse electron capture depend on the nuclear structure of the isotope under consideration and its relative abundance. For example, the interaction rate in indium (l151n, matrix element B(GT)=0.17, 95.7% natural abundance) is O.Oi'/ton/day for 7Be-v's and 0.3/ton/day for pp-v's assuming SSM fluxes without oscillations.

3. Backgrounds to neutrino detection at low-energies The main challenge of real time neutrino detection at low energies are backgrounds from radioactive decays. Primordial radioactive contaminants present in detector materials such as 40K, 238U, 232Th and their progenies, as well as anthropogenic 85Kr, cosmogenic 42Ar, and radiogenic 14C dominate the detector signal if not removed carefully. Scintillation based ES experiments rely on the detection of a single recoil electron. Therefore, any radioactive decay with similar energy deposition can mimick a neutrino event. Concentration of radioactive elements need thus to be < lpBq/ton to allow a signal/background ratio > 1. This translates t o contamination limits 5 1O-l6g U(Th)/g for 7Be detection. CC experiments typically require less strigent limits since delayed coincidence tags suppress backgrounds. Further backgrounds arise from cosmic ray muon induced radio isotopes. To minimize this interference, detectors are located deep underground. A rock overburden, for example, of 3400 mwe, as encountered at the Gran Sass0 underground laboratories, reduces the muon flux to 1.1 h-' m-'. Despite a reduction of a factor lo6 with respect to the sea level flux, the

33

in-situ production of radio-isotopes by spallation reactions is still of relevance. For example, backgrounds t o pep-u detection via ES at this depth is dominated by in-situ production of l l C (tip = 20.4 min) by muons and their secondary particles. The l l C production (and decay) rate amounts 0.15/ton/day t o be compared t o 0.04/ton/day pep-u interactions". Therefore, efficient spallation cuts are required to extract a pep-u signal or alternatively, a deeper underground location.

4. Upcoming experiments The Borexino experiment is the pioneering project for real time neutrino spectroscopy at low energies". The construction of the experimental installations is nearing completion in the underground laboratories at Gran Sasso, Italy (LNGS). Startup of the experiment is now targeted for 2004, provided that legal questions related t o environmental legal issues can be overcome in due time. The primary goal of Borexino is to measure the 0.86 MeV 7Be-u line via elastic neutrino-electron scattering (ES). Further physics goals comprise the detection of pep and CNO neutrinos, the low energy part of the *B spectrum, neutrinos from supernovae, as well as antineutrinos (ve)from distant nuclear reactors, as well as from geophysical origin. Fig. 2 displays schematically the Borexino detector. Neutrino detection occurs via ES in an ultra-pure liquid scintillator target confined in a transparent nylon vessel. The scintillator is composed of pseudocumene (PC) and P P O at a concentration of 1.5 g/l. About lo4 primary photons/MeV are emitted with a wavelength distribution peaked at 380 nm. Photon detection is realized with 2200 photomultiplier (8", 30% coverage) at single photo-electron threshold providing a yield of 2 400 photo-electrons/MeV. An energy resolution of 2 5% (la) at 1 MeV is therfore attainable. The location of the interaction within the detector is determined with an uncertainty of 5 10 cm (la) at 1 MeV by the time-of-flight method of the photons. A trigger is generated by x 15-20 PMT hits occurring in a time window of 60 ns corresponding to a threshold of about 50 keV energy deposition. The analysis threshold for recoil electrons from 7Be-u ES will be at about 250 keV, depending on the actual 14C activity in the scintillator. To achieve the ultra-low background rate within the fiducial inner volume, the detector has a onion-like structure with increasing radio purities from outside to inside. y-rays coming from detector components outside

34

the scintillation volume are attenuated by the buffer liquid surrounding the active volume. The final reduction of external activity is achieved by the outer layer of the liquid scintillator ( "self-shielding"), defining a fiducial mass of 100 ton. The cumulative background rate internal to the liquid scintillator must be 5 1 x lop6 s-l mp3 in the neutrino analysis window between 250 keV and 800 keV. This translates to limits 5 10-l6g/g for uranium and thorium, and their progenies (assuming secular equilibrium), to 5 10-14g/g for potassium, to 5 10-log / g for argon and to 5 4 x 10p16g/g for krypton. Due to the high mobility of radioactive noble gases, in particular 222Rn,39Ar, 85Kr, ultra-high vacuum leak-tightness standards of the system is required and gases in contact with the liquid scintillator, as nitrogen need to be purified. A further source of backgrounds comes from surface deposition of "'Rn progenies on detector components which are subsequent in contact with the liquid scintillator. In particular the buildup of 'lOPb (tl/2 = 22.3 a) must be controlled since it feeds the decays of "OBi (tl/z = 5 d) and 'loPo (tl/z = 138 d) which create signals in the neutrino energy window. All materials have been screened with high-purity germanium spectroscopy, and selected for low radioactive trace contaminants". Surfaces which are in contact with the liquid scintillator have been tested for radon emanation, and are specially treated to remove 'loPb and 'loPo deposits. The detector concept and in particular, the attainable radioactive trace contaminations have been studied in a pilot experiment, the Counting Test Facility at Gran Sasso (CTF)13. During construction and startup of Borexino, the CTF serves as sensitive instrument to verify the performance of the ancillary plants, as the liquid handling distribution, the various purification systems, as well as the purity levels of PC prior t o filling the Borexino detector. A similar detector, however larger in size, has been realized by the KamLAND collaboration in the Kamioka mine in Japan14. The main objective of this experiment is to probe the oscillation parameter space of the solar MSW large mixing solution with electron anti-neutrinos ( f i e ) from distant nuclear reactors. Radio purity requirements for fie-detection are less stringent compared to solar neutrino detection via ES. Data taking with reactor neutrinos started early 2002 and first results have been published7. In a second phase, with an upgraded liquid handling and purification system, it is intended t o measure solar 7Be neutrinos, provided that trace contaminations are at levels as required for Borexino.

35 Borexino

\

Holding SLllnw SlalnleSs Steel WalerTanr 18mB

2200 8.Thom EM1 PUT9

\

Sfeel SnleldinuPlates l m x ~ m x l O c m a n d I m i 4 m x 4m c

Figure 2. Schematic view of the Borexino detector at Gran Sasso. A stainless steel sphere confines the inner detector (ID) containing about 300 ton liquid scintillator and 1 kton of transparent buffer liquid. Scintillation photons are detected by 2200 photomultiplier giving energy and location of the interaction. A fiducial central mass of 100 ton can be determined in the off-line analysis. The steel sphere is housed in a water tank equipped with 210 photomultiplier. The outer detector (OD) serves as a shield against ambient radiation as well as a muon track detector.

The active volume of the KamLAND detector consists of 1000 ton of liquid scintillator composed of PC, mineral oil (dodecane) and P P O (1.5 g/l). An energy resolution of 7% (lo) a t 1 MeV has been reported and is expected t o improve to 6% in the final detector configuration. First results on uranium, thorium and potassium meet the solar-u specifications, while impurities as 85Kr and 'loPb still need to be reduced substantially to allow 7Be-u detection. N

N

5. Next generation experiments 14C/12C ratios at lo-'' in organic scintillators, as determined with the CTF1', prohibit the measurement of pp-neutrinos in ES experiments since the 156 keV ,6-decay endpoint significantly obscures the pp-u energy range. A promising approach to overcome this background is to avoid organic liquids and instead, t o use liquefied noble gas as a scintillator. Projects with helium, neon and xenon are under investigation and are listed in Tab. 1. Recent development for pp- and 7Be CC detection focuses on the isotopes 'lsIn and 17'Yb (LENS) and on looMo (MOON). Most advanced amongst the various R&D projects, listed in Tab. 1, are XMASS for ES- and LENS

36

for CC detection. In the following, experimental and conceptional details will be outlined for these two projects, exemplary for the next generation of experiments. Further details of recent progress of the various projects can be found at1711s. Table 1. R&D projects for sub-MeV solar neutrino detection. ES: Elastic scattering of neutrinos off electrons (CCSNC), CC: neutrino capture (charged current; CC); LS: liquid scintillator; CH: hydro-carbon. Technique (Target) MOON XMASS HERON CLEAN TPC

CC: looMo

23 24

ES

hybrid or LS (CH+metal) LS (Xe) LS (He) LS (He,Ne) TPC(He.CH)

The XMASS21 collaboration pursues the concept of pp- and7Be-v detection via ES in a liquid xenon scintillation detector. High density liquid xenon (3.06 g/cm3) provides efficient self shielding and a compact detector design. A geometry similar to that of Borexino, but smaller in size, could thus be realized. The scintillation photons (175 nm) will be detected with newly developed low-background photomultiplier tubes (Hamamatsu) consisting of a steel housing and a quartz window at liquid xenon temperatures (2 165 K). Main sources of backgrounds arise from 85Kr P-decay and from 2v - P,fJ decay of 136Xe. The first isotope must be less than 4 x 10-15gKr/g. If the r1p of 136Xeis 5 8 x years, as theoretically expected, then isotope separation is needed. A prototype detector containing 100 kg of liquid Xe is under construction. Milestones during this R&D phase will include the determination of the 2v-PP half-life and the optical properties of liquid xenon, such as the scattering length of scintillation light. Various candidate nuclei are being investigated by the LENS1' collaboration. The ongoing research focuses now on '"In loaded into an organic liquid scintillator with 5-10% in weight. Complexing ligands under study coAprise carboxylic acids, phosphor organic compounds as well as chelating agents. A detector containing about 10 tons of indium is under consideration. In order t o discriminate against backgrounds, dominated by the P-decay of '151n (Qp = 496 keV, 0.26 Bq/g of In) and the accompanying Bremsstrahlung, a detector with high spatial granularity is required. This will be realized by a modular design. A basic module has a cubical shape with a length of about 2 m, determined by the absorption length of the liquid scintillator. The cross section of the module varies from 5 x 5 cm2

37

to 10 x 10 cm2 depending on metal loading, scintillator performance and further optimization criteria under study. The nuclear matrix element B(GT) = 0.17, relevant for v, interaction, has been determined via (p,n) reaction. This value is sufficiently accurate to evaluate the target mass necessary for the LENS detector. However, to derive the neutrino fluxes with accuracy 576, it is planned to use an artificial 51Cr neutrino source of several MCi strength to determine the neutrino capture cross section. In order t o study the detector performance as close as possible t o the final detector geometry, the LENS Low-Background-Facility (LLBF) has been newly installed underground at the LNGS. A low-background passive shielding system with 80 tons of mass, located in a clean room, can house detector modules with dimensions up t o 70 cm x 70 cm x 400 cm. All shielding materials have been selected in order to minimize the intrinsic radioactive contamination. First results from the prototype phase are expected in 2003. Of particular interest will be the experimental study of backgrounds due t o Bremsstrahlung and t o radio impurities. 7Be-v CC detection seems feasible today, while pp-v sensitivity remains t o be demonstrated. N

6. Outlook

In near future, the detection of 7Be and, conceivably pep and CNO neutrinos via ES will be addressed by Borexino and possibly, by KamLAND. The next generation projects still have to pass the threshold from promising ideas to feasible experiments. Results from the ongoing prototype activities will show within the very near future which of the projects have the potential t o be realized. On the long term, complementary measurements via ES- and CC detection are desirable for all neutrino branches in order to scrutinize solar models as well as neutrino properties. References 1. Q.R. Ahmad et al. Phys. Rev. Lett.87 (2001) 071301. 2. S. Fukuda et al. Phys. Rev. Lett.86 (2001) 5651 3. Q.R. Ahmad et al. Phys. Rev. Lett.89 (2002) 011301 4. J.N. Bahcall, M. H. Pinsonneault, and S. Basu, Astrophys. J . 5 5 5 (2001) 990. 5. A S . Brun, S. Turck-Chihze, and J.P. Zahn, Astrophys. J. 5 2 5 , 1032 (1999); S. Turck-Chihze et al., A p . J. Lett., v. 555 July 1, 2001. 6. J.N. Bahcall, Phys. Rev. C 56 (1997) 3391.

38 7. E. Eguchi et al. hep-ex/O212021 8. G.L. Fogli et al., hep-ph/0112127; M. Maltoni, T Schwetz and J.W.F. Valle, hep-ph/012129; J.N. Bahcall, M.C. Gonzales-Garcia and C. Penya-Garay, hep-ph/0212147; H. Nunokawa et al., hep-ph/0212202; P. Aliani et al., hepph/0212212; P.C. de Holanda and A.Yu. Smirnov, hep-ph/0212270. 9. John N. Bahcall, M. C. Gonzalez-Garcia, Carlos Pena-Garay, hepph/020q 314 10. T. Hagner et al., Astropart. Phys. 14 (2000)33 11. Borexino collaboration, G. Alimonti et al., Astropart. Phys. 16 (2002) 205. 12. Borexino collaboration, C. Arpesella et al. Astropart. Phys. 18 (2002) 1. 13. Borexino collaboration, G. Alimonti et al., Astropart. Phys. 8 (1998) 141; Borexino collaboration, G. Alimonti et al., Nucl. Instrum. Meth. A406 (1998) 411. 14. A. Suzuki, 8th international workshop on neutrino telescopes, Venice, Feb. 23-26 1999; J. Busenitz et al., “Proposal for US Participation in KamLAND, ” March 1999 (unpublished), http: //kamland. lbl .gov/. 15. K. Inoue, First Sendai Int. Conf. on Neutrino Science, March 14-16, Sendai, Japan,http://www.awa.tohoku.ac.jp/conf2002/program.html.

16. Borexino Collaboration, G. Alimonti et al., Phys. Lett. B 422 (1998) 349. 17. LowNu 2002 workshop, Heidelberg, 2002, http://www.mpi-hd.mpg.de/nubis/www~lownu2002/. 18. S. Schonert, Nucl. Phys. B (Proc. Suppl.) 110 (2002) 277. 19. R.S. RaghavaqPhys. Rev. Lett. 78(1997) 3618; LENS collaboration, Letter of Intent, Laboratori Nazionali del Gran Sass0 (1999); http://www.mpi-hd.mpg.de/nubis/www~lownu2002/ 20. H. Ejiri et al., Phys. Rev. Lett. 85 (2000) 2917. 21. Y . Suzuki, LowNu2 workshop, Tokyo, 2000, http://www-sk.icrr.u-tokyo.ac.jp/neutlowe/,

22. B.

Lanou,

LowNu

2002

workshop,

Heidelberg,

2002,

http://www.mpi-hd.mpg.de/nubis/www~lownu2002/.

23. D.N. McKinsey and J.M. Doyle, J . of Low Temp. Phys. 118 (2000) 153. 24. G. Bonvicini et al., Contributed paper, Snowmass 2001, hep-ex/0109199, hep-ex/0109032

NEUTRINO OSCILLATIONS AND THE SUNSHINE

M.C. GONZALEZ-GARCIA Y.I.T.P., SUNY at Stony Brook, Stony Brook, N Y 11794-9840, USA IFIC, Universitat de Valbncia - C.S.I. C., Apt 22085, 46071 Valbncia, Spain In this talk I discuss the impact of the results from KamLAND on our understanding of neutrino properties, and, when combined with data from solar experiments, on our understanding of the Sun. This talk is based on Refs. 1 , 2 , 3 , 4 .

1. Combined Analysis of KamLAND and Solar Data KamLAND have measured the flux of Ye’s from distant nuclear reactors. In an exposure of 162 ton.yr (145.1 days), the ratio of the number of observed inverse /?-decay events to the number of events expected without N0.611 D f 0.094 for EDe> 3.4 MeV. This deficit oscillations is R K ~ ~ L A= is inconsistent with the expected rate for massless 0,’s at the 99.95% confidence level. KamLAND have also presented the energy dependence of these events in the form of the prompt energy (Eprompt N EDe mp - m,) spectrum. The measured spectrum shows a clear deficit, but there is no significant signal of energy-dependence of this effect. The KamLAND results can be interpreted in terms of Ye oscillations with parameters shown in the left panel of Fig.1. The allowed region has three local minima and it is separated into ‘islands.’ These islands correspond t o oscillations with wavelengths that are approximately tuned to the average distance between the reactors and the detector, 180 km. The local minimum in the lowest mass island (Am2= 1.5 x lOP5eV2) corresponds t o an approximate first-maximum in the oscillation probability (minimum in the event rate). The overall best-fit point (Am2= 7.1 x eV2 and tan2 0 = 0.52,1.92) corresponds approximately to the second maximum in the oscillation probability. For the same Am2, maximal mixing is only slightly less favored, Ax2 = 0.4. Thus with the present statistical accuracy, KamLAND cannot discriminate between a large and maximal mixing. Because there is no significant evidence of energy distortion, the allowed regions for the KamLAND analysis extend to high Am2 values for which

+

39

40

oscillations would be averaged and the event reduction would be energy independent. These solutions, however, are ruled out by the non observation of a deficit at shorter baselines, in particular by CHOOZ 15, which rules out solutions with Am2 2 1 (0.8) x lOP3eV2 at 30 (99% CL). In the central panel of Fig. 1 I show the results of our latest analysis of the solar neutrino data 7,8 in the framework of v, oscillations. For the solar neutrino analysis, we included the two measured radiochemical rates, from the chlorine and the gallium experiments, the 44 zenith-spectral energy bins of the electron neutrino scattering signal measured by the SuperKamiokande (SK) collaboration, and the 34 day-night spectral energy bins measured with the SNO. The most important aspect of Fig. 1is the demonstration by KamLAND that anti-neutrinos oscillate with parameters that are consistent with the LMA solar neutrino solution. Under the assumption that CPT is satisfied, the anti-neutrino measurements by KamLAND apply directly to the neutrino sector and the two sets of data can be combined to obtain the globally allowed oscillation parameters. The results of such an analysis are shown in the right panel of Fig. 1. Comparing the central and right panels of Fig. 1 we see that the impact of the KamLAND results is to narrow down the allowed parameter space in a very significant way. In particular, the LMA region is the only remaining allowed solution. The LOW solution is excluded at 4.80 and vacuum solutions are excluded at 4.90. The once ‘favored’ SMA solution is now excluded at 6.10. Within the LMA region, the main effect of KamLAND is the reduction of the allowed range of Am2 while the impact on the determination of the mixing angle is marginal (see Sec. 3). Furthermore, alternative solutions to the solar neutrino problem which predict that there should be no deficit in the KamLAND experiment (such as neutrino decay or flavor changing interactions) are now excluded at 3.60.

2. Learning About How the Sun Shines The presence of flavour conversion of solar v,, although great news from the point of view of particle physics, jeopardized the original goal of solar neutrino experiments of studying the sun. Schematically, solar neutrinos experiments measure a convolution of both the solar properties and the neutrino properties. As a consequence using solar neutrino data it is difficult t o extract solar-model independent information on the neutrino properties,

41

7

Active Solar

+

u

tde Figure 1. Allowed regions for 2-v oscillations of De in KamLAND and CHOOZ (left panel), and of v, in the sun (center panel), and for the combination of KamLAND and Solar under the hypothesis of CPT (right).

as well as directly test the model of the sun. KamLAND has provided us with the first solar-independent determination of the relevant neutrino properties, its oscillation parameters. With these results at hand one can determine the flavour conversion probability of solar neutrinos independently of the solar model (using exclusively the sun’s matter density profile). Thus in order to directly test some solar property, one can use this solar-model-independent extracted probability in the analysis of the solar data most sensitive to such property. However the precision of KamLAND is still not good enough for this strategy to be effective. This is illustrated in Fig. 2 where I show the extracted survival probability of solar neutrinos using the oscillation parameters obtained from the analysis of KamLAND data. As seen from the figure the determination is still very imprecise. In the right panel I also show the corresponding determination when both KamLAND+solar data are used. This second determination is more solar-model dependent but the gain in precision is such to make an “intermediate” approach the best. So at present, the best strategy to test our understanding of both the neutrino properties and the sun is to perform a global analysis of solar+KamLAND data in the context of oscillations allowing for departures from the solar standard model value of the “solar parameter” which we want to test, obtaining its experimentally-determined value as an output of the analysis. Schematically this corresponds to use: X;lobal(OSC

Par, sun Par) = X:olar(OSC

Par, sun Par) + X k a m L A N D (osc Par) (1)

and study the dependence on a given solar parameter by marginalizing over any other solar parameters allowed to be free and over the oscillation

42 kotmlLAND

+

S o l a r

m

c ' co 3

Z0.8

0.8

a

1

0.6 0.4 0.2

c

4

0

Figure 2. Range of values of the solar Y survival probability using the oscillation parameters obtained from the analysis of KamLAND data (left panel in Fig. l) and from the combined analysis of KamLAND+Solar (right panel in Fig. 1)

parameters. I discuss next the results obtained using such an approach to determine the total 8B flux, the contribution of the CNO cycle to the solar luminosity, and the sterile neutrino component in the solar fluxes. 2.1. Determination of ' B Flux

As described above, one can determine the allowed range of the total 8B neutrino flux using just the KamLAND determination of the neutrino oscillation parameters together with the measured CC event rate in the SNO. But this determination yields an imprecise value for the total 8B neutrino flux (la uncertainty 30%). Instead we use the approach described in Eq. (1) with the normalization of the 8B flux fB,total E being the sun parameter (@ B) ~ p o o 5.05 x 106cm-2s-1 '). Thus the analysis of Solar+KamLAND data depends on the oscillation parameters and on fB,total. In Fig. 3 I show the results of this analysis. The left and central panel show the allowed values of fp,total as a function of the oscillation parameters. The contours shown are 90%, 95%, 99%, and 99.73% (3a)confidence limits. The figure illustrates how the better determination of the mixing angle will result into an improvement of the allowed range of fB,total, while the better determination of Am2 will have a much smaller effect. In the right panel I show the dependence of the x2 with fB,total after marginalization over the oscillation parameters. Quantitatively we find: N

&

fB,total

= 1.00(1 f 0.06)

(lO)(l

f 0.18) (3ff).

(2)

We notice that this determination of the total 8B solar neutrino flux reduces

43

09

09

08 07

08 07 06

06

05 1o

-~

o-+

1

Am2 (eVZ)

L

05 lo-’

‘0.6

tan Lt?

0.8

1

1.2

1.4

f,

totd

Figure 3. Determination of the solar 8B neutrino flux from the combined analysis of SolarfKamLAND data in the framework of 2v active oscillations.

the experimental uncertainty to be more than a factor of two smaller that the uncertainties in the predicted SSM flux. This is the first occasion on which the experimental errors on a solar neutrino flux are smaller than the solar model uncertainties.

2 . 2 . Limiting the CNO Luminosity There are two nuclear fusion mechanisms by which main sequence stars like the sun could produce the energy corresponding to their observed luminosities: the p - p chain and the CNO cycle. For both the p - p chain and the CNO cycle the basic energy source is the burning of four protons to form an alpha particle,two positrons, and two neutrinos. In the p - p chain, fusion reactions among elements lighter than A = 8 produce a characteristic set of neutrino fluxes, whose spectral energy shapes are known but whose fluxes must be calculated with a detailed solar model. In the CNO chain, with 12C as a catalyst, I3N and 150beta decays are the primary source of neutrinos. In his original paper l o Bethe wrote: “It is shown that the most important source of energy in ordinary stars is the reactions of carbon and nitrogen with protons.” Bethe’s conclusion about the dominant role of the CNO cycle relied upon a crude model of the sun. Over the next two and a half decades, the results of increasingly more accurate laboratory measurements of nuclear fusion reactions and more detailed solar model calculations led to the theoretical inference that the sun shines primarily by the p - p chain rather than the CNO cycle. Currently, solar model calculations imply that 98.5% of the solar luminosity is provided by the p - p chain and only 1.5% is provided by CNO reactions.

44

The question is: can this prediction be experimentally tested? The answer is: yes but it is difficult. The fraction of the sun’s luminosity that arises from CNO reactions can be written as:

where the constant ai is the energy provided to the star by nuclear fusion reactions associated with the ith neutrino flux, ai is the ratio of the neutrino flux @i(BPOO)of the standard solar model to the characteristic solar photon flux defined by La/[47r(A.U.)2(10MeV)], and & is the ratio of the true solar neutrino flux t o the neutrino fluxes predicted by the BPOO standard solar model g . Thus measuring the three 4i associated with the CNO cycle, uniquely determines However, radiochemical experiments with chlorine and gallium do not measure the energy of the neutrinos detected; they measure the rate of neutrino induced events above a fixed energy threshold. Thus the data only gives information on the sum of all & above the detection threshold. The neutrino-electron scattering experiments, Kamiokande and SK and the heavy water detector SNO provide information about energy of neutrinos but only those that have energies well above the maximum energies of the CNO fluxes. Furthermore the goal of uniquely identifying CNO neutrinos is made even more difficult by the fact that neutrino oscillations can change in an energy dependent way the probability that electron type neutrinos created in the sun reach the Earth as electron type neutrinos. Because of these complications, previous to SK and SNO results, it was possible t o find neutrino oscillation solutions in which 99.95 % of the sun’s luminosity is supplied by the CNO cycle l l . These solutions, however, corresponded to oscillation parameters of small-mixing-angle-like solutions which are now known to be disfavoured by the observed flat spectrum of sB neutrinos at SK and SNO, and furthermore ruled out by the observation of LMA-like oscillations at KamLAND. Consequently one expects to derive a much stronger limit on the CNO contribution to the solar luminosity by the combined analysis of the updated solar and KamLAND data in the framework of oscillations. In order to do so one uses the strategy described in Eq. (1)allowing as “solar parameters” the free normalization of the solar neutrino fluxes subject to the ‘luminosity constraint’ which requires that the sum of the thermal energy generation rates associated with each of the solar neutrino fluxes be equal to the solar luminosity.

e.

45

In this analysis there are then 10 free parameters: the two oscillation parameters, Am2 and tan2 0,and the 8 neutrino fluxes, p - p , pep, 7Be,8B, and hep (from the p - p chain) and 13N 150,and 17F(from the CNO cycle). We further use some nuclear relations to reduce the range of variation of x & is~marginalized ~ ~ the parameters. In this way for each value of LCNO, over the oscillation parameters and over the neutrino flux normalizations under the luminosity constraint and the condition Eq.( 3). The results of the analysis are shown in Fig. 4. The figure shows Ax2 as a function of the CNO luminosity fraction when only solar neutrino data are used (denoted by dotted curves) and when solar and KamLAND data are used (denoted by solid curves). The minimum value of x2,relative to which Ax2 is measured, is reached in both cases for a zero value of the CNO flux. However, as is apparent from Figure 4, the global x2 is essentially flat for all values of L C N O / L o < 5%. Current experiments are not sensitive to CNO neutrino fluxes that correspond t o less than 5% of the solar luminosity. In all cases, the best fit is a LMA MSW solution. In principle, new solutions might have been found by allowing L C N O / L , to be a free parameter. In practice, no preferred new solutions are found for any value of L C N O l L o . So using both solar neutrino and KamLAND experimental data (using just

30

20 N

a" 10

0

0

0.02

0.04

0.06

0.08

0.1

0.12

'%NO

Figure 4.

Experimental bound on L C N O / L O

solar neutrino data), it can be concluded that < 7.3% (7.8%) at 30. Lo Within its expected accuracy a future 7Be neutrino-electron scattering experiment l 2 can either measure L C N o / L , or conclude that L C N O / L , < 5.6% (4.9)%. In order to measure the CNO contribution at the 1.5% level predicted by the standard solar model, one must be able to distinguish the

46

10

............

1.5

Without K2K

1.3

Amzzl (eVZ)

c

_I

1.1

0.9 0.7 0.5

io-'

10 0

1

0.05

tan2+,,

"0

2

4

Am', (1 O-'eVZ)

6

0

0.02 0.04 0.06 0.08 0.1

0.1 sinb,,

1

tanz+=

Figure 5. Global 3v oscillation analysis. Each panel on the left shows the dependence of Ax2 on each of the five parameters from the global analysis (full line) compared to the bound prior t o the inclusion of the K2K (dotted line) and KamLAND data (dashed line). The contours on the right shows the dependence of determination of f~ with ,913. The different contours correspond to the two-dimensional allowed regions at 90, 95, 99 % and 30 CL.

continuum 13N and 150neutrinos from the 7Be and pep neutrino lines, as well as from all the sources of background. This is a challenging task for future low energy solar neutrino experiments.

3. 3v Analysis I now discuss the results of our analysis of solarfKamLAND data in the framework of three neutrino oscillations needed t o describe these data in combination with the results from atmospheric l 3 and K2K l4 experiments. The combined description of all these data requires that all three known neutrinos take part in the oscillations. The mixing parameters are encoded in the 3 x 3 lepton mixing matrix U relating the flavour and the mass basis. Neglecting the CP violating phases as they are not accessible by the existing experiments, the mixing matrix can be conveniently chosen in the

47

form U = U23U13U12, where Uij is a rotation matrix in the plane ij. In general the transition probabilities will present an oscillatory behaviour with two oscillation lengths. However from the required hierarchy in the splittings Am:,, >> Am& indicated by the solutions to the solar and atmospheric neutrino anomalies it follows that: - At solar and KamLAND experiments the oscillations with the atmospheric oscillation length are averaged out and the survival probability takes the form: P,"," = sin4813 c0s4813P,2eV where for solar neutrinos P,"," is obtained with the modified sun density N , -+ cos2813Ne. So the analyses of solar+ KamLAND data constrain three of the oscillation parameters: Am;, ,812 and O13. - Conversely for atmospheric and K2K, the solar wavelength is too long and the corresponding oscillating phase is negligible. As a consequence the atmospheric and K2K data analysis restricts Am:,, 823 and 013, the latter being the only parameter common to both solar and atmospheric neutrino oscillations and which may potentially allow for some mutual influence. In summary, oscillations at solar+KamLAND on one side, and atmospheric+K2K oscillations on the other side, decouple in the limit 813 = 0. In this case the values of allowed parameters can be obtained directly from the results of the analysis in terms of two-neutrino oscillations. Deviations from the two-neutrino scenario are determined by the size of the mixing 813. This angle is constrained by the CHOOZ l5 reactor experiment, which, for Am;, <( Am:,, provides on the parameters Am:, 2: Am:, and 813. In Fig. 5 we plot the individual bounds on each of the five parameters derived from the global analysis. To illustrate the impact of the K2K and KamLAND data we also show the corresponding bounds when either K2K or KamLAND is not included in the analysis . In each panel the displayed x2 has been marginalized with respect t o the undisplayed parameters. In the right plot of Fig. 5 I show the dependence of the determination of the 8B flux on the "generic" 3v parameter 813 with the aim of testing the possible dependence of the 8B flux determination described in Sec. 2.1 on the presence of the 3u mixing structure. The figures illustrates that: The dominant effects of including KamLAND are those derived in the two-neutrino oscillation analysis of solar and KamLAND data: the determination of Am;, (panel a) to be in the LMA region and a very mild improvement of the allowed mixing angle 8 1 2 (panel b). The dominant effect of including K2K is the better determination of Am:, while it has not impact on the determination of the mixing angle 8 2 3 - Concerning the "generic" 3v mixing parameter 813, Fig. 5.c illustrates

+

-

-

48

how the inclusion of the K2K data results into a tightening of the bound on 013 (at large CL) when combined with the atmospheric and CHOOZ data. This is an indirect effect due to the increase in the lower bound on Am;, . - The determination of the boron flux is not affected by the inclusion of the t hree-mixing structure. Quantitatively we find the following la (30) CL allowed ranges (5.4) 6.7

<

< 7.7(10.) (14.) < Am&/10-5eV2 < (19.) , (0.29) 0.39 < tan2012 < 0.51 (0.82) , (1.5) 2.2 < Am~2/10-3eV2 < 3.0(3.9) , (0.45)0.75 < tan2QZ3< 1.3(2.3) , sin' OI3 < 0.02 (0.052) .

Am&/10-5eV2

4. Including Sterile Neutrinos: 4v Models

I discuss next how the global analysis of solar and KamLAND data can also give constraints on the possibility of sterile neutrinos. Sterile neutrinos are usually invoked to accommodate the LSND result together with the solar and atmospheric data in a single neutrino oscillation framework. In this case there must be at least three different scales of neutrino mass-squared differences which requires the existence of a fourth light neutrino. The measurement of the 2' boson decay width into neutrinos makes the existence of only three light active neutrinos an experimental fact. Therefore, the fourth neutrino must not couple to the standard electroweak current, that is, it must be sterile. There are six possible four-neutrino schemes, that can accommodate the results from solar and atmospheric neutrino experiments as well as the LSND result. They can be divided in two classes: (3+l) and (2+2). In the (3+1) schemes, there is a group of three close-by neutrino masses that is separated from the fourth one by a gap of the order of 1 eV2, which is responsible for the oscillations observed in the LSND experiment. In (2+2) schemes, there are two pairs of close masses separated by the LSND gap. If a (2+2)-spectrum is realized in nature, the transition into the sterile neutrino is a solution of either the solar or the atmospheric neutrino problem, or the sterile neutrino takes part in both. In this case solar v, can oscillate into a state that is a linear combination of active (v,) and sterile (v,) neutrino states, v, + cos 11 v, sin 11 v, , where 7 is the parameter that describes the active-sterile admixture. As a consequence the total 'B solar neutrino flux can be larger than inferred when assuming no-sterile states

+

49

mixed in the oscillations, Eq. (2). In this case one has: $(8B)total

=

$(ye)

+

$(~a)

+

(4)

4(vs),

where $(vs) = tan2 77 x $(va). The NC measurement of SNO is proportional to the flux of active neutrinos $(va). The analysis of solar and KamLAND data can give constraints on the sterile component of the solar 8B neutrino flux, or equivalently on the size of the active-sterile mixing parameter 77. Following the discussion in Sec. 2, the sterile component of the 8B solar neutrino flux can be more directly determined by subtracting the active 8B neutrino flux, given by the SNO NC measurement, from the total 'B neutrino flux determined as described in Sec. 2.1. This subtraction can be made in a model independent fashion using the oscillation parameters obtained from the analysis of the KamLAND data alone. However, as discussed, this direct method, while conceptually simple, still yields an imprecise determination of the sterile component of the 8B neutrino flux (la uncertainty of order 18%). The more powerful approach is to include all of the solar plus KamLAND measurements. In this case, Eq. (1) takes the form: 2

Xglobal

-

X?olar (Am2

tan2 6, .fB, total, sin2 7)

+

, tan' 6) .

XkarnLAND (Am2

(5) One determines the sterile component, by marginalization over the oscillation parameters and the total 8B flux. I show the results of this analysis in Fig. 6. The left panel show the allowed values of the sterile component, f ~ , as a function of f ~total, , both relative to the BPOO predicted standard 8B neutrino flux. The figure illustrates how the best fit corresponds to no sterile neutrinos but certain sterile component is still allowed, which in turns results into a slight relaxation of the upper bound of f ~ , t ~ comt ~ l pared t o the extracted range in the pure active case Eq. (2). The derived allowed range of the sterile admixture a t 10 (30).is

The obtained upper bound on sin2 77 from this analysis can be compared with the corresponding lower bound from the analysis of atmospheric data. In the right panel of Fig. 6 I show the corresponding comparison (the curve for the atmospheric data is taken from Ref. 16). The figure illustrates at at present 2+2 models cannot accommodate the LSND evidence due to the incompatibility of the limits on the sterile contributions to both solar and atmospheric oscillations.

50

Figure 6. Determination of the sterile component of the 8B neutrino flux in the framework of 4u mixing (left panels). The contours shown are 90%, 95%, 99%, and 99.73% (3u)confidence limits. Constraint on the active-sterile admixture parameter 17 from the combined analysis of Solar+KamLAND data (right panel).

References 1. J. N. Bahcall, M. C. Gonzalez-Garcia and C. Pena-Garay, JHEP 0302,009 (2003) 2. J.N. Bahcall, M.C. Gonzalez-Garcia and C. Peiia-Garay, Phys. Rev. C 66 (2002) 035802. 3. J. N. Bahcall, M. C. Gonzalez-Garcia and C. Pena-Garay, Phys. Rev. Lett. 90, 131301 (2003) 4. M. C. Gonzalez-Garcia and C. Pena-Garay, hep-ph/0306001. 5. See K.Inoue in these proceedings. 6. J.N. Bahcall, M.C. Gonzalez-Garcia and C. Peiia-Garay, JHEP 07, 054, (2002). 7. See M.Smy in these proceedings. 8. See M.Chen in these proceedings. 9. J.N. Bahcall, M.H. Pinsonneault and S. Basu, Astrophys. J. 555 (2001) 990. 10. H. A. Bethe, Phys. Rev. Lett. 5 5 , 434 (1939). 11. J . N. Bahcall, M. Fukugita, and P. I. Krastev, Phys. Lett. B 374, 1 (1996). 12. See S.Shoenert in these proceedings. 13. See C.Yanagisawa in these proceedings. 14. See T.Kobayashi in these proceedings. 15. M. Apollonio et al., Phys. Lett. B 466 (1999) 415. 16. See T.Schwetz in these proceedings.

SUPERNOVA RELIC NEUTRINO SEARCH RESULTS FROM SUPER-KAMIOKANDE

M. MALEK Department of Physics and Astronomy State University of New York at Stony Brook Stony Brook, NY 11794-3800, USA E-mail: [email protected] A search for the relic neutrinos from all past core-collapse supernovae was conducted using 1496 days of data from the Super-Kamiokande-I detector. This analysis looked for electron-type anti-neutrinos that had produced a positron with an energy greater than 18 MeV. In the absence of a signal, 90% C.L. upper limits on the total flux were set for several theoretical models; these limits ranged from 20 to 130 Ue cm-' s-'. These limits are a factor of 40 times better than the best limits set in previous experiments and can eliminate or constrain some models. Additionally, a model-insensitive upper bound of 1.2 Ue cm-2 s-' was set for the supernova relic neutrino flux in the energy region E, > 19.3 MeV. This limit is two orders of magnitude more stringent than the best previously published limits.

1. Introduction

During a core-collapse supernova, approximately ergs of energy are released, about 99% of which are in the form of neutrinos. To date, the only time that a burst of such neutrinos has been detected was in the case of SN1987A ','. However, it is generally believed that core-collapse supernovae have occurred throughout the universe since the formation of stars. Thus, there should exist a diffuse background of neutrinos originating from all the supernovae that have ever occurred. Detection of these supernova relic neutrinos (SRN) would offer insight about the history of star formation and supernovae explosions in the universe. All types of neutrinos and anti-neutrinos are emitted from a corecollapse supernova, but not all are equally detectable. The f i e is most likely to be detected by Super-Kamiokande (SK). It interacts primarily through inverse p decay ( V , p + n e+, E, = E, - 1.3 MeV) with a cross section that is two orders of magnitude greater than that of neutrino-electron elastic scattering. All further discussion of the SRN refers only to the V e .

51

52

Several methods have been used t o model the SRN flux and spectrum with flux predictions ranging from 2 - 54 cm-’ s-l. In this paper, SK search results are compared t o SRN predictions based on a population synthesis model 4 , a cosmic gas infall model 5 , cosmic chemical evolution studies 6 , and observations of heavy metal abundances 7 . A model that assumes a constant supernova rate was also considered, as well as a model that includes the effects of large mixing angle (LMA) neutrino oscillation. 3,4153637,8,

2. Data Reduction

This paper presents the results of a search for SRNs in the SuperKamiokande detector. SK is a water Cherenkov detector, with a fiducial mass of 22.5 kton. The data reported here were collected between 31 May 1996, and 15 July 2001, yielding a total livetime of 1496 days. Backgrounds to the SRN signal are solar neutrinos, atmospheric neutrinos, and muoninduced spallation products. Spallation is the most serious background, and the ability to remove it determines the lower threshold of the SRN search. A likelihood function uses information about cosmic ray muons to identify and remove spallation events. Furthermore, all events that occur less than 0.15 s after a cosmic ray muon are rejected. The spallation cut is applied t o all events reconstructed with E < 34 MeV. No discernible spallation events with energies above 18 MeV remain in the data after this cut is applied and so 18 MeV was set as the lower analysis threshold. The sub-event cut removes muons produced by atmospheric v p via charged current quasi-elastic scattering (vp N + p N’). Muons with low energies will stop in SK and produce a decay electron; often the muon and decay electron are found in the same event. When this happens, the decay electron is referred t o as a “sub-event.” After the vertex of each event was found and the flight time of the Cherenkov photons was subtracted, the event’s timing window was searched; if more than one timing peak was present, then the event was removed. Most remaining muons are removed by the Cherenkov angle cut. This cut exploits the mass difference between the muon and the positron, which results in a difference in their Cherenkov angles 8 ~ all ; particles with 8C < 37” were removed from the data. The efficiency of this selection criterion for retaining signal is 98%. Applying the Cherenkov angle cut and the sub-event cut together results in the rejection of > 99% of the muon

53

" 3

: I ?

z

2

' IAfter sub-event cut A After Cherenkov cut 0 After solar direction cut

1

10

P

(0

II . m

In

c

5>

10

U

2 u)

1

-1

10

I

20

30

40

50

60

70

.

...

1 1

80

Energy (MeV)

Figure 1. Energy spectrum at each reduction step. In the final data set, the spallation cut and solar direction cut are only applied in the first four bins. The lines represent the event-rate predictions for the various SRN models.

background. The Cherenkov angle cut was also used t o remove events with Bc > 50". This eliminated events without clear Cherenkov rings, such as multiple y rays emitted during a nuclear de-excitation. Finally, a cut on the direction of the event was made t o remove contamination from solar neutrinos. Events with E < 34 MeV were removed if the reconstructed event direction pointed back t o within 30" of the Sun. The efficiency of the full data reduction is 47 & 0.4% for E 5 34 MeV, and 79 & 0.5% for E > 34 MeV. Figure 1 plots the energy spectrum after applying each cut t o events at all energies; note that in the final data set, the spallation cut and the solar direction cut will only be applied t o the first four energy bins.

3. Analysis and Results After applying the selection criteria, two irreducible backgrounds remain. The first is atmospheric u, events. The second comes from atmospheric up that interact t o form a muon that is below the Cherenkov threshold. These

54

E

5

14

I

s x.12 cy

.

10

0 c

w 5

8 6

4 2 0 Energy (MeV)

Figure 2. Energy spectrum of SRN candidates. The dotted and dash-dot histograms are the fitted backgrounds from invisible muons and atmospheric u,. The solid histogram is the sum of these two backgrounds. The dashed line shows the sum of the total background and the 90% upper limit of the SRN signal.

muons are said to be invisible and their decay electrons are not tagged as background events. The energy spectra of these backgrounds have shapes that are very different from each other and from the SRN signal shape. Therefore, a three-parameter shape fit was used to search for the SRN. The initial shape of the decay electrons was determined by the Michel spectrum; the initial shape of the atmospheric v, events was obtained from previous works ',lo. Background simulations were subjected to the full reduction, and the shapes of the resulting spectra were used to fit the data; each of the SRN models was treated similarly. The data were divided into sixteen energy bins, each 4 MeV wide (see Figure 2), and the following x2 function was minimized with respect t o a , p, and y:

55 Table 1. The SRN search results are presented for six theoretical models. Theoretical model Population Synthesis Cosmic gas infall Cosmic chemical evolution Heavy metal abundance Constant supernova rate Large mixing angle osc.

Event rate limit (90% C.L.) < 3.2 events/year < 2.8 events/year < 3.3 events/year < 3.0 events/year < 3.4 events/year < 3.5 events/year

SRN flux limit (90% C.L.) < 130 f i e cm-’ s-l < 32 f i e cm-2 s-l < 25 f i e cm-2 s-l < 29 f i e cm-’ s c l < 20 f i e cm-2 s-l < 31 f i e cm-’ s-l

Predicted flux 44 f i e cm-’ 5.4 cm-’ s-l 8.3 & cm-2 s-1 < 54 f i e cm-’ s-’ 52 & cm-2 s-l 11 oe cm-2 s-l

In this equation, the sum 1 is over all energy bins and Nl is the number of events in the lth bin. Al, Bl, and Cl represent, respectively, the fractions of the SRN, Michel, and atmospheric v, spectra that are in the l t h bin. The efficiency-corrected event rate spectrum of SRN candidates and the results of the fit are displayed in Figure 2, which shows that the expected backgrounds fit the data well. For all six models, the best fit to a was zero and the minimum x2 value was 8.1 for 13 degrees of freedom. Thus, a 90% C.L. limit on a was set for each model and used to derive a 90% C.L. limit on the SRN flux from each model. The number of SRN events is. related to the total flux F by the following equation: a

F= NP

s E 3 MeV f(EL’)a(E,)E(Eu)dEL’

(2)

In this equation, N p is the number of free protons in SK (1.5 x T is the detector livetime (1496 days), c ( E ) is the signal detection efficiency, a ( E ) is the cross section for the inverse /3 decay (9.52 x E e pe), and f ( E )is the normalized SRN spectrum shape. The integral spans the energy range of the neutrinos that produce positrons in the observed energy region. The SRN limits shown in Table 1 vary greatly, based on the shape of the theoretical SRN spectrum at energies that are below SK’s SRN analysis threshold. To remove this strong model dependence, a limit was set for E, > 19.3 MeV. In this region, all six models have similar energy spectrum shapes, and so an experimental limit that is insensitive to the choice of model can be obtained:

Flux limits in this energy region were the same for all models considered: 1.2 6, cm-’ s-’. Previously, the best SRN flux limit in this region was

56

226 0, cm-2 s-l

ll;

the current SK limit is two orders of magnitude lower.

4. Discussion For most of the models considered, the dominant contribution to the SRN flux comes from supernovae in the early universe, so the neutrino energy is red-shifted below the 18 MeV threshold. The heavy metal abundance model primarily considers supernovae at red-shifts z < 1, so SK is sensitive to more of the SRN flux. For this model, the flux limit is smaller than the calculated total flux However, this prediction is only a theoretical upper limit, so these results can constrain this model but cannot eliminate it. The total SRN flux predicted by the constant model scales with the rate of core-collapse supernovae. The SRN flux limit (20 0, cmP2 s-l) corresponds to a supernova rate limit that is too low to be consistent with the observed abundance of oxygen 1 2 , 4 , which is synthesized within the massive stars that become supernovae. Thus, the constant model can be ruled out by these results. 5. Conclusion

A search for the diffuse 0, from all previous core-collapse supernovae was conducted at the Super-Kamiokande detector. No appreciable signal was found in 1496 days of SK data. Using various models, 90% C.L. limits were set on the total SRN flux. A limit of 1.2 Ue cmP2 s-l was set for the SRN flux above a threshold of E,, > 19.3 MeV. These limits are more than an order of magnitude better than previous results, and they can constrain or reject some theoretical models of the supernova rate in the universe. References 1. K.S. Hirata et al., Phys. Rev. D 38, 448 (1988). 2. C.B. Bratton et al., Phys. Rev. D 37, 3361 (1988). 3. T. Totani and K. Sato, Astropart. Phys. 3,367 (1995). 4. T. Totani, K. Sato, and Y. Yoshii, Astrophys. J. 460, 303 (1996). 5. R. A. Malaney, Astropart. Phys. 7, 125 (1997). 6. D. H. Hartmann and S. E. Woosley, Astropart. Phys. 7, 137 (1997). 7. M. Kaplinghat et al., Phys. Rev. D 6 2 , 043001 (2000). 8. S. Ando, K. Sato, and T. Totani, Astropart. Phys. 18, 307 (2003). 9. Y. f i k u d a et al., Phys. Lett. B 433, 9 (1998). 10. G. Barr, T. K. Gaisser, and T. Stanev, Phys. Rev. D 39, 3532 (1989). 11. W. Zhang et al., Phys. Rev. Lett. 61, 385 (1988) 12. W. D. Arnett et al., Astrophys. J. 339, L25 (1989).

SUPERNOVA RELIC NEUTRINOS AND NEUTRINO OSCILLATION

SHIN'ICHIRO A N D 0 Department of Physics, School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

E-mail: ando63utap.phys.s.u-tokyo.ac.jp

KATSUHIKO S A T 0 Department of Physics and Research Center f o r the Early Universe, School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, J a p a n

We investigate the flux and the event rate of supernova relic neutrinos (SRN) at the Super-Kamiokande (SK) detector for various neutrino oscillation models with parameters inferred from recent experimental results. We discuss the detectability of SRN at SK, comparing this SRN flux with other background neutrinos in more detail than previous studies, and it is found that in the energy range 17 - 25 MeV, ten-year observation might enable us to detect SRN signal (at one sigma level). We also set 90% C.L. upper limit on the SRN flux for various oscillation models using the recently released observational result by SK. In the near future, further reduced upper limit is actually expected, when the current SK data are reanalyzed using some technique to reduce background events against the SRN signals. It is expected that the reduced upper limit is sufficient to provide useful implications for neutrino oscillation.

1. Introduction

It is generally believed that the core-collapse supernova explosions have traced the star formation history in the universe and have emitted a great number of neutrinos, which should make a diffuse background. This supernova relic neutrino (SRN) background is one of the targets of the currently working large neutrino detectors, such as Super-Kamiokande (SK) and Sudbury Neutrino Observatory (SNO). Comparing the predicted SRN spectrum with the observations by these detectors provides us potentially valuable information on the nature of neutrinos as well as the star formation history in the universe. This SRN background has been discussed in a number of previous papers.'

57

58

In this paper, we calculate the SRN flux and the event rate at SK, and discuss the detectability of SRN,2 with the following new aspects compared with previous studies: (1) Realistic neutrino oscillation parameters are incorporated based on the recent solar and atmospheric neutrino experiments, (2) a realistic neutrino spectrum from one supernova explosion is used, which is obtained from a numerical simulation by the Lawrence Livermore group,3 and (3) we have examined other contaminating background events against the detection of SRN, in more detail than previous studies. Recent experimental data of a t m ~ s p h e r i c , solar,5 ~ and reactor neutrinos6 strongly indicate the evidence of neutrino oscillation. Although several previous SRN studies mentioned the possibility of neutrino oscillation, no quantitative calculation of SRN has been made incorporating the realistic oscillation parameters. In supernovae, produced Vp,T are converted into V , which are mainly detected at the SK detector. Because V p , . interact with matter only through the neutral-current reactions in supernovae, they are weakly coupled with matter compared to 17,. Thus, the neutrino sphere of Vfi,T locates at deeper in the core than V , and their temperatures are higher than those of V e . Therefore neutrino oscillation enhances the average Ve energy and enhances event rate at the SK detector. Recently, the SK Collaboration set an upper bound of 1.2 V e cmP2 s-l for the SRN flux in the energy region E, > 19.3 MeV.? It is the same order as our typical theoretical prediction.’ For example, as illustrated more in detail below, we predict that the total SRN flux integrated over entire energy is 11 cm-’ s - ~ ,while ~ the corresponding SK limit is 31 cmP2 s-l.? Since the theoretical calculations contain many ambiguities such as the supernova rate in the universe and neutrino spectrum from each supernova, this severe observational SRN limit can provide a number of valuable information on various fields in astrophysics and cosmology. For the very reason, we repeat the discussions given in the recent SK paper7 and obtain the 90% C.L. upper limit for the SRN flux estimated using various oscillation models.8

2. Models and Formulation We use a realistic neutrino spectrum from a collapse-driven supernova calculated by the Lawrence Livermore group,3 instead of the Fermi-Dirac (FD) spectrum with zero chemical potential used in all of the past studies.’ This is because neutrinos are not in the thermal equilibrium states in supernovae (due to opacity dependence on energy), and neutrino transfer equa-

59

tion should be solved. Actually, clear difference from the FD distribution is seen in Fig. 2 of Totani et d 3Recently, their calculation is criticized since it lacks the relevant neutrino processes such as neutrino bremsstrahlung and neutrino-nucleon scattering with nucleon recoils, which were not recognized to be important of the calculation date. However, since there are no other groups which have succeeded supernova explosion except for them, it is premature t o conclude that their result is no longer reliable and we adopt their results. We also include the effects of neutrino oscillation on the SRN flux. The parameters adopted in this study are inferred from the latest atmospheric4 and solar neutrino experiment^.^^^ In particular, from solar neutrino observations, we adopt the most favorable solution, so called the Large Mixing Angle (LMA) solution. We first assume the normal mass hierarchy (m3 >> ml) of the neutrino mass, although the inverted hierarchy has not been ruled out yet (the case of the inverted mass hierarchy is addressed later). In this case, since the results are insensitive to 013, which has not been sufficiently constrained, we do not concentrate on dependence on that parameter. In addition, we also investigate in case of no oscillation, for comparison. With these models, the SRN flux can be calculated by the formula

+

where EL = ( 1 z ) E u , R S N ( Zis) a supernova rate per comoving volume at redshift z , d N u / d E u is the number spectrum of emitted neutrinos, and z,, is the redshift when the gravitational collapses began, which we assumed to be 5. As the supernova rate, we use the most reasonable model to date, which is based on the rest-frame UV observation of star formation history in the universe by the Hubble Space Teles ~ o p e In .~ this model, the supernova rate exponentially increases with z , peaks around z 1.5, and exponentially decreases in further high-z region. N

3. Results and Discussions

In Fig. 1, we show the calculated SRN flux for no oscillation model, and in Fig. 2 the expected event rate at SK detector for both no oscillation and LMA models. Above 10 MeV, we expect more event rate for the LMA model, because Vp,T which have higher average energy at production have more changed into V e . We show in Table 1, the integrated flux over the entire neutrino energy range and event rate at SK integrated for detection N

60

energy range 17 < (T,/MeV) for detection is given below).

< 25 (the reason why this range is selected

-invisible /I

__--=

-

_ / - -

r e a c t o r Fe

"0

10

20

30

40

50

60

70

60

90

100

Neutrino Energy [MeV]

Figure Number flux Of SRN 'Ompared to other background neutrinos. No oscillation model is assumed for SRN flux.

Figure 2. Event rate at SK detector of SRN and invisible ,u decay products. Two oscillation models are shown (no oscillation and LMA)

Table 1. Number flux of SRN and expected event rate at SK. Flux is integrated over the entire energy range and event rate is over the detection range. Flux

Model

I

LMA

I

11.2 cm-2 s-1

Event rate for 17 < (T,/MeV) 0.73 vr-l

< 25

I

3.1. Detectability of the supernova relic neutrinos

There are several background events which hinder the detection of SRN. These includes atmospheric and solar neutrinos, antineutrinos from nuclear reactors, spallation products, and decay electrons from invisible muons. We should find the energy region which is not contaminated by these background events and then calculate the detectable event rate of SRN. By careful examination of these events, we found that there is a narrow energy window from 19 MeV to 27 MeV, which is free from solar, atmospheric, and reactor neutrinos (see Fig. 1). (Although the solar neutrino events can

61

be avoided owing to the directional analysis,there are also another serious background due t o spallation products below 16 MeV. See Ando et aL2 for details .) However, it is known that, for water Cherenkov detector, electrons or positrons from invisible muons are the largest background in the energy window. This invisible muon event is illustrated as follows. The atmospheric neutrinos produce muons by interaction with the nucleons (both free and bound) in the fiducial volume. If these muons are produced with energies below Cherenkov radiation threshold (kinetic energy less than 53 MeV), then they will not be detected (“invisible muons”), but their decayproduced electrons and positrons will be. Since the muon decay signal will mimic the Pep + n e f process in SK, it is difficult to distinguish SRN from these events. In Fig. 2, the SRN event rate is compared with the invisible muon events. Thus, it appears there is no energy window of SRN, but still we can detect the SRN events by statistical analysis with the other background events. Consider the energy range 17 < (T,/MeV) < 25. This range corresponds to 19 < (EPe/MeV) < 27 by a simple relation, Eue= T, 1.8MeV. There are two advantages in using this energy region. First, the SRN event rate is rather large, and second, the background (invisible muon) event rate is fairly well known by the SK observation. The SRN event rate at SK in this energy range is 0.4 - 0.7 yr-’ (Table l),in contrast, the event rate of the invisible muon over the same energy range is 3.4 yr-’. When the SRN event rate is larger than the statistical error of the background event rate, we can conclude that SRN is detectable as a distortion of the expected invisible muon background event. Unfortunately, only one year observation does not provide any useful information about SRN, however, we can expect that ten-year observation provides several statistically meaningful results. The statistical error of invisible muon events in ten years is = 5.8, which is smaller than the event rate of the LMA model. In consequence, although there is no energy window, in which the SRN signal is the largest, the statistically meaningful SRN signals might be detected using the data for ten years or so.

+

3.2. Implications of the recent observational results Recently (September 2002), SK collaboration set very severe constraint on the SRN flux,? which is only factor three larger than typical theoretical predictions. For example, while Ando et d 2predicted that the total SRN

62

flux integrated over the entire energy range was 11 cm-’ s-l, the corresponding SK limit is 31 cm-’ s-l. Since the theoretical calculations contain many ambiguities such as the supernova rate in the universe and neutrino spectrum from each supernova, this severe observational SRN limit can provide a number of valuable information on the various fields in astrophysics and cosmology. Further, in the near future, it is expected that the upper limit will be much lower (about factor 3) when the current SK data of 1,496 days are reanalyzed using some technique to reduce invisible muon background .lo Thus, it is obviously important and very urgent to give a prediction for the SRN flux with the oscillation parameters, which has not been considered; while in the previous subsection we gave the prediction with the LMA parameters in the case of the normal mass hierarchy, here we also include the case of the inverted mass hierarchy, which is not ruled out at all. Note that in that case, the resonance also occurs in the antineutrino sector, and it is expected that the SRN spectrum would be quite different from that in the case of the normal mass hierarchy. From this point on, we use four parameter sets, named as NOR-S, NOR-L, INV-S, and INV-L, where NOR and INV represent the normal and inverted mass hierarchy respectively, and the suffixes -L and -S attached to NOR and INV stand for large (0.04) and small (lop6) values for sin’ 21313, respectively. Further, when we calculate the neutrino conversion probability in supernova, we adopt the realistic t i m e - d e p e n d e n t density and Ye profiles, which are calculated by the Lawrence Livermore group.’’ This is because during the neutrino burst (- 10 sec), the shock wave propagating the supernova matter changes density profile dramatically, and it is expected to affect the adiabaticity of resonance points. In addition, we also include the Earth matter effect, which was neglected in almost all the past publications including Ando et a1.’

Figure 3 shows the SRN flux for the various oscillation models; the case of no oscillation is also shown for comparison. We also repeated discussions given in the SK paper7 and obtained the 90% C.L. upper limit for the various SRN fluxes; the results of the calculation is summarized in Table 2. As shown in the table, all the oscillation models are not excluded yet, since the theoretical predictions are still smaller than the corresponding SK limit, while the observational upper limit is more severe for the INV-L model. However, since theoretical predictions contain many uncertainties, we cannot trust the values given in Table 2 without any doubt. Now, we consider the future possibility to detect SRN or to set severer

63

Figure 3. Number flux of SRN for various neutrino oscillation models. The spectra for NOR-S, NOR-L, and INV-S are degenerated, while that for INV-L is the hardest one. The flux of atmospheric Ve is also shown.

Table 2. The predicted SRN flux for various oscillation models and the corresponding SK limit (90% C.L.). The ratio between the prediction and the limit is shown in the fourth column. Model NOR-S NOR-L INV-S INV-L

Predicted flux 11 11 cm-2 spl

SK limit (90% C.L.)

< 34 < 34 cm-2 < 12 cm-2

Prediction/Limit

spl spl 0.17

constraint on neutrino models. As noted above, the largest background against the SRN detection at SK is the invisible muon decay products. In the near future, however, it will be plausible to distinguish the invisible muon signals from the SRN signals, using the gamma rays emitted from nuclei which interacted with atmospheric neutrinos." Therefore, if we can detect gamma ray events, whose energies are about 5 - 10 MeV, before invisible muon events by the muon lifetime, we can subtract them from the candidates of SRN signals. In that case, the upper limit would be much lower (by factor "3) when the current data of 1,496 days are reanalyzed," and the SRN signal might be detected or the more powerful information on the combined quantities of the supernova rate and the neutrino mixing

64

parameters would be obtained. Then, without invisible muon events, the SK data of 1,496 days would be sufficient to permit the SRN detection and set very severe constraint on the neutrino mixing parameters. In particular, inverted mass hierarchy with large 813 (INV-L model) would be ruled out first among five models we have considered. There is another possibility to enhance the average pe energy, or resonant spin-flavor conversions. This mechanism is induced by interaction between nonzero magnetic moment of neutrinos and supernova magnetic field. We investigate this mechanism in other papers in detai1.12>13

Acknowledgments This research was supported in part by Grant-in-Aid for Scientific Research provided by the Ministry of Education, Science and Culture of Japan through Research Grant No.Sl4102004 and No.14079202. S. A.’s work is supported by Grant-in-Aid for JSPS Fellows.

References 1. T. Totani, K. Sat0 and Y. Yoshii, Astrophys. J. 460, 303 (1996); R.A. Malaney, Astropart. Phys. 7, 125 (1997); D.H. Hartmann and S.E. Woosley, Astropart. Phys. 7, 137 (1997); M. Kaplinghat, G. Steigman and T.P. Walker, Phys. Rev. D62, 043001 (2000). 2. S. Ando, K. Sat0 and T. Totani, Astropart. Phys. 18, 307 (2003). 3. T. Totani, K. Sato, H. E. Dalhed and J. R. Wilson, Astrophys. J. 496, 216

(1998). 4. Y. Fukuda et al. (The Super-Kamiokande Collaboration), Phys. Rev. Lett. 82, 2644 (1999). 5. S. Fukuda et al. (The Super-Kamiokande Collaboration), Phys. Lett. B539, 179 (2002); Q. R. Ahmad et al. (SNO Collaboration), Phys. Rev. Lett. 89, 011301 (2002); ibid. 89, 011302 (2002). 6. K. Eguchi et al. (KamLAND Collaboration), Phys. Rev. Lett. 90, 021802 (2003). 7. M. Malek et al. (The Super-Kamiokande Collaboration), Phys. Rev. Lett. 90, 061101 (2003). 8. S. Ando and K. Sato, Phys. Lett. B559, 113 (2003). 9. P. Madau, H. C. Ferguson, M. E. Dickinson, M. Giavalisco, C. C. Steidel and A. Fruchter, Mon. Not. R. Astron. SOC.283, 1388 (1996). 10. Y . Suzuki, talk at Tokyo-Adelaid Joint Workshop on Quarks, Astrophysics, and Space Science (Tokyo, 2003). 11. K. Takahashi, K. Sato, H. E. Dalhed and J. R. Wilson, astro-ph/0212195. 12. S. Ando and K. Sato, Phys. Rev. D67, 023004 (2003). 13. S. Ando and K. Sato, Phys. Rev. D68 (2003), in press (hep-ph/0305052).

SOLAR AND REACTOR NEUTRINO ANALYSIS: RESULTS AND DESIDERATA

G. L. FOGLI, E. LISI:A. MARRONE, A. PALAZZO, A. M. ROTUNNO Dipartimento d i Fisica and Sezione INFN di Ban’ Via Amendola 173, 70126 Bari, Italy D. MONTANINO Dipartimento d i Scienza dei Materiali and Sezione INFN d i Lecce Via Arnesan,n, 73100 Lecce, Italy

We critically discuss the ingredients and the results of the combined analysis of solar and reactor data, which currently provide multiple solutions in the so-called Large Mixing Angle (LMA) region of the parameter space. We also emphasize the importance of a public release of the individual, time-averaged neutrino reactor yields at the KamLAND site, which are crucial for future precision analyses.

1. Introduction

At the time of this workshop (february 2003), neutrino physicists have

‘

already become familiar with the structure of the post-KamLAND oscillation fit to solar and reactor data. Figure 1 shows such structure in the parameter space spanned by the relevant 2v neutrino oscillation parameters, namely, the squared mass difference Sm2 = m: - rn; and the mixing angle 012 E [0,7r/2], mapped through sin2 642 E [0,1] in linear scale. [Mixing with the third neutrino v3 will be discussed later.] The globally allowed region, usually referred t o as “large mixing angle” (LMA) solution to the solar neutrino problem, should be largely affected by neutrino propagation through background matter in the Sun (and possibly in the Earth), although there is no unmistakable evidence for such matter effects yet *. The subregions in Fig. 1 may be called, from bottom to top, LMA-I and LMA11, plus a possible LMA-I11 region marginally allowed at the highest values of 6m2. (See also for similar results.) 315

*Speaker.

65

66

16

\.

-2

16

v

"E

W 16

2 d.0.f.

...........

9 0 % C.L

95

'

z

99 z . '.. 99.7371

16

Figure 1. Results of the global 2v fit to solar and reactor data. See

for details.

In this contribution to the Workshop, we shall try to answer, at least partially, the following questions: ( i ) What is the origin of the multiple LMA-n solutions (n =I, 11, ... )? (ii)How robust are such solutions? (iii) What is needed to disentangle them? 2. The role of KamLAND data

The first KamLAND data have clearly demonstrated the global disappearance of reactor (anti)neutrinos over long baselines '$. Additional information is contained in the energy spectrum of neutrino events, as shown in Fig. 5 of Ref. '. Although there is no unmistakable evidence for spectral shape distortions in KamLAND, it is fair to say the most of the disappearance effect seen in KamLAND is currently concentrated in a few energy bins above the 2.6 MeV analysis threshold, i.e., near (or just above) the spectrum peak. No clear evidence for disappearance in instead visible in the high-energy tail of the experimental spectrum in Ref. ', also because of the poor statistics. Therefore, current KamLAND data are expected to prefer oscillated spectra with sizeable suppression at the peak but with small suppression in the high-energy tail.

67

= 0.31)

KamLAND e+ spectrum 20

20

no oscillation 15 10

Am' = 2.0 E-5 eV' 6rn' = 3.0 E-5 eVZ

l5 I 10

~

6m' = 4.0 E-5 eVZ 6rn' = 5.0 E-5 eV'

-

5-

5 -

20

Lo

cu " ,

>

15-

6rnZ = 6.0 E-5 eV' Amz= 7.0 E-5 eV2

0

10:

l5

6rn2 = 8.0 E-5 eV 6m2= 9.0 E-5 eV

10

-w

'z

2 0

v

Q,

5i

5

.

0

1 , I ,

1

2

3

4

5

6

7

8

9

6m' = 1 .O E-4 eV2

0

1

2

3

4

15

5

6

7

8

9

6rn2 = 2.0 E-4 eV rn2 = 3.0 E-4 eV

10 5

0

1

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

8

9

Evis (MeV)

Evis (MeV)

Figure 2. Oscillated spectra of (visible) positron energy in KamLAND, for fixed sin' 812 = 0.31 and for twelve representative values of 6m'. The unoscillated spectrum is also shown for reference in each panel.

The relative peak/tail suppression pattern is a strong function of 6m2 (variations of sin2 1312 providing only an energy-independent suppression), as shown in Fig. 2. In this figure, theoretical energy spectra of positrons in KamLAND (from v, p + e+ n reactions) are calculated for fixed sin2 1912 = 0.31 (corresponding the best fit for LMA-I), and for twelve representative values of 6m2. One can recognize spectra with more suppression at the peak than in the upper tail, and vice versa. The latter (and the corresponding 6m2 values) are expected to be rejected by the data analysis. Indeed, Fig. 3 shows that the fit to KamLAND data only is characterized by a tower of alternate allowed and forbidden intervals of am2.

+

+

68 2u KarnlAND 108

-2

f0 8

v

i Y)

---

10'

1o-6

0

0.1

_.-

...-.._......-_

,

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

sinz$,,

Figure 3.

Results of the 2v analysis of KamLAND data. See

for details.

This tower of solutions, combined with the LMA region coming from solar data alone produces the LMA-n structure in Fig. 1. We emphasize that the current pattern of relative peak/tail suppression which leads to such structure is based on a modest statistics (54 events), and can thus change considerably with further KamLAND data. Therefore, one should not attach too much significance to the exact shape of the current LMA-n regions, and should not stick too much t o the current best-fit oscillation values (which belong t o the LMA-I region), as they can be subject t o change. 798,

3. The role of solar neutrino data Solar neutrino data play an important role in narrowing the range of sin2 eI2 below maximal mixing, and in disfavoring relatively high values of bm2,as it is well known. Here we would like t o emphasize that such features of the global solar I/ analysis are not completely settled yet, although they might soon be corroborated by new upcoming SNO data For this purpose, we show in Fig. 4 the separate 2v analyses of the Chlorine (Cl), Gallium (Ga), Super-Kamiokande (SK) and SNO data. It can be seen that, in the LMA region, only SNO (and, t o a lesser extent, the C1 experiment) really 418.

69

2v active oscillations

-3

Go rote -12

,

,A

, ,,,,,.., , ,,,,,,,I ,

,,,.,1

, , ,,,,,,, , , ,,,,,,, , , , , , , , , , , , , , , , ,

10

/,

+ W-S

SNO spectrum (34 bin -12

10

1 lo-*

, ,,,,,,,,

, ,,,,,,,,

lo-’

i

10

t o n2d,, Figure 4.

Break down of solar 2u analysis into the main four experimental subsets

disfavors both maximal mixing and large bm2, as a results of a marked preference for Pee = ( P ~ , - + ~<, )1/2 However, since P,, = 1/2 cannot be ruled out yet a t 30 by SNO, it would be premature to base any firm conclusions on this experiment alone. In practice, this means that there is still a marginal possibility of having maximal mixing and/or high bm2 in solar neutrino fits, especially if future SNO data will move the best-fit P,, closer t o 1/2. Conversely, future SNO data confirming Pee < 1/2 with high confidence will strengthen the indications in favor of sin2 812 < 112 coming from the current global fits.

70

4. The role of matter effects

About twenty years ago, Mykheev, Smirnov and Wolfenstein (MSW) emphasized that forward neutrino scattering in a matter background can profoundly modify oscillations. In particular, ve’s propagating through an electron background with density N , (x)get an extra interaction energy (as compared with u @ , ~ ’equal s ) to V = &‘GFN,E, where E is the v energy. The oscillation physics within the LMA region is generally affected by adiabatic MSW effects in the solar matter. These effects might be supplemented by small Earth matter effects in the lower part of the LMA region (say, LMA-I), while all matter would basically vanish for 6m2 > few x lo-* eV2. Confirmation of the MSW predictions would thus not only strengthen our confidence in the standard LMA interpretation of solar+KamLAND data, but would also narrow the oscillation parameter space. We emphasize that present data favor, but do not prove yet the existence of matter effects. In particular, if a free parameter UMSW is introduced to rescale the interaction energy, V + U M S W Vit, turns out that, although UMSW O(1) is favored, the allowed range is very large (- 3 decades) ‘. In other words, the size of V has not been “measured” yet.

-

double ratio

SNO CC/NC

-7

10

-

T

1

,=o

n1

d4

N

b

W

N

E

Lo

1o

-~

-6

i, n -

4 0

0.2

0.4

0.6

sin2+,,

0.8

1

0

0.2

0.4

0.6

0.8

1

s in2+,,

Figure 5. Comparison of CC/NC predictions in SNO, with (left) and without (right) matter effects. See for details.

71

There is, however, the potential to improve the situation with upcoming SNO data from neutral current (NC) and charged current (CC) neutrino interactions in deuterium. The predicted CC/NC ratio is a sensitive probe of a M S W in the LMA region, as shown in Fig. 5 where the cases U M S W = 1 (standard) and U M S W = 0 (no MSW effects) are compared. A value of CC/NC significantly below 1/2 would definitely rule out the case U M S W = 0, prove the occurrence of MSW effects, and narrow the allowed mass-mixing parameter space (see for details). Increasing the KamLAND statistics by an order of magnitude will also be important in this respect ‘.

3u oscillations

(Atrn.

+ KZK) + CHOOZ + KornlAND

I 0-’

n a

IO-‘

b i Lo W

lo5

lo-=

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

1 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

I 0-’

n

2

lo-’

W

”€

Lo

1o - ~

102

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Figure 6. Upper and lower bounds on “solar” mass-mixing parameters from terrestrial neutrino data, for four different values of sin’ 013

72

5. The role of CHOOZ and of 3v mixing

-

The CHOOZ experiment has not observed reactor Ye disappearance over a baseline 1 km. This fact places strong bounds on the mixing matrix element Ue3 which connects v, and the third neutrino mass eigenstate v3: U,"3 = sin2 613 < few x lop2. It also imposes an upper bound on 6m2 (< 7 x eV2) which, if violated, would lead to (unobserved) 6m2-driven oscillations in CHOOZ l o . It is perhaps not generally known that the upper bounds on sin2 613 and on 6m2 are anti-correlated: i.e., the larger sin2 613, the stronger the upper bound on 6m2 This feature is clearly shown in the fit to terrestrial (reactor ' > l o ,accelerator 12, and atmospheric 13) data in Fig. 6, as taken from 2 , to which we refer the reader for details. Therefore, for sin2 613 close to its upper limits, the upper bound on 6m2 from CHOOZ can become stronger than the one placed by solar neutrino data alone. Figure 6 also shows that terrestrial data alone put upper and lower bounds on both mass-mixing solar neutrino parameters: a very satisfactory result. It thus appears that terrestrial neutrino data (besides KamLAND) bring qualitatively different and independent information in analyses of the (6m2,612) bounds coming from solar+KamLAND data, and should be properly taken into account in 3v fits 2i11.

215,11

6. Desiderata for future analyses

We have already emphasized that upcoming SNO data will be decisive to prove matter effects and (in case of positive evidence) to strengthen upper bounds on 6m2 and sin2 012. New KamLAND data will instead be decisive to reduce the LMA-n solution multiplicity. For instance, the bins just above and below the current analysis threshold (2.6 MeV) will be very important to disentangle the LMA-I and LMA-I1 solutions, which have the largest spectral difference there '. The analysis of the first bin below threshold will be affected, however, by geo-neutrinos 6 . Here we emphasize that, irrespective of how helpful future KamLAND data will be, such data should be supplemented by additional and public information about the relative contributions from each reactor. In partic-

ular, at is crucial to know the percentage contribution of each rector to the the total unoscillated neutrino event rate in KamLAND. This information is known within the experimental collaboration, but has not been released in Ref. '. Lack of such information outside the collaboration might lead to biased results in analyzing future, higher-statistics data sets.

73

In order to better appreciate this point, we show in Fig. 7 the breakdown of the total KamLAND rate (for the LMA-I) solution in terms of individual contributions from the i-th reactor at distance Li. At a specific reactor location, such contribution is given by the unoscillated rate (lower vertical bar) times the survival neutrino probability a t distance Li (upper curve). It can be seen that the minima and maxima of the probability modulate each reactor contribution in a different way, so that individual reactor neutrino rates (the set of lower bars) must be known exactly to avoid biases in forming the total rate at KamLAND. This is especially true for data taken during this year (2003), due to the scheduled shutdown of several nuclear reactor plants for inspection 6 . In conclusion, we would like t o invite the KamLAND collaboration to publish the individual reactor neutrino rates (unoscillated, and timeaveraged over the relevant KamLAND lifetime) together with each release of new spectral data. This important information will allow a proper study of such crucial data also outside the Collaboration.

7. Conclusions The synergy between solar (Cl, Ga, SK, SNO) and reactor (CHOOZ, KamLAND) data has already produced very important results, including strong evidence for the LMA solution to the solar neutrino problem. Further data are required, however, to reduce the current LMA substructure (i.e., the LMA-n solution ambiguity) and to the prove the existence of predicted MSW effects in adiabatic regime. In particular, upcoming SNO data in the salt phase might soon reduce the range of possibilities. In the meantime, sticking too much to the currently favored LMA-I MSW solution would not be wise: The best fit might well change in the (near) future. Future KamLAND data will also be crucial to settle the pending questions about the LMA-n solutions. Their analysis (outside the Collaboration) will greatly benefit of the breakdown of the total unoscillated neutrino rate in KamLAND into individual reactor components: Publicity of this information will be essential to perform unbiased global fits in the future.

References 1. 2. 3. 4. 5.

KamLAND Collabor., K. Eguchi et al., Phys. Rev. Lett. 90, 021802 (2003). G.L. Fogli et al., Phys. Rev. D67, 073002 (2003). A.Yu. Smirnov, these Proceedings. G.L. Fogli et al., Phys. Rev. D67, 073001 (2003). C. Gonzalez-Garcia, these Proceedings.

74

Figure 7. Breakdown of separate reactor contributions t o the KamLAND total signal. The energy-averaged probability (upper curve, for the LMA-I case) modulates the individual contributions of reactors placed at different distances L (lower vertical bars).

6. 7. 8. 9. 10. 11. 12. 13.

K. Inoue for the KamLAND Collaboration, these Proceedings. M. Smy for the Super-Kamiokande Collaboration, these Proceedings. M. Chen for the SNO COllaboration, these Proceedings. G.L. Fogli et al., Phys. Rev. D66, 053010 (2002). Reactor v talks by M. Shaevitz, T. Lasserre, F. Suekane, these Proceedings. G.L. Fogli et al., Phys. Rev. D66, 093008 (2002). T. Kobayashi for the K2K Collaboration, these Proceedings. C. Yanagisawa for the Super-Kamiokande Collaboration, these Proceedings.

CAN FOUR NEUTRINOS EXPLAIN GLOBAL OSCILLATION DATA INCLUDING LSND & COSMOLOGY?

T. SCHWETZ Institut fur Theoretische Physik, Physik Department Techn. Univ. Munchen, James-Franck-Str., 0-85748 Garching, Germany

M. MALTONI, M.A. TORTOLA, J.W.F. VALLE Instituto de Fisica Corpuscular C.S.I. C./Universitat de Val6ncia Edificio Institutos de Paterna, Apt 22085, E-46071 Valencia, Spain -

We present an analysis of the global neutrino oscillation data in terms of fourneutrino mass schemes. We find that the strong preference of oscillations into active neutrinos implied by solar+KamLAND as well as atmospheric neutrino data allows to rule out (2+2) mass schemes, whereas (3+1) schemes are strongly disfavoured by short-baseline experiments. In addition, we perform an analysis using recent data from cosmology, including CMB data from WMAP and data from 2dFGRS large scale structure surveys. These data lead t o further restrictions of the allowed regions for the (3+1) mass scheme.

1. Introduction The neutrino oscillation interpretations of the solar1i2 and KamLAND3 neutrino experiments, a t m o ~ p h e r i c ~neutrino $~ data, and the LSND experiment6 require three neutrino mass-squared differences of different orders of magnitude7. Since it is not possible to obtain this within the Standard Model framework of three active neutrinos it has been proposed to introduce a light sterile neutrino' to reconcile all the experimental hints for neutrino oscillations. Here we present an analysis of the global neutrino oscillation data in terms of four-neutrino mass schemes, including data from solar, KamLAND and atmospheric neutrino experiments, the LSND experiment, as well as data from short-baseline (SBL) experiment^^>^^>^' and reactor experiments12 reporting no evidence for oscillations. We find that for all possible types of four-neutrino schemes different sub-sets of the data are in serious disagreement and hence, four-neutrino oscillations do not provide a satisfactory description of the global oscillation data including LSND. The details of our calculations can be found in Refs. 13, 14, 15.

75

76

(3;l)

Figure 1.

(2k)

The six four-neutrino mass spectra, divided into the classes (3+1) and (2+2).

2. Notations and approximations Four-neutrino mass schemes are usually divided into the two classes (3+1) and (2+2), as illustrated in Fig. 1. We note that (3+1) mass spectra include the three-active neutrino scenario as limiting case. In this case solar and atmospheric neutrino oscillations are explained by active neutrino oscillations, with mass-squared differences and , and the fourth neutrino state gets completely decoupled. We will refer to such limiting scenario as (3+0). In contrast, the (2+2) spectrum is intrinsically different, as there must be a significant contribution of the sterile neutrino either in solar or in atmospheric neutrino oscillations or in both. Neglecting CP violation, in general neutrino oscillations in four-neutrino schemes are described by 9 parameters: 3 mass-squared differences and 6 mixing angles in the unitary lepton mixing matrix. Here we use a parameterisation introduced in Ref. 13, which is based on physically relevant quantities: the 6 parameters Am&,,, QsoL, OATM, am^,,,, QLsN, are similar to the two-neutrino mass-squared differences and mixing angles and are directly related to the oscillations in solar, atmospheric and the LSND experiments. For the remaining 3 parameters we use qs,qe and d,. Here, qs (7,) is the fraction of vs (ve)participating in solar oscillations, and (1 - d p ) is the fraction of vp participating in oscillations with AmK, (for exact definitions see Ref. 13). For the analysis we adopt the following approximations: (1) We make use of the hierarchy Am&,, << AmiTM<< Am:,,,. This means that for each data set we consider only one mass-squared difference, the other two are set either to zero or to infinity. (2) In the analyses of solar and atmospheric data (but not for SBL data) we set qe = l, which is justified because of strong constraints from reactor experiments11i12. Due to these approximations the parameter structure of the fourneutrino analysis gets rather simple. The parameter dependence of the

77

Figure 2.

Parameter dependence of the different data sets in our parameterisation.

four data sets solar, atmospheric, LSND and NEV is illustrated in Fig. 2. The NEV data set contains the experiments KARMEN', CDHSl', Bugey" and CHOOZ/Palo Verde", reporting no evidence for oscillations. We see that only q, links solar and atmospheric data and d, links atmospheric and NEV data. LSND and NEV data are coupled by Am& and d,,,. 3. (2+2): ruled out by solar and atmospheric data

The strong preference of oscillations into active neutrinos in solar and atmospheric oscillations leads to a direct conflict in ( 2 + 2 ) oscillation schemes. We will now show that thanks to the latest solar neutrino data (especially from SNO') in combination with the KamLAND experiment3, and the improved SK statistic on atmospheric neutrinos4 the tension in the data has become so strong that (2+2) oscillation schemes are essentially ruled out." The thin lines in the left panel of Fig. 3 show the Ax2 of latest solar data as a function of q,, the parameter describing the fraction of the sterile neutrino participating in solar neutrino oscillations. The 99% CL bounds qs 5 0.44, when the SSM constraint on the 'B-flux is included, and q, 5 0.61 for free sB-flux reflect the strong preference for active neutrino oscillations of solar data. Recently, the outstanding results of the KamLAND reactor experiment3 confirmed the LMA solution of the solar neutrino problem16,18. Apart from this very important result the sensitivity of KamLAND to an admixture of a sterile neutrino is rather limited (see think lines in Fig. 3). The combined analysis leads to the 99% CL bound q, 5 0.5 for 'B free, whereas in the SSM constrained case the bound is unchanged. "Details of our analyses of the solar, KamLAND and atmospheric neutrino data can be found in Refs. 15, 16. For an earlier four-neutrino analysis of solar and atmospheric data see Ref. 17.

78

atm+SBL

N

d"

11,

11s

Figure 3.

Left: Ax2 from solar and KamLAND data as a function of vs. Right: Ax&, as a function of vs in (2+2) oscillation schemes.

AX;^^+^^^ and X&bal

In contrast, in (2+2) schemes atmospheric data imply vs 2 0.65 at 99% CL, in clear disagreement with the bound from solar data. In the right panel of Fig. 3 we show the x2 for solar data and for atmospheric combined with SBL data as a function of vs. Furthermore, we show the x2 of the global data defined by

From the figure we find that only if we take both data sets at the 99.95% CL a value of vs exists, which is contained in the allowed regions of both sets. This follows from the X2-value x;c = 12.2 shown in the figure. In Refs. 14, 19 we have proposed a statistical method to evaluate the disagreement of different data sets in global analyses. The parameter goodness o f f i t (PG) makes use of the X 2 defined in Eq. (1). This criterion evaluates the GOF of the combination of data sets, without being diluted by a large number of data points, as it happens for the usual GOF criterion (for details see Ref. 19). We find x$G XLin = 23.5, leading to the marginal P G of 1.3 x lop6. We conclude that (2+2) oscillation schemes are highly disfavoured by the disagreement between the latest solar and atmospheric neutrino data. This is a very robust result, independent of whether LSND is confirmed or disproved.b

--

bSub-leading effects beyond the approximations adopted here should not affect this result significantly. Allowing for additional parameters to vary might change the ratio of some observab1es2O,however, we expect that the absolute number of events relevant for the fit will not change substantially.

79

10'

loo

10-l 10-1

loo

Figure 4. Upper bound on sin22&D from NEV and atmospheric neutrino data in (3+1) schemesz3 compared to the allowed region from global LSND data6 and decay-atrest (DAR) LSND data24.

4. (3+1): strongly disfavoured by SBL data

It is known for a long time21f22that (3+1) mass schemes are disfavoured by the comparison of SBL disappearance datalOJ1 with the LSND result. In Ref. 23 we have calculated an upper bound on the LSND oscillation amplitude sin2 28,SND resulting from NEV and atmospheric neutrino data. From Fig. 4 we see that this bound is incompatible with the signal observed in LSND at the 95% CL. Only marginal overlap regions exist between the bound and global LSND data if both are taken at 99% CL. An analysis in terms of the parameter goodness of fit14 shows that for most values of AmZsNDNEV and atmospheric data are compatible with LSND only at more than 3c, with one exception around AmZsND 6 eV2, where the PG reaches 1%.These results show that (3+1) schemes are strongly disfavoured by SBL disappearance data.

-

5 . Comparing (3+1), (2+2) and (3+0) hypotheses

With the methods developed in Ref. 13 we are able to perform a global fit to the oscillation data in the four-neutrino framework. This approach allows to statistically compare the different hypotheses. Let us first evaluate the GOF of (3+1) and (2+2) spectra with the help of the PG method described

80 Table 1. Parameter GOF and the contributions of different data sets to xgG in (3+1) and (2+2) neutrino mass schemes.

I

1

(3+1) (2+2)

I

I

SOL 0.0 14.8

ATM 0.4 6.7

LSND 7.2 2.2

NEV 7.0 9.7

I I

I

I 14.6 32.4

I

I

PG 5.6 x 10W3 1.6 x lop6

I

in Ref. 19. We divide the global oscillation data in the 4 data sets SOL, ATM, LSND and NEV. Following Ref. 14 we consider

where Ax$ = x$ ( X = SOL, ATM, NEV, LSND). In Tab. 1 we show the contributions of the 4 data sets to x ; = ~ %kinfor (3+1) and (2+2) oscillation schemes. As expected we observe that in (3+1) schemes the main contribution comes from SBL data due to the tension between LSND and NEV data in these schemes. For (2+2) oscillation schemes a large part of x$G comes from solar and atmospheric data, however, also SBL data contributes significantly. This comes mainly from the tension between LSND and KARMEN24, which does not depend on the mass scheme and, hence, also contributes in the case of (2+2). Therefore, the values of x $ in Tab. 1 for (2+2) schemes are higher than the one given in Sec. 3, where the tension in SBL data is not included. The parameter goodness of fit is now obtained by evaluating x;G for 4 DOF". This number of degrees of freedom corresponds to the 4 parameters qs,d,, OLSND,Am:,,, describing the coupling of the different data sets (see Eq. (2) and Fig. 2). The best GOF is obtained in the (3+1) case. However, even in this best case the P G is only 0.56%. The P G of 1.6 x for (2+2) schemes shows that these mass schemes are essentially ruled out by the disagreement between the individual data sets. Although we have seen that none of the four-neutrino mass schemes can provide a reasonable good fit to the global oscillation data including LSND, it might be interesting t o consider the relative status of the three hypotheses (3+1), (2+2) and the three-active neutrino scenario (3+0). This can be done by comparing the x2 values of the best fit point (which is in the (3+1) scheme) with the one corresponding t o (2+2) and (3+0). First we observe that (2+2) schemes are strongly disfavoured with respect to ( 3 f l ) with a Ax2 = 17.8, implying a CL of 99.87% for 4 DOF. Further we find that (2+2) is only slightly better than (3+0), which is disfavoured with a Ax2 = 20.0 with respect to (3+1).

~

81

-

10'

N

Figure 5 . Left: Allowed regions at 90% and 99% CL for (3+1) schemes without (solid and dashed lines) and including data from cosmology (coloured regions). The grey region is the 99% CL region of LSND6. Right: Ax2 from cosmological dataz8 as a function of AmZs,,.

6. Adding information from cosmology

Recently a precision measurements of the cosmic microwave background (CMB) radiation has been published by the WMAP ~ o l l a b o r a t i o n ~ Under ~. certain assumptions about the cosmological model and in combination with other cosmological data a stringent upper bound on the sum of the neutrino masses Em, 5 0.7 eV is ~ b t a i n e d ~Since ~ > ~this ~ . bound is of the same order as it will lead to further restrictions in four-neutrino mass schemes27. To combine this information with data from oscillation experiments we use the results of an analysis performed by S. Hannestad2'. There, WMAP25 results have been combined with other CMB data2g,data from the large scale structure survey 2dFGRS3', the HST Hubble key project31, and Type Ia supernovae observation^^^. It has been found that a non-zero E m,, can be compensated partially by an increase in the effective number of neutrino species. Therefore, the original bound obtained in Ref. 2 5 , which was calculated assuming three neutrinos, cannot be applied in a straightforward way. In the case of four neutrinos a somewhat weaker bound of Ern, < 1.38 eV (95% CL) is obtained2'. To combine this result with data from oscillation experiments we use the x2 from cosmology for four neutrinos, shown in Fig. 6 of Ref. 28. In the following analysis we consider (3+1) schemes of the hierarchical type (first two spectra in Fig. 1) and neglect the masses of the three lower

d

K

82

d z . c

AX^^^^^^^^^

mass states, such that C m , M The from Ref. 28 under this assumption is shown in the right panel of Fig. 5 as a function of AmZsN,,. From the left panel of this figure one finds that cosmology excludes the region Am:sND 2 3 eV2. However, the islands at Am;,,, 0.91 eV2 and 1.7 eV2 are practically unaffected by cosmological data. Performing a GOF analysis shows that adding cosmological data gives xCG = 17.1 and 19.6 for the two islands. This should be evaluated for 5 DOFi9, leading to a P G of 0.43% and 0.15%, respectively, which is comparable to the value given for (3+1) in Tab. 1. We note, however, that a modest improvement of the bound on C m, by future cosmological data will drastically worsen the fit of the last remaining islands in the four-neutrino parameter space. A further cosmological constraint on four-neutrino schemes comes from Big Bang nucleo synthesis ( B B N ) ” I ~ ~ In. the absence of any non-standard mechanism, like a large lepton number asymmetry, (3+1) as well as (2+2) schemes will lead to an effective number of neutrino species Nu = 434. This is in conflict with the upper bound on N,, derived in recent analyses28>35>36 including CMB and BBN data. Taking into account the uncertainty related to the primordial abundances of He and D, upper bounds in the range Nu < 3.1 - 3.3 ( 2 ~ are ) obtained. ~ ~

-

7. Conclusions Performing a global analysis of current neutrino oscillation data we find that four-neutrino schemes do not provide a satisfactory fit to the data: 0 The strong rejection of non-active oscillation in the solar+KamLAND and atmospheric neutrino data rules out (2+2) schemes, independent of whether LSND is confirmed or not. Using an improved goodness of fit method especially sensitive to the combination of data sets we obtain a GOF of only 1.6 x lop6 for (2+2) schemes. 0 (3+1) spectra are disfavoured by the disagreement of LSND with short-baseline disappearance data, leading to a marginal GOF of 5.6 x If LSND should be confirmed we need more data on v, and/or up SBL disappearance to decide about the status of (3+1). 0 Recent cosmological data lead to further restrictions of the allowed parameter space. Only two islands aground Am:,,, 0.91 eV2 and 1.7 eV2 in hierarchical (3+1) schemes survive. N

‘Note that all other four neutrino schemes will be much more disfavoured, since more mass states will contribute at the LSND mass scale.

83

Our analysis brings the LSND hint to a more puzzling status, and the situation will become even more puzzling if LSND should be confirmed by the up-coming MiniBooNE e ~ p e r i m e n t Recently ~~. an explanation in terms of five neutrinos has been proposed38. In such a (3+2) scheme solar and atmospheric data are explained dominantly by active oscillations, similar to the (3+1) case. The fit of SBL data is improved with respect to (3tl) by involving two large mass splittings Amil 0.9 eV2 and Am& 20 eV2. Alternative explanations of LSND by anomalous muon decay39 seem to be in disagreement with the negative result of KARMEN, or require a very radical modification of standard physics, like C P T violation4’. Acknowledgements: T.S. would like to thank the organisers for the very interesting workshop and for financial support. Furthermore, we thank S. Hannestad for providing us with the x2 of cosmological data, and S.Pastor for discussions. This work was supported by Spanish grant BFM200200345, by the European Commission RTN grant HPRN-CT-2000-00148 and by the ESF Neutrino Astrophysics Network. M.M. was supported by Marie Curie contract HPMF-CT-2000-01008, T.S. was supported by the “Sonderforschungsbereich 375-95 fur Astro-Teilchenphysik” der Deutschen Forschungsgemeinschaft and M.A.T. was supported by the M.E.C.D. fellowship AP2000- 1953.

-

N

References 1. S. Fukuda et al., Phys. Lett. B 539 (2002) 179; M. Smy, these proceedings; B.T. Cleveland et al., Astrophys. J. 496, 505 (1998); D.N. Abdurashitov et al., Phys. Rev. C60, 055801 (1999); astro-ph/0204245; W. Hampel et al., Phys. Lett. B447, 127 (1999); C. Cattadori, Nucl. Phys. B (Proc. Suppl.) 110 (2002) 311. 2. Q. R. Ahmad et al., SNO Coll., Phys. Rev. Lett. 89, 011301 (2002); Phys. Rev. Lett. 89, 011302 (2002); M. Chen, these proceedings. 3. K. Eguchi et al., KamLAND Coll., Phys. Rev. Lett. 90 (2003) 021802; K. Inoue, these proceedings. 4. M. Shiozawa, Neutrino 2002, http://neutrino2002.ph.tum.de/; Y. Fukuda et al., Phys. Rev. Lett. 81 (1998) 1562; C. Yanagisawa, these proceedings. 5. MACRO Coll., M. Ambrosio et al., Phys. Lett. B 434 (1998) 451; A. Surdo, TAUP 2001, http://www.lngs.infn.it/. 6. A. Aguilar et al., LSND Coll., Phys. Rev. D 64 (2001) 112007. 7. For a review see e.g., S. Pakvasa and J. W. Valle, hep-ph/0301061. 8. J. T. Peltoniemi, D. Tommasini and J. W. F. Valle, Phys. Lett. B 298 (1993) 383; J. T. Peltoniemi and J. W. F. Valle, Nucl. Phys. B 406, 409 (1993); D.O. Caldwell and R.N. Mohapatra, Phys. Rev. D 48 (1993) 3259. 9. B. Armbruster et al., KARMEN Coll., Phys. Rev. D 65 (2002) 112001. 10. F. Dydak et al., CDHS Coll., Phys. Lett. B 134 (1984) 281.

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11. B. Achkar et al., Bugey Coll., Nucl. Phys. B 434 (1995) 503. 12. M. Apollonio et al., CHOOZ Coll., Phys. Lett. B 466 (1999) 415; F. Boehm et al., Palo Verde Coll., Phys. Rev. D 64 (2001) 112001. 13. M. Maltoni, T. Schwetz and J.W.F. Valle, Phys. Rev. D 65 (2002) 093004. 14. M. Maltoni, T. Schwetz, M.A. T6rtola and J.W.F. Valle, Nucl. Phys. B 643 (2002) 321 [hep-ph/0207157]. 15. M. Maltoni, T. Schwetz, M.A. T6rtola and J.W.F. Valle, Phys. Rev. D 67 (2003) 013011 [hep-ph/0207227]. 16. M. Maltoni, T. Schwetz and J. W. Valle, Phys. Rev. D 67 (2003) 093003. 17. M.C. Gonzalez-Garcia, M. Maltoni and C. Pena-Garay, Phys. Rev. D 64 (2001) 093001 [hep-ph/0105269]. 18. J.N. Bahcall, M.C. Gonzalez-Garcia and C. Pena-Garay, JHEP 0302 (2003) 009; M.C. Gonzalez-Garcia, these proceedings; G.L. Fogli, et al., Phys. Rev. D 67 (2003) 073002; E. Lisi, these proceedings; P.C. de Holanda and A.Y. Smirnov, JCAP 0302 (2003) 001; A.Y. Smirnov, these proceedings. 19. M. Maltoni and T. Schwetz, hep-ph/0304176. 20. H. Pas, L. g. Song and T. J. Weiler, Phys. Rev. D 67 (2003) 073019. 21. S.M. Bilenky, C. Giunti and W. Grimus, Proc. of Neutrino '96, Helsinki; Eur. Phys. J. C 1 (1998) 247; V. Barger, et at., Phys. Rev. D 58 (1998) 093016; S.M. Bilenky, et al., Phys. Rev. D 60 (1999) 073007; O.L. Peres and A.Y. Smirnov, Nucl. Phys. B 599 (2001) 3; C. Giunti and M. Laveder, JHEP 0102 (2001) 001; W.Grimus and T. Schwetz, Eur. Phys. J. C 20 (2001) 1. 22. N. Okada and 0. Yasuda, Int. J. Mod. Phys. A 12 (1997) 3669. 23. M. Maltoni, T. Schwetz and J . W. F. Valle, Phys. Lett. B 518,252 (2001). 24. E.D. Church et al., Phys. Rev. D 66 (2002) 013001 [hep-ex/0203023]. 25. C.L. Bennett et al., astro-ph/0302207; D.N. Spergel et al., astro-ph/0302209. 26. 0. Elgaroy and 0. Lahav, JCAP 0304 (2003) 004 [astro-ph/0303089]. 27. A. Pierce and H. Murayama, hep-ph/0302131; C. Giunti, hep-ph/0302173; A. Strumia, hep-ph/0201134~4. 28. S. Hannestad, JCAP 05 (2003) 004 [astro-ph/0303076]. 29. X. Wang, M. Tegmark, B. Jain and M. Zaldarriaga, astro-ph/0212417. 30. J.A. Peacock et al., Nature 410 (2001) 169; M. Tegmark, A. J. Hamilton and Y. Xu, Mon. Not. Roy. Astron. SOC.335 (2002) 887 [astro-ph/0111575]. 31. W.L. Freedman et al., Astrophys. J. Lett. 553 (2001) 47. 32. S. Perlmutter et al., Astrophys. J. 517 (1999) 565. 33. S.M. Bilenky, C. Giunti, W. Grimus and T. Schwetz, Astropart. Phys. 11 (1999) 413 [hep-ph/9804421]. 34. K. Enqvist, K. Kainulainen and M.J. Thomson, Nucl. Phys. B 373 (1992) 498; P. Di Bari, Phys. Rev. D 65 (2002) 043509; K.N. Abazajian, Astropart. Phys. 19 (2003) 303. 35. P. Crotty, J. Lesgourgues and S. Pastor, astro-ph/0302337. 36. V. Barger et al., hep-ph/0305075. 37. E. Zimmerman, MiniBooNE Coll., hep-ex/0211039; these proceedings. 38. M. Sorel, J. Conrad and M. Shaevitz, hep-ph/0305255. 39. K. S. Babu and S. Pakvasa, hep-ph/0204236. 40. G. Barenboim, L. Borissov and J. Lykken, hep-ph/0212116.

UNIVERSAL TEXTURE OF QUARK A N D LEPTON MASS MATRICES

YOSHIO KOIDE Department of Physics, University of Shizuoka, 52-1 Yada, Shizuoka, 422-8526 Japan E-mail: [email protected]

HIROYUKI NISHIURA Department of General Education, J u n i o r College of Osaka Institute of Technology, Asahi-ku, Osaka, 535-8585 J a p a n E-mail: [email protected]. ac.j p

KOICHI MATSUDA, TATSURU KIKUCHI, AND TAKESHI FUKUYAMA Department of Physics, R i t s u m e i k a n University, Kusatsu, Shiga, 525-8577 Japan E-mail: sph30101 @se.ritsumei.ac.jp, [email protected], and [email protected] Against the conventional picture that the mass matrix forms in the quark sectors will take somewhat different structures from those in the lepton sectors, a possibility that all the mass matrices of quarks and leptons have the same form as in the neutrinos is investigated. For the lepton sectors, the model leads to a nearly bimaximal mixing with the prediction (Ue3I2 = m,/2mp = 0.0024 and tan2 B s o l r m,l/m,z, and so on. For the quark sectors, it can lead to reasonable values of the CKM mixing matrix and masses: lVusl r = /,, l v u b l ‘2 l v c b l lvtdl ~ ‘2 ~ l v~ c b l I v u s I , and SO On.

1. Model Recent neutrino oscillation experiment^^^^^^^^ have highly suggested a nearly bimaximal mixing (sin2 2812 1, sin2 2823 E 1) together with a small ratio R Am:2/Ami3 l o p 2 . On the other hand, we know that the observed quark mixing matrix VCKMis characterized by small mixing angles. Thus, the mixing matrices of quarks and leptons are very different from each other. Therefore, usually, the following picture is accepted: the mass matrix forms in the quark sectors will take somewhat different structures from those in

-

-

85

86

the lepton sectors. Against such a conventional picture, we investigate a possibility that all the mass matrices of quarks and leptons have the same forms as in the neutrino sector:

where Pf = diag(eisl , cis:, ei6:), and the mass matrix M f is invariant under a permutation symmetry between second and third generations. The mass matrix parameters at, b f , and c f can be expressed in terms of the mass bf = ( m f 3 / 2 )[I (mf2 - mfi)/mf3], eigenvalues as af = and Cf = - ( m f 3 / 2 ) [I - (mf2 - mfi)/mf3]. The mass matrix form (2) was suggested from the neutrino mass matrix form which leads t o a nearly bimaximal mixing f

h

Jw, cv

uv-

Qv

c,

(3)

z

mv2,mv3) and

= cos ev = / T, mu2

0

2 -8)

JZJZ where UTMvUv = diag(-m,l,

+

+ mv1

s, = sin

e,

=/ T. mv2

+

(4)

mv1

Note that the matrix form (1) with (2) is almost invariant under the renormalization group equation (RGE) effects, so that we can use the expression (1) with (2) for the predictions of the physical quantities in the low-energy region, as well as those at the unification scale. The zeros in this mass matrix are constrained by a discrete symmetry 2 3 that is discussed in Ref.‘, defined at a unification scale (the scale does not always mean “grand unification scale”). This discrete symmetry 23 is broken below p = M E , at which the right-handed neutrinos acquire heavy Majorana masses. Therefore, the matrix form (1) will, in general, be changed by the RGE effects. Nevertheless, we can use the expression (1) with (2) for the predictions of the physical quantities in the low-energy region, as discussed in Ref.

‘.

87

2. Quark mixing matrix

The quark mass matrices with the form (1) are diagonalized by the bit of, unitary transformation Df = uLfk f fU R f, where ULf PLf URf PAfof, and o d (0,) is given by

(For simplicity, hereafter, we will take PR = PL, so that the matrix M f becomes a symmetric matrix. However, this assumption is not essential for the results in the present model.) Then, the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix V is given by

v = Ul,ULd

=

(

CuCd

o~pup,'Od

1

+ psusd

cusd

pcusd

SuSd

Sucd -

-usd

-

+

psucd

): :

(6)

pcucd

gcd

where p and u are defined by

,, = -1( e i J 3

P

- ,iJa)

2

.

(7)

Here we have put P diag(eisl, eisa, eiJ3), and we have taken PUP,' S1 = 0 without loss of generality. From the expression (6), we obtain the phase-parameter independent predictions (the 3rd generation quark-mass independent predictions 7,

which are almost independent of the RGE effects. Next let us fix the parameters S3 and S2. From the relation lxbl

=

1 b3 - b2 dy sin l + m /m 2 '

(9)

and the observed value lvebl = 0.0412 k 0.0020, we obtain S3 - 6 2 = 4.59' & 0.21'. Also, from the expression of JV,,J,we can obtain the value S3 + 6 2 = 93' f 22'. Because of the small value sin(& - & ) / 2 Y 0.04, we obtain the following approximate relations

88

which are consistent with the present experimental data In the present model, the rephasing invariant Jarlskog parameter J is given by

Therefore, the phase factor 6 in the standard expression of V corresponds t o Y 6 3 + 6 2 / 2 in the present model. We predict IJI = (1.91 f 0.38) x

6

3. Lepton mixing matrix We assume that the neutrino masses are generated via the seesaw mechanism M , = -MD M i 1M:. Here MD and M R are the Dirac neutrino and the right-handed Majorana neutrino mass matrices. Note that when we assume the same matrix forms ( 1 ) for MD and M R , the effective neutrino mass matrix Mv = - M 0 M i 1 M ~is again given by the same texture (1):

Therefore, we obtain the lepton mixing matrix U CeCv

+

PvSeSu

CeSv

- PvSeCv

secv -pvcesv

sesv +pvcecv

-gvsv

UVCV

-uvSe bvce

)

7

(13)

PV

where P E Pep? e diag(ei”l, e i s v a ,eisv3). Hereafter we will again take 6,1 = 0 without loss of generality. Note that V = OzPOd, while U = OTPO,, so that all the mixing formulae in the lepton sectors are given by the replacement (mu,m,, mt) + ( m e m , p ,m,) and (md,m a ,mb) + ( m v l ,mv2,mv3) in those in the quark sectors. However, this does not means that the physics in the up-quark (down-quark) sector corresponds to the physics in the charged lepton (neutrino) sector. In fact, as we see in Table 1, the parameter values in each sector are different from the other. We obtain the phase-parameter independent predictions

The neutrino mixing angle Oat,,, under the constraint given by

>>

is

89 Table 1. Input values m; and output values a f , bf and c f . The numerical values are given in unit of GeV except for the neutrino sector (in unit of eV). The input values are those at p = m e except for the neutrino sector (for the neutrinosector, see the text).

outputs

f

-

at

bt

-Cf

U

0.00233

0.677

181

0.0280

d

0.00469

0.0934

3.00

0.0148

90.8 1.54

e

0.000487

0.103

1.75

0.00500

0.924

0.822

0.0030

0.0088

0.050

0.0036

0.028

0.022

Y -

90.2 1.46

We assume the maximal mixing between up and v,, so that we take Sv3 6,2 = ~ 1 2 Then, . the model predicts 1 me = 0.00236, IU13l2 = 2mp+me

which is consistent with the constraint IU131fx, < 0.03 from the CHOOZ data '. The mixing angle Odora+ is given by

which leads to the relation m,l/mv2 N tan28,,~,,. Therefore, the best fit value tan2 8solaT = 0.34 predicts the neutrino mass ratio m,l/m,2 N 0.34, so that we can obtain the neutrino masses m,l = 0.0030 eV

,

mv2 = 0.0088 eV , mv3 = 0.050 eV

,

(18)

where we have used the best fit values of Am:ora, = 6.9 x eV2 and Am:,, = 2.5 x eV2. We also obtain the averaged neutrino mass (m,) eV, but the explicit value is highly dependent on the value of 6, (6,3+6,2)/2. At present, we cannot fix the value of 6,. 411

-

4. Conclusion

In conclusion, stimulated by recent neutrino data, which suggest a nearly bimaximal mixing, we have investigated a possibility that all the mass matrices of quarks and leptons have the same texture as the neutrino mass matrix. In spite of the assumption of the universal texture for all the fermion mass matrices, we can obtain the differences between V&ar]e and Keptm as follows: (i) the mixing between 1st and 2nd generations is given

90

d z ,

by tan812 = so that the well-known empirical relation lV,,/ 2: is due to the observed mass rations %/me << md/mr << 1, and the nearly maximal mixing lVe21 l / f i is due t o the approximate degeneracy m,l mv2 and the observed mass ratio me/mp << 1; (a) the mixing between 2nd and 3rd generations is given by the relation (9) (and the corresponding relation in the lepton sector), so that the small value lVcbl 2: 0.04 means (S3 - &)/a cz 0.04 and m,/m, << 1, and the maximal mixing Vp3 2: 1 / 4 means S3 - S2 E n/2 together with m e / m p << 1. The present data in the quark sectors have already fixed the C P violating phase parameters S3 and S2, while the present neutrino data have yet not fixed the parameter (SV3 S,2)/2, although they have fixed the value of (S,3 - S,2)/2. We hope that future experiments on the C P violation will fix our remaining parameter S,. Then, we will be able t o obtain a clue to the origin of our phase parameters Si (SVi). Since, in the present model, each mass matrix M f (i.e. the Yukawa coupling Yf) takes different values of the parameters a f , b f , and so on, the present model cannot be embedded into a GUT scenario. In spite of such a demerit, however, it is worth while noting that the present model can give a unified description of quark and lepton mass matrices with the same texture.

d

z

-

-

+

References

1. M. Shiozawa, 2. 3. 4. 5.

6.

7. 8. 9.

talk at Neutrino 2002 (http://neutrino.t30.physik.tumuenchen.de/) . SNO collaboration, Q.R. Ahmad e t al., Phys. Rev. Lett. 89,011302 (2002). CHOOZ collaboration, M. Apollonio e t al., Phys. Lett. B466, 415 (1999). KamLAND collaboration, K. Eguchi, e t al., Phys. Rev. Lett. 90, 021802 (2003). T.Fukuyama and H. Nishiura, hep-ph/9702253;in Proceedings of the International Workshop on Masses and Mixings of Quarks and Leptons, Shizuoka, Japan, 1997,edited by Y.Koide (World Scientific, Singapore, 1998), p. 252; E. Ma and M. Raidal, Phys. Rev. Lett. 87, 011802 (2001); C. S. Lam, Phys. Lett. B507, 214 (2001);K. R. S. Balaji, W. Grimus and T. Schwetz, Phys. Lett. B508, 301 (2001);W. Grimus and L. Lavoura, Acta Phys. Pol. B32, 3719 (2001). Y.Koide, H.Nishiura, K. Matsuda, T. Kikuchi and T. Fukuyama, Phys. Rev. D66, 093006 (2002). G. C. Branco and L. Lavoura, Phys. Rev. D44,R582 (1991). Particle Data Group, K. Hagiwara e t al., Phys. Rev. D66, 010001 (2002). H.Fusaoka and Y. Koide, Phys. Rev. D57, 3986 (1998).

NEUTRINO MASSES AND BEYOND FROM SUPERSYMMETRY

OTTO C . W. KONG* Department of Physics, National Central University Chung-li, TAIWAN 32054 & Theory Group, KEK, Tsukuba, Ibaraki, 305-0801, Japan E-mail: [email protected]

A generic form of the supersymmetric SM naturally gives rise to the lepton number violating neutrino masses and mixings, without the need for extra superfields beyond the minimal spectrum. Hence, SUSY can be considered the origin of beyond SM properties of neutrinos. We have developed a formulation under which one can efficiently analyze the model. Various sources of neutrino masses are discussed. Such mass contributions come from lepton number and flavor violating couplings that also give rise to a rich phenomenology of the neutrinos and other leptons, also to be discussed.

1. Introduction From the theoretical point of view, low-energy supersymmetry (SUSY) is by far the most popular candidate theory for physics beyond the Standard Model (SM). On the experimental size, we now do have results confirming beyond SM properties of neutrinos, which at least includes oscillations among different neutrino spieces. The most natural way to have neutrino oscillations is to have massive neutrinos. Here, we are particularly interested in properties of such massive neutrinos that could actually be considered as arising from SUSY. Within the SM, neutrino mass terms may be described by VEVs of dimension five operators of the form

La ( H ) ( H )L j M

,

~

*Work partially supported by grant NSC91-2112-M-008-042 of the National Science Council of Taiwan.

91

92

where M denotes some high energy scale. The non-renormalizable dimension five operators should be considered as obtained from integrating out some beyond SM physics underlying, physics of which can be probed only at scale beyond M . Neutrino masses are usually classified as Dirac or Majorana. Dirac mass terms involve singlet fermions usually named right-hand neutrinos (vR or vs) giving rise to terms of the form Qs,(H)Lj . Lepton number violating Mujoruna mass terms at scale M are typically introduced. Integrating out the heavy neutrino degrees of freedom leaves the seesaw induced effective SM neutrino Majorunu masses. Direct introduction of such Majorana masses without heavy neutrino degrees of freedom have also been considered. The simplest way to do that is to introduce a Higgs triplet with VEV, giving rise t o

Li(T)Lj .

9

An effective triplet VEV ( T )= is always needed, though it can also come from a loop diagram. Typically, we do need extra scalar bosons in the theory one way or another’. So, the old question of whether neutrinos are Dirac or Majorana is not quite the right question to ask. Experimentally speaking, a (physical) neutrino is just a light neutral fermion that experiences weak interactions. As long as low energy phenomenology is concerned, we only need to know how many neutral fermion degrees of freedom are within reach, and what is the generic mass matrix. 2. Supersymmetry and Neutrinos

A supersymmetric extension of the SM has four extra neutral fermions apart from the SM ones. And nonzero masses are generally admissible for the full set of seven neutral fermions including the neutrinos. From the early history of supersymmetry (SUSY), there had been thinking about its usage in the obviously non-supersymmetric low-energy phenomenology. One of the first idea was the identification of the neutrino as a goldstino, ie. the Goldstone mode from (global) SUSY breaking2. Nowadays, the question : “ISthe masslessness of the neutrino a result of SUSY (breaking)?” is obvious an uninteresting one. Nevertheless, neutrinos and SUSY just may have everything to do with one another; after all, nonzero masses of neutrinos may be a result of SUSY. The latter is related to the notion of R-parity violation.

93

The notion of R parity came about also early in the history of SUSY3. In those days, baryon and lepton number symmetries might look even better than the standard model (SM) itself. R parity then seemed quite natural. However, global symmetries are since understood to be far less than sacred. The basic theoretical building blocks of the SM are nothing more than the field spectrum and the gauge symmetries, while we have now strong evidence of nonzero neutrino masses that very likely cannot be fit into the pure Dirac mass picture. Why should one stick to R-parity conservation? If the accidental symmetries of baryon number and lepton number in the SM are to be preserved in the supersymmetric SM, they would have to be added in by hand, i.e. imposed as extra global symmetries on the Lagrangian. R parity, defined in terms of baryon number, lepton number, and spin as R = ( - l ) 3 B + L + 2does s exactly that. This is, however, at the expense of making particles and superparticles having a categorically different quantum number. R parity is actually not the most effective discrete symmetry to control superparticle mediated proton decay resulted from having both B and L violation4, but is most restrictive in terms of what is admitted in the Lagrangian, or the superpotential alone. Most importantly, it separates the four extra neutral fermion states (called neutralinos) from the SM neutrinos, and keeps the latter massless. Giving up the ad hoc notion of R parity, we naturally have massive neutrinos within the supersymmetric SM without the need to add any extra superfields to the minimal spectrum. In this way, one obtain massive neutrinos, from supersymmetry. More interestingly, the theory also gives a rich range of lepton number violating phenomenology from the same set of couplings that are responsible for the neutrino masses. 3. The generic supersymmetric Standard Model

The generic supersymmetric SM is a supersymmetrized SM with no extra symmetry, R parity or otherwise, imposed. The model Lagrangian is simply the most general one constructed using the necessary (minimal) superfield spectrum, the gauge symmetries and renormalizability requirement, as well as the idea that SUSY is softly broken. One does expect some mechanism or symmetry to take care of the proton decay problem, which may also be naively taken as having a large enough suppression among the B violating couplings, from the phenomenological point of view. The lepton number and flavor violating couplings are good for incorporating the beyond SM properties of the neutrinos. The most general renormalizable superpotential for the generic super-

94

symmetric SM can be written as

where (a,b) are S U ( 2 ) indices, (i,j,k) are the usual family (flavor) indices, and ( a , @are ) extended flavor index going from 0 to 3. In the limit where X i j k , A’ijk, A’:jk and pi all vanish, one recovers the expression for the R-parity preserving case, with L o identified as iid. Without R-parity imposed, the latter is not a pn’on’ distinguishable from the i i ’ s . Note that X is antisymmetric in the first two indices, as required by the S U ( 2 ) product rules, as shown explicitly here with sI2= -czl = 1. Similarly, A” is antisymmetric in the last two indices, from SU(3),. Doing phenomenological studies without specifying a choice of flavor bases is ambiguous. It is like doing SM quark physics with 18 complex Yukawa couplings, instead of the 10 real physical parameters. As far as the SM itself is concerned, the extra 26 real parameters are simply redundant. There is simply no way to learn about the 36 real parameters of Yukawa couplings for the quarks in some generic flavor bases, so far as the SM is concerned. For instance, one can choose to write the SM quark Yukawa couplings such that the down-quark Yukawa couplings are diagonal, while the up-quark Yukawa coupling matrix is a product of (the conjugate of) the CKM and the diagonal quark masses, and the leptonic Yukawa couplings diagonal. Doing that is imposing no constraint or assumption onto the model. On the contrary, not fixing the flavor bases makes the connection between the parameters of the model and the phenomenological observables ambiguous. In the case of the GSSM, the choice of flavor basis among the 4 La’s is a particularly subtle issue, because of the fact that they are superfields the scalar parts of which could bear VEVs. A parameterization called the single-VEV parameterization (SVP) has been advocated since Ref.5. The central idea is to pick a flavor basis such that only one among the La’s, designated as LO, bears a non-zero VEV. There is to say, the direction of the VEV, or the Higgs field H d , is singled out in the four dimensional vector space spanned by the La’s. Explicitly, under the SVP, flavor bases are chosen such that : 1/ (Ei) G 0, which implies 2 0 Eid; 2 / y j e k ( z X o j k = - X j O k ) = ~ uod i a g { m l , m , , m , } ; 3 /

=

Y;k(=

A’ojk)

where

‘uo

=

L ,” diag{md,%,mb}; 4/

a(&) and

‘u,

= &(flu).

KKM diag{mu,mc,mt}, = The parameterization is optimal,

yyk

95

apart from some minor redundancy in complex phases among the couplings. We simply assume all the admissible nonzero couplings within the SVP are generally complex. The big advantage of the SVP is that it gives the complete tree-level mass matrices of all the states (scalars and fermions) the simplest structure6. 4. Neutrino Masses in the GSSM The GSSM has seven neutral fermions corresponding to the three neutrinos and four, heavy, neutralinos. The heavy states are supposed to be mainly gauginos and higgsinos, but there is now admissible mixings among all seven neutral electroweak states. In the case of small pi’s of interest, it is convenient to use an approximate seesaw block diagonalization to extract the effective neutrino mass matrix. Note that the effective neutrino mass here is actually written in a basis which is approximately the mass eigenstate basis of the charged leptons, i. e., the basis is roughly (v,, v f i ,v,). The tree-level result is very well-known7. There have also been many papers devoted to the studies of radiatively generated neutrino masses from R-parity violation. Here, we focus only on discussions under, essentially, the current f o r m u l a t i ~ n12. ~~~~~~~ The neutral fermion mass matrix MN can be written in the form of block submatrices:

<

where Mn is the upper-left 4 x 4 neutralino mass matrix, is the 3 x 4 block, and mu is the lower-right 3 x 3 neutrino block in the 7 x 7 matrix. Starting with the generic formula

casted in the electroweak basis, the effective neutrino mass matrix at 1-loop level may be obtained as

where the II’s and C’s denote two-point functions t o be evaluated atl-loop order. There are many pieces of contributions involving various lepton number violating couplings. A neutrino mass term involves violation of lepton number by two units, and basically any combination of two lepton number

96

violating couplings in the model contributes. Moreover, t o the extent that we are quite ignorant about the related phenomena, it is dangerous to make any assumption about the relative strength of such contributions, which is done quite often. We have indeed argued previously that the maximal mixing observed among neutrino flavors is likely t o indicate a flavor structure here very different from what we see among the other SM fermions7. Hence, it is rather necessary to check all the possible contributions and have the general result ready. We have given exactly such a listing". To keep within the length limit, we have to satisfy with only illustrating some general feature of the detailed results. We are interesting in 1-loop two-point functions with fermions and scalars, both charged or both neutral, running in the loop. An exact evaluation requires using mass eigenstates for the running particles. We have given exact tree-level mass matrices for the five charged fermions, seven neutral fermions, eight charged scalars, and ten neutral scalars6. Perturbational formulae for the elements of the diagonalization matrices are available6. The latter are very useful for an analytical understanding of the lepton flavor violating origin/structure of each of the neutrino mass term. For instance, we have the charged loop contribution

where GEm and c,t;, -are the effective couplings of the ui and uj to the m-th charged scalar (1,) and R- and L-handed parts of the n-th charged fermion (x;), respectively. Taking the A-coupling term in Gfrn and the gauge coupling term in C,k,, in particular, would resulted in a contribution proportional to

We note here that the result is actually very sensitive to the i tt j symmetrization. The dominant result in the expression above is from the case with the ( j 2)th charged scalar running in the loop. This is approximately the i j slepton. The symmetrization and the fact that X i j h = - A j i h suggest a perfect cancellation of the result in the limit of degenerate sleptons which correspond roughly to the li and lj statesg>lO.

+

5 . Beyond Neutrino Masses

Our approach easily connect the neutrino mass results with a wide range of other phenomenologies. An interesting class of such we have been studying

97

is electromagnetic dipole moments of the various fermions. Published results are available for diagonal electric dipole moments of quark contributing to neutron electric dipole moment14 and an example of transitional moments for the charged lepton giving rise to the p + e y decay15. One common important feature among such dipole moment contributions is an interesting kind of contributions coming from a combination of a bilinear and a trilinear lepton number violating coupling - a p f A ~ , , for d-quark dipole moment and a &Xizl for p + e y . The constraints on the couplings we obtained from studies are actually close to comparable to neutrino mass constraints. Analyzes of similar type of constraints from b + s y and neutrino dipole moment and radiative decays have are in progress. We summarize results from our numerical study on the B R < 1 . 2 ~ experimental constraint on p + e y15 in the following table for your interest.

The numbers are based inputs as given by

iw, (GeV) 100

M2 (GeV)

po (GeV)

200

100

m; (lo4 GeV’)

fii: (lo4 GeV2)

A , (GeV)

diag{l,l, l}

100

diag{2,1,1, l}

tanP 10

6 . Concluding Remarks

Supersymmetry could be considered a source of neutrino masses and other beyond SM properties of neutrinos. Promoting the field multiplet spectrum of SM t o superfields gives naturally lepton number and flavor violating couplings admissible by the gauge interactions. In that sense, the result generic supersymmetric SM is the simplest supersymmetric model incorporating neutrino masses. Other alternatives require extra superfields

98

beyond the minimal spectrum, and usually also ad hoc global symmetries, in some case with specifically assumed symmetry breaking patterns. Another attractive feature of the generic supersymmetric SM is that the same set of couplings giving the neutrino masses also give rise to a width range of lepton number and flavor violating interactions. There is then correlation between the neutrino masses and other (collider) phenomenologies t o be explored. Our formulation, called single-VEV parameterization, has been demonstrated to give a very effective framework to simplify any analytical studies of the model, making the task within easy reach. The whole discussion here is based on a purely phenomenological perspective. We are suggesting studying all the experimental constraints we could obtained on the set of couplings without theoretical bias. The hope to that we could eventually find some pattern among them and learn about the problem of the flavor structure among them. The lesson we learned so far ,from neutrino masses and mixings, is that the usually hierarchical flavor structure established among the Yukawa couplings of the quarks and charged leptons simply does not apply here. However, the lepton number violating couplings revealed through neutrino properties and otherwise may one day help to shed a light on the general flavor problem. References 1. A very good example is given by the Zee model; A. Zee, Phys. Lett. 93B,

389 (1980). 2. D.V. Volkov and V.P. Akulov, Phys. Lett. 46B, 109 (1973). 3. G. Farrar and P. Fayet, Phys. Lett. 76B, 575 (1978). 4. L.E. Ibkiiez and G.G. Ross, Nucl. Phys. B368, 3 (1992). 5. M. Bisset, O.C.W. Kong, C. Macesanu, and L.H. Orr, Phys. Lett. B430, 274 (1998); Phys. Rev. D62, 035001 (2000). 6. O.C.W. Kong, IPAS-HEP-k008, hep-ph/0205205, to be published in Int. J.

Mod. Phys. A (2003). See, for example, O.C.W. Kong, Mod. Phys. Lett. A14, 903 (1999). K. Cheung and O.C.W. Kong, Phys. Rev. D61, 113012 (2000). O.C.W. Kong, JHEP 0009, 037 (2000). S.K. Kang and O.C.W. Kong, IPAS-HEP-kOO9, hep-ph/0206009. Y . Grossman and H.E. Haber, hep-ph/9906310. S. Davidson and M. Losada, JHEP 0005, 021 (2000); Phys. Rev. D65, 075025 (2002). 13. E.J. Chun and S.K. Kang, Phys. Rev. D61, 075012 (2000). 14. Y.-Y. Keum and O.C.W. Kong, Phys. Rev. Lett. 86, 393 (2001); Phys. Rev. D63, 113012 (2001). 15. K. Cheung and O.C.W. Kong, Phys. Rev. D64, 095007 (2001).

7. 8. 9. 10. 11. 12.

NEUTRINO PHYSICS AFTER KAMLAND

A. SMIRNOV International Centre for Theoretical Physics Strada Gostiera 11 , 34 Old Trieste, Italy E-mail: [email protected]

The neutrino anomalies were driving force of developments in the neutrino physics during last 30 - 35 years. I will consider a status of the anomalies after the first KamLAND result. The main questions to be addressed are What is left? and What is the next? In the new phase, the phenomenological objectives of neutrino physics consist of accomplishing the program of reconstruction of the neutrino mass and flavor spectrum and searches for physics beyond the “standard” picture. The latter includes searches for new (sterile) neutrino states, new neutrino interactions, effects of violation of the fundamental symmetries in the neutrino sector.

1. Introduction 1.1. Before and After “After KamLAND” means essentially after confirmation of the large mixing MSW (LMA) solution of the solar neutrino problem. In this sense the neutrino physics “after KamLAND” has started much before the announcement of the first KamLAND result Since 1999 most of the papers (on phenomenology and theoretical implications) have been written in the context of LMA solution. 1998 was the turn point: the SuperKamiokande results on atmospheric and solar neutrinos have destroyed the prejudice of small mixings which was the dominating idea during many years. Later in 1998, the solar neutrino data gave some hint that the large mixing MSW effect could be the correct solution of the solar neutrino problem With more data appeared, LMA became favored and then the most plausible solution. On the basis of LMA, detailed predictions for KamLAND have been done 5 . The KamLAND result is the culmination of about 40 years of the solar neutrino studies. This result is the confirmation of not only LMA (in assumption of CPT symmetry), but also the whole oscillation picture behind the neutrino anomalies including the oscillations of atmospheric neutrinos.

‘.

99

100

1.2. The end of era of the neutrino anomalies?

Neutrino anomalies, both real and fake, were driving force of developments in the field. The famous triplet is solar-atmospheric-LSND. The atmospheric neutrino anomaly and the solar neutrino problem turned out to be real (not related t o some experimental or systematic errors), confirmed and practically resolved. The LSND anomaly is badly resolved, not confirmed, but not yet excluded. The main questions now are “What is left?” and “What is the next?” 2. Is the solar neutrino problem solved? 2.1. Solar neutrinos and KamLAND

The first KamLAND result (see analysis in7>*and fig. 1 froms) 0 has confirmed (in assumption of CPT) the LMA MSW solution and excluded other suggested effects at least as the dominant mechanisms. 0 has further shifted the allowed region and the best fit point to larger values of Am2: Am2 = (5 + 7) . lop5 eV2, put the lower bound Am2 > (4- 5) . 10-5eV2 - for smaller Am2 strong distortion of the spectrum is predicted which contradicts the data. 2.2. LMA: precision measurements

Further diminishing of the allowed Am2 - tan2 8 region is needed for many reasons: for theoretical implications, further phenomenological and experimental developments, and also for precise understanding the physical picture of neutrino conversion. The forthcoming improvements are expected from further operation of SNO and KamLAND. In the fig. 1 we show the contours of constant ratio CC/NC and the Day-Night asymmetry in the plane of oscillation parameters. The expected accuracy of the measurements of CC/NC is about lo%, so that the two regions (h- higher and 1 - lower) can be distinguished. In the range Am2 < lop4 eV2 the SNO will give more precise determination of the mixing angle and more stringent bound on the deviation from maximal mixing. Later KamLAND will achieve 10% accuracy in Am’. 2.3. Consistency checks

Till now no a single signature of the LMA solution (day-night asymmetry, upturn of the spectrum) has been observed a t a statistically significant level. The following expectations correspond t o the present best fit region 8:

101 10"

1o - ~

tg'e

Figure 1.

The allowed 1u and 3u regions (shadowed) of oscillation parameters from the combined analysis of the solar neutrino data and K a m L A N D . Shown are also contours of the constant Day-Night asymmetry (dotted lines) and the CC/NC ratio (dashed lines).

the Day-Night asymmetry at SNO and SK: A D N ( S N O ) = (2 ) (1- 3)%, 5)%, A D N ( S K = 0 spectrum distortion: the 5 - 10 % upturn is expected at low energies between 8 and 5 MeV, 0 suppression of the signal at the intermediate energies (BOREXINO and KamLAND): RE = (0.6 - 0.65)R5ss", 0 small seasonal variations: the expected winter-summer asymmetry of the signal a t SNO and SK, Aws < 0.5%, is practically unobservable, for the p p neutrino flux one expects the suppression: R,, = 0.6 which can be tested in future low energy solar neutrino experiments. Tests of these predictions have the threefold implication: (i) further confirmation of LMA: one needs to over determine the solution to perform its cross-checks; (ii) precise determination of the neutrino parameters; (iii) searches for physics "Beyond the LMA" . 0

2.4. Homestake anomaly?

Quality of description of the available data by the LMA solution is very good. This is also confirmed by the pull-of diagram. A visible deviation appears in one place only: LMA predicts about 20 higher Ar-production

-

102

rate as compared with the Homestake result. Possible interpretation? (i) just a statistical fluctuation; (ii) systematics, probably related to the claimed time variations of the Homestake signal, (iii) neutrino physics beyond LMA. The latter can be related t o another observation: the absence of apparent upturn of the spectrum (ratio of the observed spectrum to the SSM prediction) at low energies. Neither SK nor SNO see any upturn, though the sensitivity may not be enough. Both the lower Ar-production rate and the absence (suppression) of the upturn can be due to effect of an additional (sterile) neutrino which mixes very weakly with active neutrinos (us - u l ) and has small mass split with the lightest state: sin2 219,~=

-

Am& = (0.5 - 1) . 10-5eV2.

(1)

Such a neutrino produces an additional dip in the suppression pit in the range 0.8 - 5 MeV, thus suppressing the Be-neutrino line orland diminishing the upturn of the spectrum. BOREXINO and KamLAND can check this.

2 . 5 . Solar neutrinos versus KamLAND From independent 2u analysis of the solar neutrino data and the KamLAND results one finds that values of parameters in the best fit points

(Am2,tan2 8 ) s o l a r x (Am2,tan2 B ) K L

(2)

within la. This indicates that C P T is conserved in the leptonic sector. It is interesting to further check the equality with increasing accuracy. Mismatch of parameters can testify for the C P T violation or for certain physics beyond LMA. If some effect influences the KamLAND signal it should also show up in the solar neutrinos. Inverse is not correct: a number of effects can influence the solar neutrinos but not KamLAND. Some examples: an additional neutrino state with small Am2 orland tan2 8, the neutrino spin-flip in the Sun, non-standard interactions of neutrinos. There is another interesting aspect of the comparison of oscillation parameters extracted from the solar neutrinos and KamLAND: the test of theory of the conversion and oscillations. Indeed, physics behind the solar neutrino conversion and the oscillations of reactor neutrinos is different. In the case of solar neutrinos we deal with the adiabatic conversion; the matter effect dominates (at least in the high energy part of the spectrum), the oscillation phase is irrelevant. The effect is described by the adiabatic conversion formula. In contrast, in the case of KamLAND, the vacuum

103

oscillations occur; the matter effect is very small; the oscillation phase is crucial and here we use the vacuum oscillation formula. The coincidence of parameters (2) testifies for correctness of the theory (phase of oscillation, matter potential, etc..).

2.6. B e y o n d L M A or Physics of sub-leading eflects The physics of sub-leading effects becomes one of the main subjects of studies. The name of the game is “ LMA something”, where LMA provides the leading effect, and “something” can be Ue3, SFP (spin-flavor precession), new neutrino states, NSI (non-standard interactions) VEP (violation of the equivalence principle), etc.. In what follows we comment on the “LMA + SFP” scenario. If no new neutrino states exist, the only relevant mass difference is For such a large Am2 the spin-flip occurs in the central regions of the sun (radiative zone) where the potential V ArniMA/2E. Signatures of the effect are time variations of signals and appearance of the antineutrino flux. For the Boron neutrinos the ratio of V,- flux to the original ve- flux equals l o

+

-

where p,, is the magnetic moment of neutrino, ,LLBis the Bohr magneton. For B = 7 MG, at the level of present upper bounds ‘I and p,, = 1 0 W 1 2 p ~ we get FBIFB = 7 . loW3%,which is, 2 orders of magnitude below the present limit 1 2 . The spin-flip effect can be much larger, if new neutrino states exist with Am2 <<

3. Atmospheric neutrinos: Any problem? There is a compelling evidence that the up - v, vacuum oscillations are the dominant mechanism of the atmospheric neutrino transformations 1 3 , 1 4 , 1 5 , 1 6 . Nothing statistically significant beyond this interpretation has been found so far. What is the next? As in the case of solar neutrinos: the next is physics of the sub-leading effects and also geo- and cosmo- physics. Among objectives are searches for (i) the u,- and V , oscillations, (ii) effects of s13, (iii) sterile neutrinos, (iv) CP-violation, (v) CPT-violation, (vi) specific oscillation effects related to the earth density profile (parametric enhancement of oscillations for core - mantle crossing trajectories), etc..

104

3.1. Oscillations of Atmospheric u, After KamLAND we can say that even for 5 1 3 = 0 ue-, Ve- oscillation effects must appear at some level due t o the solar/KamLAND oscillation parameters. The signature of these oscillations is an excess (or deficit) of the e-like events in certain energy range with specific energy and zenith angle dependences. The e-like event excess (deficit) can be due to (i). oscillations driven by the solar Am?,, $12, (mainly in the sub-GeV region), (ii). oscillations driven by nonzero $13 and atmospheric Am?, (mainly in the multi-GeV region), (iii). interference of the above effects.

3 . 2 . Oscillations due t o Am:,, 812

The relative change of the ve- flux due to the oscillations equals

FP F,o

- - 1 = P,(Tcos2$23 - l),

l8

(4)

where Pz = P(Am:,, $12) is the 2u transition probability up + u ~ , in . the F,o/F:. The effect is strongly suppressed by matter of the Earth, and r the “screening factor” (in the brackets of (4)) in spite of large transition probability. Indeed, in the sub-GeV region T = 2 and the oscillation effect is zero for the maximal 2-3 mixing. This feature can be used to search for deviations of 2-3 mixing from maximal: The excess (deficit) of the events is directly proportional t o this deviation. In the Table we show the excess 6 3 N , /N: - 1 in the sub-GeV region for different values of sin2 2623 and for the best fit points of the LMA-1 and LMA-h regions. The excess increases

sin2 2023 0.91 0.96 0.99

€1,

%

2.8 1.9 0.9

Eh,

%

4.8 3.2 1.6

with Am:,, but does not exceed 5%. Once the LMA parameters are well known, measurements of 6 will allow to restrict a deviation of the 2-3 mixing from the maximal one. To realize this one needs high statistics experiment and a possibility t o identify the excess due to oscillations.

105

3.3.

Effect of513

The oscillations driven by non-zero 513 and the atmospheric Am:, produce significant modification of the u,- flux in the multi-GeV region, where the oscillations are enhanced by the matter effects (MSW resonances in the mantle and core, the parametric enhancement of oscillations) 19. In contrast t o the sub-GeV sample at higher energies T significantly deviates from 2 and the screening 0: (T sin2 823 -1) is weaker. The oscillation effect can be identified by the up-down asymmetry: AU,D = 2 ( U - D ) / ( U + D ) , where U and D are numbers of e-like events in the intervals of zenith angles c o s 0 = (-1 t -0.6) and c o s 0 = (0.6 t 1) correspondingly. For sin2 2823 = 1 and Am:, = (2 - 3) . lop3 eV2 the asymmetry in the multiGeV region can reach (5 - 8) % for the maximally allowed 1-3 mixing.

3.4. Induced interference If 513 # 0 one should take into account the interference of effects produced by the solar oscillation parameters and 513. In the sub-GeV range, the non-zero ~ 1 induces 3 the interference of the survival, A,,, and transition, AeP,amplitudes of the 2u system with Am:, and 012. The relative change of the u, flux can be written as 2o

s : , [ 2 ( 1 - ~ s i n ~ e ~+ ~~ )2 ( r - 2 ) ] ,

(5)

=

where P 2 \Aep12.The interference effect given by the second term in the RH side has the following properties: (i) it is linear in ~ 1 3 (ii) , has no screening factor, (iii) has opposite sign for neutrinos and antineutrinos, (iv) maximal for Am:, = 7 . lop5 eV2. In fig. 2 from 2o we show the zenith angle distributions of the e-like events for different values of mixing. The interference term gives the dominant contribution to the excess of e-like events if 2-3 mixing is close to the maximal one. In maximum we find: eint 0 . 1 6 ~ ~ ~ . N

3.5. Sterile neutrinos The up - us oscillations are excluded as the dominant solution of the atmospheric neutrino problem. The data give also strong bound on partial transition to the sterile component, up + cos B,u, +sin 8,u,,: sin2 8, < 0.2 - 0.3 in the context of single Am2.

106

0

i

2

1.4 SK-SUB (p.< 0.4GeV)

I

1.3

I

1.2

1.1

..................

1

.I.

....................................

.......................... ...................................... .......................................................................................................................

0.9 0.8

-

.......

sin2(28,,)=

- sinz(20,,)= 0.7

-

0.6

-

sin2(20,,)= ...... sin2(20,,)=

............

0.9 U.,=0.3

0.9U.,=o 1 u,,=o 1 U.,=0.3

Figure 2. The zenith angle distributions of the e - like events (ratio of number of events with, N e , and without, NZ,oscillations) in the sub-GeV range (p < 0.4 G e V ) for Am12 = 5.1OP5 e p and different values of sin2 2823 and IUe31 8 1 3 . Dotted line - no s13 effect, and completely screened effect of 1-2 mixing; solid line - effect of 1-2 mixing only ( ~ 1 3= 0); dashed line - the effects of interference for maximal 2-3 mixing (direct 1-2 contribution is screened); the dash-dotted line - the effect of interference and 1 - 2 mixing. For presently favored value of Am:, all the effects which involve 1-2 mixing should be enhanced by factor 1.5. Also shown are the SuperKamiokande experimental points.

-

Existence of sterile neutrinos can lead to new manifestations in the context of more than one Am’. The fourth neutrino with Am2 (0.5 - 1) eV’ (motivated by LSND) has the MSW resonances in matter of the Earth in the energy range (0.5 - 1.5) TeV 2 1 . For the (3+1) scheme with normal mass hierarchy the resonances, and consequently, the resonance enhancement of oscillations, are in Y, - v, and Vp,T - V , channels. This leads to (i) modification of the the zenith angle distribution of the upward-going muons (disappearance due to transition into sterile state), (ii) appearance of fluxes of the electron neutrinos (strongly suppressed in the original flux at high energies) and tau neutrinos. These fluxes produce via the CC interactions an additional contribution to the cascade events. For neutrinos crossing the core of the Earth the parametric enhancement of oscillations takes place. These results can be studied by the Ice-Cube detector 2 1 .

107

4. LSND: ultimate neutrino anomaly? Three different possibilities to reconcile the LSND signal with the solar and atmospheric neutrino results are under discussion: (i). Additional sterile neutrinos in the context of (3+1) or (3+2) schemes; (ii). Non-standard neutrino interactions; (iii). CPT violation. KamLAND and some other recent results have changed status of these possibilities. 4.1. ( 3

+ 1) scheme +

The main problem of the (3 1) scheme is that the predicted LSND signal, which is consistent with the results of other short base-line experiments (BUGEY, CHOOZ, CDHS, CCFR, KARMEN) as well as the atmospheric neutrino data, is too small: the probability is about 30 below the LSND measurement. Introduction of the second sterile neutrino with Am2 > 8 eV2 may help 2 3 . It was shown 24 that the second neutrino with Am2 22 eV2 and specific mixing parameters can enhance the predicted LSND signal by (60 - 70) % in comparison with (3 1) scheme. N

+

4.2. Non-standard neutrino interactions

The LSND signal could be due to the anomalous decay of muon

+ u,Vie+,

25:

(6) Violation of the lepton number by two units lALl = 2 allows to avoid stringent bound from non-observation of the p -+ eee mode. The decay (6) can be induced by the exchange of new neutral scalar boson (A4 300 - 500 GeV). As a result, the Lorentz structure of the decay differs from the standard one: the Michel parameter p = 0 is predicted. The problem of this interpretation is to reconcile “LSND with KARMEN”. Now one cannot play with difference of baselines and the situation is equivalent to the averaged oscillation case (large Am2)where KARMEN gives stronger bound essentially excluding the LSND result. The p = 0 feature of new interaction does not help 2 6 . New experiment TWIST at TRIUMPF 27 will measure Michel parameter with higher accuracy which will allow us to check deviations from the standard value p = 314. p+

(i = e,p,T).

N

4.3. CPT-violation After KamLAND the ultimate possibility is the spectrum with Am%un and Am:,, splittings in the neutrino channel and Am;,, and Am:, split-

108

tings in the antineutrino channel 28,29. The main problem of the model is description of the atmospheric neutrino data. In the antineutrino channel, the oscillations driven by Am&ND are averaged and the effect due t o Am&, is relatively weak. Furthermore, according to ”, the best fit corresponds to non-maximal Dp - D, mixing. In this case the screening factor (4) is not small and one expects significant oscillation effect of fie driven by the KamLAND oscillation parameters. A rough estimation gives (5 - lo)% excess of the e-like sub-GeV events.

5 . Supernova Neutrinos

KamLAND has important impact both on the interpretation of the signal from SN1987A and on the program of future SN neutrino detection. “After KamLAND” we can definitely say that the effects of antineutrino flavor conversion have been observed already in 1987: namely, effects of 0 Ye conversion inside the star, (probably) oscillations in the matter of the Earth, furthermore these oscillations effects were different for Kamioka, IMB and Baksan detectors. In the case of the normal mass hierarchy the adiabatic f i e 4 01 and Vp,T + VZ transitions occurred inside the star and then u1 and v2 oscillated inside the Earth 30. With future SN burst detections one can (i) get information about ~ 1 3 (ii) establish the mass hierarchy, (iii) test existence of sterile neutrinos.

5.1. LBL with supernova neutrinos Study of the Earth matter effects on the SN neutrinos is one possibility to get “star model-independent” information on neutrino parameters. In a sense one can perform the long baseline experiment with SN neutrinos. Comparison of signals from the two detectors allows one to establish effect of oscillations inside the Earth. Some examples of results: If sin2 $13 > the appearance of the Earth matter effect in fie (ve)channel will testify for the normal (inverted) mass hierarchy. Independently of sin2 013 value the very fact of absence of the Earth matter effect in the Y, ( f i e ) will exclude inverted (normal) mass hierarchy 31. Actually, an existence of the Earth matter effect can be established with one detector: a t high energies one predicts an oscillatory distortion of the energy spectrum with amplitude which increases with energy 32,31.

,

109

5.2. Shock wave effect

It was argued recently that the shock wave may reach the region of the neutrino conversion, p lo4 g/cc, after t, = (3 - 5) s from the bounce (beginning of the burst) 3 3 . Changing the density profile and therefore the adiabaticity condition, the shock front influences the conversion in the hresonance characterized by the atmospheric Am:, and sin2 0 1 3 , provided that sin2013 > lop6. The following shock wave effects should be seen at some level in the neutrino (antineutrino) for normal (inverted) hierarchy: 1) Change of the total number of events in time 3 3 ; 2) Wave of softening of the spectrum which propagates in the energy scale from low energies to high energies 34; 3) Delayed Earth matter effect in the “wrong” channel (e.g., in neutrino channel for normal mass hierarchy) 3 5 . Modification of the density profile by the shock wave leads to appearance of additional resonances below the front. Effects of these resonance have been considered recently in 3 6 . Monitoring the shock wave with neutrinos is challenging but really exiting problem which certainly deserves further consideration. Studying the shock wave effects on the properties of neutrino signals one can (in principle) get information on (i) time of shock wave propagation, (ii) shock wave revival time, (iii) velocity of propagation, (iv) density gradient in the front, (v) size of the front. This can shed a light on the mechanism of explosion.

-

6. Standard and Non-standard

What is standard in the neutrino physics now: three neutrinos masses below 0.5 - 1 eV bi-large or large-maximal mixing non-zero 1-3 mixing, probably close to the present upper bound smallness of neutrino mass related to the neutrality of neutrinos and their Majorana nature. What is beyond the standard picture? (i) new neutrino states (sterile neutrinos), (ii) new neutrino interactions; (iii) large anomalous magnetic moments, etc.. What is exotic? Effects of violation of the Lorentz invariance, C P T violation, equivalence principle, etc.. With the KamLAND result and resolution of the solar neutrino problem we made next (after establishing oscillations in atmospheric neutrinos) major step in reconstruction of neutrino mass and mixing spectrum: - the mass squared split of v1 and v2 states, Am?,, is determined

‘

110

“2

v3

NORMAL

Figure 3. chies.

INVERTED

Neutrino mass and flavor spectra for the normal and inverted mass hieTUT-

- distribution of the electron flavor in u1 and uz states is measured (the best fit corresponds to IVe1l2 x 2 1 U , ~ 1 ~ ) , - distribution of the muon and tau flavors in u1 and uz can be found with precision O(s13) from the unitarity condition. The figure 3 shows what is known now and what should be determined to accomplish the picture:

ue3

0

type of mass hierarchy (in the case of hierarchical spectrum) or ordering of the states: (normal, inverted) type of spectrum: hierarchical, non hierarchical, partially degenerate, completely degenerate, which is equivalent to determination of the absolute mass scale ml.

What we cannot see in the plot is the CP-violating phases: Dirac phase

6, and if neutrinos are Majorana particles, two Majorana phases. One needs also to establish Nature of neutrinos: measure of their Majorana character. In this connection, the ppov decay experiments are of the highest priority: the results will contribute (together with other measurements) to determination of all unknown elements listed above.

7. Conclusions The main developments in neutrino physics during last 30-35 years where related to various neutrino anomalies both real and fake. What is left? LSND? What are perspectives? One can imagine several scenarios:

111

“Standard scenario”: there is a well defined program of reconstruction of the neutrino mass and flavor spectrum. It is characterized in terms of further tests, precision measurements, searches for new physics. Confirmation of LSND will open new perspectives related to existence of new light neutral fermions, or CPT violation, or new interactions. New anomalies may appear which will lead to something unexpected (some hints from NuTeV, 2’-width measurements?). “Without anomalies”: we will work on well defined program which consists of 1). Determination of masses, mixings, CP-phases; precision measurements of parameters. Here, we face “technological problems” : determinations of the absolute mass scale and CP-phases are indeed big challenge. 2). Searches for new physics beyond standard picture, restrictions on exotics. The main issues are new neutrino interactions, new neutrino states, effects of violation of CPT, Lorentz invariance, equivalence principle, Pauli principle. 3). Identification of origins of the neutrino mass and mixing: that can include reconstruction of neutrino mass matrix, tests of the see-saw mechanism and other possibilities (flavor violation processes, leptogenesis, high energy experiments). 4). Applications of our knowledge of neutrino mass and mixing to Geophysics, Astrophysics, Cosmology. Notice that future high energy experiments (LHC, TESLA ...) may have serious impact on this program. Acknowledgments

I am grateful to H. Minakata and Y. Suzuki for invitation to give this talk and for hospitality during my stay in Kanazawa. References 1. K. Eguchi et al. (KamLAND), Phys. Rev. Lett, 90 021802 (2003). 2. Y . Fukuda, et al. Phys. Rev. Lett.. 81,1562 (1988). 3. Y. Fukuda. et al. (Super-Kamiokande) Phys. Rev. Lett. 8 2 , 1810 (1999), Phys. Rev. Lett. 82, 2430 (1999). 4. J. N. Bahcall, P. I. Krastev, A. Yu. Smirnov, Phys. Rev. D 60 093001 (1999); M.C. Gonzalez-Garcia, P.C. de Holanda, Carlos Pena-Garay, J.W.F. Valle, Nucl. Phys. B 573,3 (2000). 5. J. N. Bahcall, M. C. Gonzalez-Garcia, and C. Pena-Garay, JHEP 079 (2002) 0054; P. Holanda, A.Yu. Smirnov, Phys. Rev. D 66 113005 (2002).

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6. A. Aguilar et al. (LSND Collaboration) Phys. Rev. D 64 112007 (2001). 7. V. Barger, D. Marfatia, Phys. Lett. B 555, 144 (2003), G.L. Fogli, E. Lisi, A. Marrone, D. Montanino, A. Palazzo, A.M. Rotunno, Phys. Rev. D 67 073002 (2003); M. Maltoni, T. Schwetz, J.W.F. Valle, Phys. Rev. D 67, 093003 (2003); A. Bandyopadhyay, S. Choubey, R. Gandhi, S. Goswami, D.P. Roy, Phys. Lett.B 559 121, (2003); J. N. Bahcall, M.C. Gonzalez-Garcia, Carlos Pena-Garay, JHEP 0302:009, (2003); H. Nunokawa, W.J.C. Teves, R. Zukanovich Funchal, Phys. Lett.B562:28, (2003); P. Aliani, V. Antonelli, M. Picariello, E. Torrente-Lujan, hep-ph/0212212. 8. P. de Holanda, A.Yu. Smirnov, JCAP 0302:001, (2003). 9. G. L. Fogli, et al., Phys. Rev. D 67,073001 (2003). 10. E. Kh. Akhmedov and J. Pulido, hep-ph/0209192 11. A. Friedland, A. Gruzinov, astro-ph/0211377. 12. Y. Gando, et al. (Super-Kamiokande), Phys.Rev.Lett. 90,171302, (2003). 13. S. Fukuda, et al. (Super-Kamiokande), Phys. Rev. Lett. 85,3999 (2000). 14. M. Ambrosio et al. (MACRO), Phys. Lett. B 517,59 (2001). 15. W. W. Allison et al. (SOUDAN-2), Phys. Lett. B 449, 137 (1999). 16. M. H. Ahn et al. (K2K Collaboration), Phys. Rev. Lett. 90 041801 (2003). 17. John M. LoSecco, hep-ph/0305022. 18. 0. L. G. Peres, A.Yu. Smirnov, Phys. Lett. B 456 204, (1999). 19. E. K. Akhmedov, et al., Nucl. Phys. B 542,3 (1999). 20. 0. Peres, A. Yu. Smirnov, hep-ph/0201069. 21. H. Nunokawa, O.L.G. Peres, R. Zukanovich Funchal, Phys. Lett. B 562,279 (2003) hep-ph/0302039. 22. B. Armbruster et al. (KARMEN), Phys. Rev. D 65,112001 (2002). 23. 0. L. G. Peres, A.Yu. Smirnov, Nucl. Phys. B599, 3 (2001). 24. M. Sorel, J. Conrad, M. Shaevitz, hep-ph/0305255. 25. K. S. Babu and S. Pakwasa, hep-ph/0204226. 26. B. Armbruster, et al. (KARMEN), Phys. Rev. Lett. 90 181804, (2003). 27. N. R. Rodning et al, (TWIST Collaboration) TRIUMF, Talk given at TAU2000, TRIUMF, Canada (2002). 28. A. Strumia, Phys. Lett. B 539,91 (2002). 29. G. Barenboim, L. Borissov, J. Lykken, hep-ph/0212116. 30. C. Lunardini, A.Yu. Smirnov, Phys. Rev. D 63 073009, (2001); M. Kachelriess, A. Strumia, R. Tomas, J.W.F. Valle, Phys. Rev. D 65 073016 (2002). 31. C. Lunardini, A.Yu. Smirnov, Nucl. Phys. B616 307, (2001); K.Takahashi, K. Sato, Phys. Rev. D66, 033006 (2002); A. S. Dighe, M. T. Keil, G. G. RafTelt, hep-ph/0304150. 32. A. S. Dighe, A. Yu. Smirnov, Phys. Rev. D 62 033007 (2000). 33. R.C. Schirato G. M. Fuller, astro-ph/0205390. 34. K. Takahashi et al., astro-ph/0212195. 35. C. Lunardini, A.Yu. Smirnov, hep-ph/0302033. 36. G.L. Fogli, E. Lisi, D.Montanino, A. Mirizzi, hep-ph/0304056.

Session 2

Accelerated Neutrinos and Future Neutrino Oscillation Experiments

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RESULTS IN K2K AND FUTURE

TAKASHI KOBAYASHI FOR K2K COLLABORATION Institute for Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK) 1-1 Oho, Tsukuba, 305-0801, Japan E-mail: [email protected] The K2K experiments had accumulated 4.8 x lo1’ protons on target, about half of the proposed amount, by July 2001. After the reconstruction of the SuperKamiokande has finished, the K2K experiment resumed in December 2002. These proceedings describe the latest results based on the data by July 2001, report the current status and future prospects.

1. Introduction

The KEK t o Kamioka (K2K) experiment is the first accelerator-based long baseline neutrino experiment’ t o probe the same Am2 region as that explored with atmospheric neutrino^^,^. The up beam is produced at KEK and detected by the Super-Kamiokande (SK) at a distance of 250 km. Primary purpose is a search for the up disappearance. Number of events and energy spectrum are measured at SK and compared with expectation with or without oscillation to test the oscillation scenario. The experiment started in June 1999 and has been accumulating data for typically about 6 month in a year until July 2001. After the SK accident in Nov. 2001, the reconstruction work was done in 2002. In Dec. 2002, the work finished and the K2K experiment resumed with about half density of PMT’s. In this paper, latest results based on the data collected before SK accident are presented4. Also current status and future prospect are briefly mentioned.

2. Experiment The 12 GeV proton beam from the KEK proton synchrotron hits an aluminum target and the produced positively charged particles, mainly pions, are focused by a pair of pulsed electromagnetic horns The neutrinos

115

116

produced from the decays of these particles are 98% pure muon neutrinos with a mean energy of 1.3 GeV. The direction of the beam is monitored on a spill-by-spill basis by observing the profile of the muons from the pion decays with a set of ionization chambers and silicon pad detectors located just after the beam dump. Properties of the neutrino beam just after the production are measured by a set of near neutrino detectors (ND) located 300 m from the proton target. The ND consists of two detector systems: a 1 kiloton water Cherenkov detector (1KT) and a fine-grained detector (FGD) system. The FGD is comprised of a scintillating fiber and water detector (SciFi) 6, a lead-glass calorimeter (LG), and a muon range detector (MRD) The measurements made a t the ND are used to verify the stability and the direction of the beam, and to determine the flux normalization and the energy spectrum before the neutrinos travel the 250 km t o SK. The flux at SK is estimated from the flux of the ND by multiplying the Far/Near (FIN) ratio, the ratio of fluxes between the far detector(SK) to that of the ND. The ratio is estimated by the beam Monte Carlo (MC) simulation which is validated by measurements of a pion monitor (PIMON) placed just downstream of the second horn’. The neutrino energy is reconstructed from muon momentum and angle with respect to the neutrino direction, assuming quasi-elastic (QE) interactions, and neglecting Fermi moment um:

where m ~E,,, m,, P, and 8, are the nucleon mass, muon energy, the muon mass, the muon momentum and the scattering angle relative to the neutrino beam direction, respectively. The analysis is based on data taken from June 1999 to July 2001, corresponding to 4.8 x 10’’ protons on target (POT). 3. Neutrino Flux and Spectrum at the near site

The flux normalization is measured by the 1KT to estimate the expected number of events at SK. Since the 1KT has the same detector technology as SK, most of systematic uncertainties on the measurement are canceled. Event selection criteria for the flux normalization are the same as those in reference’. The measurement has a 5% systematic uncertainty, of which the largest contribution comes from the vertex reconstruction’. The energy spectrum is measured by analyzing the muon momentum and angular distributions in both detector systems. In l K T , event sam-

117

ple of single-ring p-like (1Rp) events which stop in the detector is used for the spectrum measurement. In the FGD, events containing one or two tracks with vertex within the 5.9 ton fiducial volume of the SciFi are used. The SciFi events are divided into three categories: 1-track, 2-track QE enhanced, and 2-track non-QE enhanced samples. The 2-track QE (non-QE) enhanced sample is selected by requiring the angle between the direction of the observed second track and a calculated direction of a proton assuming QE interaction to be 5 25 (> 30) degrees. The 2-dimensional distributions of the muon momentum versus angle with respect to the beam direction of four event categories (the 1KT event sample and the three SciFi event samples) are used to constrain the neutrino spectrum. The MC expected distributions are fitted to the observed ones by adjusting the weighting factor on each energy bin in the neutrino spectrum and on non-QE/QE ratio (Rnw1. Table 1. The central values of the flux weighting factors for the spectrum fit at ND ( @ N D ) and the percentage size of the energy dependent systematic errors on @ N D , F / N ratio, and E S K .

1.02 1.01 = 1.00 0.95 0.96 1.18 1.07

0.5-0.75 0.75-1.0 1.0-1.5 1.5-2.0 2.0-2.5 2.5-3.0 3.0-

12 9.1 ~

7.1 8.4 19 20

4.3 4.3 6.5 10 11 12 12

4.3 4.3 8.9 10 9.8 9.9 9.9

The x2 at the best fit point is 227.2 with the degree of freedom 197. The best fit values of the flux weighting factors are shown in Table 1 and the best fit spectrum is plotted in Figure 1 together with the beam MC prediction. The muon momentum and angular distributions of 1Rp events in the l K T , and the muon momentum distributions of the 2-track QE enhanced and non-QE enhanced events in SciFi are overlaid with the re-weighted MC in Figure 2. The fit result agrees well with the data. The F/N ratio from the beam simulation is used to extrapolate the measurements at the ND to those at SK. The errors including correlations above' 1 GeV, where the PIMON is sensitive, are estimated based on the PIMON measurements. The errors on the ratio for E, below 1 GeV are estimated based on the uncertainties in the hadron production models used in the K2K beam MC The diagonal elements in the error matrix for the

'.

118 Neutrino Spectrum at KEK

%

!

8rr!

-

FD Measurements

0Beam MC

1-

ntegrated

4 0.5

00-

-

A+

"1 I

I

1

1

2

3

Figure 1. Neutrino spectra measured by ND (points with error bars) and predicted by beam MC (solid histogram). They are normalized by area and the vertical axis is arbitrary.

F / N ratio are summarized in Table 1. 4. Observation at SK and Oscillation Analysis

The criteria to select neutrino beam events at SK are the same as those in the previous paper': the event time within the time window of expected beam arrival, no activity in outer detector, energy deposit greater than 30 MeV, a reconstructed vertex within the 22.5 kiloton fiducial volume. This sample of events is referred to as the fully contained (FC) sample. The efficiency of this selection is 93% for CC interactions. Fifty-six events satisfy the criteria. The expected number of FC events at SK without oscillation is estimated to be 80.1Tg::. The major contributions to the errors come from the uncertainties in the F/N ratio ( and the normalization (5.0%), dominated by uncertainties of the fiducial volumes due to vertex reconstruction both at the 1KT and SK. An oscillation scenario with vF disappearance is tested by the maximumlikelihood method assuming two flavor oscillation. In the analysis, both the

z;::;)

119

e

-

g3000 -

.

i Data

0 7

mMC(QE)

,2000

L

flooo06

1

a300 5100

00

1

2

3 P, [GeV/c]

Figure 2. (a) The muon momentum distribution of the 1KT 1 R p sample, (b) the angular distribution of the 1KT 1 R p sample, (c) the muon momentum distribution of the SciFi QE enhanced sample, and (d) that of the SciFi non-QE enhanced sample. The crosses are data and the boxes are MC simulation with the best fit parameters. The hatched histogram shows the QE events estimated by MC simulation.

number of FC events and the energy spectrum shape for 1 R p events are used. The likelihood is defined as Ctotal = L,,,, x Lshapex Lsyst. The normalization term ~ n o r m ( N o bNezp) s , is the Poisson probability to observe Nabs events when the expected number of events is Ne,(Am2, sin2 28, f ) . The shape term, Cshape= P(Ei;Am2,sin2 20, f ) ,is the product of the probability for each 1 R p event to be observed at Et;ec = Ei, where P is the normalized EF distribution estimated by MC simulation and N ~ is the number of 1 R p events. The term Lsyst is a constraint term for a set of parameters f with systematic errors. In the oscillation analysis, the whole data since June 1999 is used for L,,,,, i.e. Nohs = 56. The data taken in June 1999 are discarded for Cshape. The spectrum shape in June 1999 was different from that for the rest of the running period because the target radius and horn current were different. The estimation of errors on the spectrum has not been completed for this period. The discarded data correspond to 6.5% of total P O T and the number of 1 R p events observed excluding the data of June 1999 is 29. The parameters f consist of the weighting factor on neutrino spectrum measured at the ND (QND),the F / N ratio, the reconstruction efficiency ( E S K ) of SK for 1 R p events, Rnqe,the SK energy scale and the overall

nz?

120

normalization. The errors on the first 3 items depend on the energy and have correlations between each energy bin. The diagonal parts of their error matrices are summarized in Table 1 as described earlier. The error on the SK energy scale is 3% '.

v) $2

a, > W

I0

8 6

4

2

0 L '

!

Figure 3. The reconstructed E, distribution for 1 R p sample (from method 1). Points with error bars are data. Box histogram is expected spectrum without oscillations, where the height of the box is the systematic error. The solid line is the best fit spectrum. These histograms are normalized by the number of events observed (29). In addition, the dashed line shows the expectation with no oscillations normalized to the expected number of events (44).

The best fit point in the physical region of oscillation parameter space is found to be at (sin228, Am2)=(1.0,2 . 8 ~ 1 eV2). 0 ~ ~ At the best fit point the total number of predicted events is 54.2, which agrees with the observation of 56 within statistical error. The observed EY" distribution of the 1 R p sample is shown in Figure 3 together with the expected distributions for the best fit oscillation parameters, and the expectation without oscillations. The no-oscillation probabilities are calculated to be 0.7% from the likelihood ratio between the best fit point to no-oscillation case. Allowed regions of oscillation parameters are drawn in Figure 4. The 90% C.L. contour crosses the sin228 = 1 axis at 1.5 and 3.9 x lop3 eV2 for Am2. Also drawn in

121

the figure is the log likelihoods as a function of Am2 at maximum mixing sin2 28 = 1 for normalization and shape terms separately. Both suppression of number of events and distortion of the spectrum indicate the same Am2 region.

-

4

-

'O 0

0.2

0.4

0.6

0.8 1 sin%

Figure 4. (Left) Allowed regions of oscillation parameters. Dashed, solid and dotdashed lines are 68.4%, 90% and 99% C.L. contours, respectively. The best fit point is indicated by the star. (Right) Log likelihood functions as a function of Am2 at sin' 28 = 1. Solid, dashed and dotted lines are - InLCtotal, - InLShapeand - InLnoTm, respectively.

5 . Status and future

In Dec. 2002, the K2K experiment resumed after the long shutdown during the SK reconstruction. By the end of May 2003, about 2.1 x lo1' POT have been DELIVERED after the restarting. In order to maximize the sensitivity on neutrino oscillation, precise knowledge on the neutrino interactions at low energy of 5 1 GeV is necessary. For that purpose, full-active scintillator tracker, called SciBar detector, are being installed as a replacement of the LG detector. Detailed description of the SciBar is found elsewhere". The fiducial mass will be about 11 tons. The LG detector has been already removed and 4 layer modules out of 64 have been installed in Jan. 2003. Remaining part will be installed during the next Summer shutdown in 2003. In the current analysis, one of the sources of the dominant systematic error is the F / N ratio. The uncertainty comes from the error of the PIMON

122

measurements. In order to improve the precision of the F/N ratio, hadron production from a replica of the K2K target was measured at the HARP experiment at CERNll. Analysis of the data is in progress. The K2K experiment will accumulate at least lo2' POT. 6. Summary

The K2K experiment observed the indication of neutrino oscillation. Observed number of events is 56 while expected one without oscillation is 80.1t6,::. Both the number of observed neutrino events and the observed energy spectrum at SK are consistent with neutrino oscillation. The probability that the measurements at SK are explained by statistical fluctuation is less than 1%. The measured oscillation parameters are consistent with the ones suggested by atmospheric neutrinos. After long shutdown, K2K restarted on Dec. 2001 and is accumulating data. New detector is being installed in near site to improve the sensitivity of the experiment. It is planned to accumulate lo2' POT at least. References 1. S. H. Ahn et al. Detection of accelerator produced neutrinos at a distance of 250-km. Phys. Lett., B511:178-184, 2001. 2. Y. Fukuda et al. Evidence for oscillation of atmospheric neutrinos. Phys. Rev. Lett., 81:1562-1567, 1998. 3. S. Fukuda et al. Determinatio of solar neutrino oscillation parameters using 1496 days of super-kamiokande i data. Phys. Lett., B539:179-187, 2002. 4. M. H. Ahn et al. Indications of neutrino oscillation in a 250-km long- baseline experiment. Phys. Rev. Lett., 90:041801, 2003. 5. M. Ieiri et al. Magnetic horn for a long-baseline neutrino oscillation experiment at kek. 1997. Prepared for 11th Symposium on Accelerator Technology and Science, Hyogo, Japan, 21-23 Oct 1997. 6. A. Suzuki et al. Design, construction, and operation of scifi tracking detector for k2k experiment. Nucl. Instrum. Meth., A453:165-176, 2000. 7. T. Ishii et al. Near muon range detector for k2k experiment: Construction and performance. Nucl. Instrum. Meth., A482:244-253, 2002. 8. T. Maruyama. First observation of accelerator origin neutrino beam after passing through 250 km of earth. Ph.D. thesis (Tohoku Unversity), 2000. 9. Y. Fukuda et al. Measurement of a small atmospheric v p / u e ratio. Phys. Lett., B433:9-18, 1998. 10. M Yoshida. K2k: Full active scintillator tracker. Talk presented at International Workshop on Nuclear and Particle Physics at 50-GeV PS, 2002 at Kyoto University, http://www-jhf.kek.jp/NP02. 11. Emilio Radicioni. Harp: A hadron production experiment. 2002.

BOONE AT SIX MONTHS

E. D. ZIMMERMAN* University of Colorado Boulder, Colorado 80309 USA E-mail: edzOco 1 o r a d o . e d u

E898, the MiniBooNE experiment at Fermi National Accelerator Laboratory, has been collecting data since August 2002. The experiment will test the neutrino oscillation signal reported by the Liquid Scintillator Neutrino Detector at Los Alamos National Laboratory.

1. LSND and KARMEN In addition to oscillation evidence from solar' and atmospheric' neutrinos, there is a neutrino oscillation signal from a lone accelerator experiment, LSND at Los Alamos, which observed an excess of De events from a predominantly D~ source3. LSND used a beam-stop neutrino source at the 800 MeV LAMPF proton accelerator at Los Alamos National Laboratory. The primary source of neutrinos was K+ and p+ decays at rest (DAR) in the target, which yielded u p , Y p , and u, with energies below 53 MeV. In addition, K+ and K - decays in flight (DIF) provided a small flux of higher-energy up a,nd V p . The 0, flux was below lop3 of the total DAR rate. The LSND data were collected between 1993 and 1998. The first data set, collected 1993-1995, used a water target which stopped all hadrons and provided 59% of the DAR data set; the remainder of the data came from a heavy metal target composed mostly of tungsten. The collaboration searched for De appearance using the reaction Pep + e+n in a 167-ton scintillator-doped mineral oil (CHa) target/detector. The detector sat 30 m from the target, providing an oscillation scale L I E 0.6 - 1 m/MeV. The detector, which was instrumented with 1220 8-inch photomultiplier tubes (PMTs), observed a Cerenkov ring and scintillation light from the positron emitted in the neu-

-

'For the BooNE collaboration

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124

N

a

-2

10

Io

-~

Io

-~ 1 o-2 s in22$

lo-’

1

Figure 1. LSND 90% and 99% confidence level allowed regions (shaded) along with KARMENP and Bugey 90% confidence level exclusion limits.

trino interaction. An additional handle was the detection of the 2.2 MeV neutron-capture gamma ray from the reaction n p -+dy. The appropriate delayed coincidence (the neutron capture lifetime in oil is 186 p s) and spatial correlation between the e+ and y were studied for DAR 0, candidates. In 2001, LSND presented the final oscillation search results, which gave a total Fe excess above background of 87.9 22.4 f 6.0 events in the DAR energy range. The dominant background was beam-unrelated events, primarily from cosmic rays. These backgrounds were measured using the 94% of detector livetime when the beam was not on. No significant signal was observed in DIF events; the total ve/O, excess above background was 8.1 f.12.2 f 1.7 events, consistent with the DAR result. The total events and energy distributions of the DAR and DIF events were used t o constrain the oscillation parameter space (Fig. 1). Another experiment of similar design, the Karlsruhe-Rutherford Medium Energy Neutrino (KARMEN) experiment at the ISIS facility of the Rutherford Laboratory, also searched for fiP + Pe oscillations. KARMEN

+

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used a similar beam-stop neutrino source, but with a segmented smaller neutrino target (56 tons). KARMEN’s sensitivity was enhanced because the lower beam duty factor (lov5) allowed beam-unrelated events to be removed more effectively with a timing cut. In addition, KARMEN had higher flux because it was closer to the target (18 m versus 30 m). This did, however, reduce KARMEN’s sensitivity to low-Am2 oscillations compared to LSND. KARMEN’s most recent published result4, using data collected from 1997 t o 2001, reported 15 Oe oscillation candidates with an expected background of 15.8 f 0.5 events. This result does not provide evidence for oscillations, and indeed can be used to rule out most of the high-Am2 portions of the LSND allowed region. However, an analysis of the combined LSND and KARMEN data sets has found regions of oscillation parameter space which fit both experiments’ data well5. The LSND data indicate a much larger Am2 than atmospheric or solar experiments: Am2 0.1 - 10 eV2. This led to the paradox of three Am2 values all of different orders of magnitude; this is impossible if there are only three neutrino masses. The more common way to account for all the existing oscillation data is to introduce one or more “sterile” neutrino flavors6. A more recent idea, motivated by extra-dimensions models, has been to introduce maximal CPT violation in the neutrino mass matrix, thereby giving neutrinos and antineutrinos differing mass hierarchies7. The recent KAMLAND8 3, disappearance results sharply restrict the parameter space available for CPT-violating solutions to this “too many Am2” problemg. N

2. MiniBooNE Overview

MiniBooNE (Experiment 898 at Fermilab)lo is a short-baseline neutrino oscillation experiment which is designed to confirm or rule out LSND unequivocally. It uses an 8 GeV proton beam from the Fermilab Booster to produce pions, which are focused by a horn into a decay pipe, where they decay in flight to produce a nearly pure v p beam. The neutrinos are detected a t a mineral oil Cerenkov detector 500 m away. The detector uses Cerenkov ring shape information to distinguish charged-current v p from v, interactions, searching for an excess of v, which would indicate oscillations. Data collection began in late summer 2002 and is expected to last two to three years. MiniBooNE is the first stage of the BooNE program, which will continue with a two-detector experiment to make precise measurements of oscillation parameters if LSND is confirmed. There are several major differences between MiniBooNE and LSND,

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which should assure that systematic errors are independent. First, MiniBooNE operates at an energy and oscillation baseline over an order of magnitude greater than LSND: E, 500- 1000 MeV, compared to 30- 53 MeV at LSND. The baseline L = 500 m, versus 30 m at LSND. L I E remains similar, ensuring that the oscillation sensitivity is maximized in the same region of parameter space as LSND. MiniBooNE uses the quasielestic neutrino scattering reaction ue1’C -+ e-X with the leading lepton’s Cerenkov ring reconstructed, rather than LSND’s antineutrino interaction with a hydrogen nucleus followed by neutron capture. Finally, MiniBooNE’s goal is a factor of ten higher statistics than LSND had.

-

3. Beam Details

The BooNE neutrino beam begins with an 8 GeV primary proton beam from the Fermilab Booster accelerator. The beam arrives in 1.6 ps pulses, with five pulses per second. Protons from the primary beam strike a 71 cm beryllium target located within a magnetic focusing horn. A horn was chosen because it gives higher angular and momentum acceptances than other focusing systems. It can be made to withstand high radiation levels, has cylindrical symmetry, and also gives sign selection. The inner conductor shape and current were optimized by using GEANT l1 to maximize the ufi flux between 0.5-1 GeV at the detector while minimizing flux above 1 GeV. The horn was designed to run at 170 kA for lo8 pulses with < 3% fatigue failure probability. Despite focusing, a highly divergent hadron beam exits the horn and enters the decay pipe. This beam consists mainly of unscattered and scattered primary protons and mesons. The decay pipe is 50 m long and six feet in diameter; most of the kaons and about a quarter of the pions decay before reaching its end. At the end of the decay pipe, 50 m from the target, is a beam absorber which stops all the hadrons and low-energy muons. Located 25 m from the target is an intermediate absorber which can be lowered into the beam. This design feature was introduced to provide a systematic check on muon-decay u, background. The neutrino flux which results from this design was simulated using GEANT with the standard FLUKA hadron interaction package. Efforts to simulate the flux using the MARS l 2 simulation package are underway. All beamline elements, including the horn, shielding, and absorbers, were simulated. The up flux a t 500 m (in the absence of neutrino oscillations) for a detector on the z-axis with 6 m radius is shown as the solid histogram

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Figure 2. A view of the focusing horn. Beam enters from the upper left. All elements shown are aluminum. The outer conductor is rendered transparent. The target resides inside the narrow neck of the upstream end of the inner conductor. The inner conductor is six feet long, and the horn's diameter is two feet. Image by Bartoszek Engineering.

in Fig. 3. Using a Gaussian fit, the peak of the spectrum is at 0.94 GeV. Forty-eight percent of the spectrum is in the optimal range, between 0.3 and 1.0 GeV. The intrinsic v, background is shown as well; it results primarily from K + , K;, and p+ decays. An additional beam monitor, the Little Muon Counter (LMC), will be placed adjacent to the secondary beamline in late summer 2003. This muon detector, connected to the decay pipe by an evacuated drift pipe 7" off the beam axis, will constrain the kaon flux by measuring the momentum spectrum of muons emitted at this angle. Due to the low Q-value of pion decay, the only source of high-momentum muons at large angles is kaon decay. 4. Detector Details

The MiniBooNE detector is a 40-foot spherical tank filled with 800 tons of clear mineral oil and instrumented with 1520 8-inch PMTs. An optical barrier mounted 35 cm from the tank wall separates the inner fiducial region from an outer oil region which is used as a veto. The inner volume is lined with 1280 PMTs mounted directly on the optical barrier. The remaining 240 PMTs are mounted in the veto region. Most of the PMTs were acquired from LSND. The detector records the hit arrival time and total charge for each PMT

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v ENERGY (GeV)

Figure 3. The up flux (solid) at the MiniBooNE detector compared to the ue background (dashed).

with 2 1 photoelectron in each 100 ns clock cycle. From the P M T information, Cerenkov rings and delayed scintillation light are reconstructed. The oil was not doped with scintillator; the natural scintillation properties of mineral oil are near optimal for the experiment. The Cerenkov ring allows the track direction and location to be calculated, as well as providing the primary means of particle identification. Electrons are identified by their characteristic ring shape, a result of the electromagnetic shower profile. Muons have a ring shape characteristic of a penetrating track with little scattering: the outer edge of the ring is well-defined and the ring is significantly filled in due to the extended track. Muons are further identified by their decay electron, except for the 8% of p - which are captured by nuclei. Finally, a source of potential background to the v, signal is neutral-current production of nucleon resonances which decay t o 7ro. The 7ra + yy decay produces two electromagnetic showers, each one of which appears very similar to an electron ring. In asymmetric decays, one ring may not be reconstructed. The recoil nucleon from the resonance decay, while usually below Cerenkov threshold, produces additional scintillation light which can help distinguish 7ro events from v,. In

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the end, the 7ro misidentification background is expected to be comparable to or below an anticipated oscillation signal. Muon misidentification levels should be lower yet. Neutral pion events with two reconstructed rings can be used as a check on the detector performance. Reconstruction of the invariant yy mass yields a peak at the no mass (Fig. 4). The peak width is consistent with our expected energy resolution of 20%.

31 I4 13368 22%

Figure 4.

Reconstructed two-photon invariant mass for

7ro

280

k 195 & 2 13

candidate events.

5. Status and Conclusion

MiniBooNE began taking neutrino physics data in August 2002. As of early July, approximately one hundred thousand neutrino events have been recorded. A blind analysis is being performed, removing u, candidates from the samples which are open to study. An early up candidate event display is shown in Fig. 5. The beam and detector were commissioned quickly, and within a few weeks of the first neutrino data protons were being delivered reliably a t a rate of 10l6 per hour. This is, however, an order of magnitude below the nominal intensity. Since then, some hardware replacements and tune adjustments have permitted the rate to increase to 3-4 x10l6 per hour. The Booster's ability to deliver beam is limited by radiation losses in the accel-

130

Figure 5. Neutrino event from first running period. The sizes of the blobs indicate the total charge on each P M T .

erator and extraction system. Work is ongoing to improve this rate, and with luck the Booster will be delivering nearly the full requested intensity to MiniBooNE after a scheduled shutdownin September 2003. This will allow MiniBooNE to publish results addressing LSND in early 2005. References 1. Y. Fukuda et al., Phys. Rev. Lett. 82 2430 (1999), J.N. Abdurashitov et al., Phys. Rev. Lett. 83 4686 (1999), B. Cleveland et al., Astrophys. J . 496 505 (1998), GALLEX Collab., Phys. Lett. B447 127 (1999), Q. R. Ahmad et al., nucl-ex/0204008 2. Y. Fukuda et al., Phys. Rev. Lett. 81 1562 (1998). 3. A. Aguilar et al., Phys. Rev. D64 112007 (2001). 4. B. Armbruster et al., Phys. Rev. D65 (2002). 5. E. Church et al., Phys. Rev. D66 013001 (2002). 6. V. Barger et al.. Phys. Lett. B489 345 (2000). 7. G. Barenboim et al., J . High Energy Phys. 0210 001 (2002). 8. K. Eguchi et al., Phys. Rev. Lett. 90 021802 (2003). 9. G. Barenboim, L. Borissov, and J. Lykken, e-print hep-ph/0212116 (2002). 10. http://www-boone.fnal.gov 11. Applications and Software Group, CERN, Program Library Report Q123. 12. http: //www-ap.fna1 .gov/MARS.

THE ICARUS PROJECT: AN UNDERGROUND OBSERVATORY FOR ASTRO-PARTICLE PHYSICS

A. EREDITATO

(ON BEHALF O F THE ICARUS COLLABORATION) I N F N Napoli, Napoli, Italy E-mail: antonio. [email protected] The ICARUS project aims at the realization of a large-mass, high-sensitivity observatory at the Gran Sasso underground Laboratory for the observation of rare astro-particle reactions, such as the interaction of astrophysical and accelerator neutrinos, and the nucleon decay. The detection technique exploits large-volume Time Projection Chambers filled with liquid Argon (LAr T P C ) . The general principles of this technique are briefly recalled, together with the milestones in the establishment of the present status. The main focus is given t o the realization and tests of the first large-mass (600 ton) detector module, built with fully industrial methods, suitable t o be cloned in order to reach the final detector mass of about 3000 ton by 2006.

1. Introduction The technology of the Liquid Argon Time Projection Chamber was originally conceived as a tool for a uniform, high-accuracy imaging of very large masses (several thousand tons). The operational principle of the LAr T P C is based on the fact that in highly purified LAr, with less than 0.1 part per billion 0 2 equivalent contamination, electrons produced by ionizing tracks can be transported practically undistorted by a uniform electric field over distances of the order of meters. Imaging is provided by planes of wires with different orientations placed at the end of the drift path, continuously reading out the charge induction signals from the drifting electrons. The LAr TPC has been developed in the context of the ICARUS program and finds its main application for the study of some of the major issues of underground astro-particle physics: the detection of astrophysical neutrinos, neutrino oscillations with accelerator beams, nucleon decay and other rare processes. The feasibility of the technology has been demonstrated by an extensive R&D programme, that includes ten years of studies on

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small LAr volumes (proof of principle, LAr purification methods, readout schemes, electronics) and five years of studies with prototypes of increasing mass (purification technology, collection of physics events, pattern recognition, long term operation, readout technology). The largest of these devices had a mass of 3 tons of LAr and has been continuously operated for more than four years, collecting a large sample of cosmic-ray and gamma-source events. Furthermore, a smaller device (50 liters) was exposed to the CERN WANF neutrino beam, demonstrating the high recognition capability for neutrino interactions. A rather complete list of references can be found on the ICARUS Web page '. The ICARUS project has now entered an industrial phase, a necessary path t o proceed towards the realization of larger volume detectors. The first step has been the realization of a large prototype (14 ton) operated a t the INFN Gran Sasso Laboratory (LNGS). The second step is represented by the construction of the T600 module: a 600 ton detector suitable t o study astro-particle physics at the LNGS. The ICARUS T600 project has been funded by INFN during the years 1996-97, and its design and construction lasted about four years. After completion, a full test of the experimental setup has been carried out in a dedicated surface hall in Pavia during 2001. All technical aspects of the system, namely cryogenics, LAr purification, readout chambers, detection of LAr scintillation light, electronics and DAQ were tested and performed as expected. Statistically significant samples of cosmic-ray events (long, penetrating muons and high multiplicity muon bundles, electromagnetic and hadronic showers, low energy events) were collected. The successful ICARUS T600 test provided the proof that the technology, developed over many years, has finally reached maturity. The T600 module will act as the premise for a larger scale detector with a considerably higher experimental impact. The initial physics program with the T600 module at LNGS is reported in '. Even though in this phase the available mass is limited, the detector will allow to address some important issues of underground astro-particle physics such as the study of solar and atmospheric neutrino interactions, of nucleon decay for some specific channels and the detection of v, 's following a Supernova explosion. The ICARUS Collaboration has then proposed the extension of the sensitive detector mass to about 3000 ton (T3000), in view of the operation of the CNGS neutrino beam from CERN t o LNGS, by cloning the present T600 module 7 . This proposal has been recently approved by CERN and INFN and already partially funded by INFN and other international agen-

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cies. The ICARUS T3000 detector will constitute the CERN CNGS2 experiment for the search of neutrino vP-vT oscillations in the parameter region relevant for atmospheric neutrino oscillations. The large detector mass will also allow to search for the nucleon decay with improved sensitivity and to study astro-particle neutrinos with high statistics. 2. The T600 detector module

Figure 1. Inner volume of the first-half (300 ton) of the T600. module.

ICARUS T600 (Fig. 1) is a large cryostat split in two identical, adjacent half-modules, each one with internal dimensions 3.6 m (width) x 3.9 m (height) x 19.9 (length) each. General considerations on solar and atmospheric neutrinos event rates led the Collaboration to adopt a solution with two coupled containers for a total LAr volume of about 550 m3. Each halfmodule (T300) houses an internal detector composed by two TPC’s, the field shaping system, monitors and probes, and by a system for the LAr scintillation light detection. The half-modules are externally surrounded

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by thermal insulation layers. Outside the detector are located the read-out electronics (on the top side) and the cryogenic plant composed of a liquid Nitrogen cooling circuit and of LAr purifiers. The internal structure of each T300 consists of two TPC’s separated by a common cathode. Each TPC is made of three parallel planes of wires, 3 mm apart, oriented at 60 degrees with respect to each other, with a wire pitch of 3 mm. The three planes are held by a sustaining frame positioned onto the longest walls of the half-module. The total number of wires in the T600 detector is about 55000. A uniform electric field perpendicular to the wires is established in the LAr volume of each half-module by means of a high voltage (HV) system to force the drift of the ionization electrons. The cathode plane is placed in the center of the LAr volume at a distance of about 1.5 m from the wires of each side, hence defining the maximum drift path. The HV system is completed by field shaping electrodes to ensure the uniformity of the field along the drift direction, and by a HV feed-trough to set the required voltage on the cathode. At a nominal voltage of 75 kV, corresponding to 500 V/cm of electric field, the maximum drift time is about 1 ms. The top side of the cryostat hosts the exit flanges equipped with cryogenic feed-throughs for the electrical connection of the wires with the readout electronics, and for the internal instrumentation (PMT’s, LAr purity monitors, level and temperature probes, etc.). The electronic chain is designed t o allow continuous read-out, digitization and wave-form recording of signals from each wire of the TPC. It is composed of three basic units: the “Decoupling Board”, which receives analogue signals from the T P C wires via vacuum tight feed-through flanges and passes them t o the “Analogue Board”; the latter houses the signal amplifiers and performs the data conversion (10 bit) at 40 MHz rate; the “Digital Board” employs custom chips (DAEDALUS) implementing a hit finding algorithm. Ionization in LAr is accompanied by scintillation light emission. Detection of this light can be used to provide an absolute time measurement of the events and an internal trigger signal. This is done by 8” PMT’s directly immersed in the LAr. The scintillation light is a monochromatic radiation with X = 128 nm and provides a prompt (< Ips) photon emission ( M 2 x lo4 photons per MeV at 500 V/cm). Such photons propagate in LAr with negligible attenuation thanks to the high degree of purity, mostly experiencing coherent Rayleigh scattering. The PMT’s have been made sensitive to the LAr photons by coating the glass window with a fluorescent wavelength shifter (TetraPhenyl-Butadiene). The global quantum efficiency has

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=

been measured to be 10% at LAr temperature. The spatial reconstruction of ionizing tracks inside the LAr volume is performed by the simultaneous exploitation of the charge and of the light release in the ionization processes. Electrons from ionization induce detectable signals on the T P C wires during their drift motion towards and across the wire planes. UV photons from scintillation provide a prompt signal on the PMT’s that allows the measurement of the absolute drift time and hence of the distance traveled by the drifting electrons. Each of the wire planes of the T P C provides a two-dimensional projection of the event image, with one coordinate given by the wire position and the other by the drift distance. A full 3-D reconstruction of the event is obtained by the correlation of signals from two different planes and the drift distance. One T300 half-module of ICARUS T600 has been fully instrumented in 2000 and commissioned in the assembly hall in Pavia in April 2001. The main purpose of the following tests was the check of the overall detector functionality and also a concluding demonstration of the detector technology as realized with industrial construction techniques at a scale suitable for physics. The test was made with the first half-module fully assembled and instrumented while the second one was left empty, although functional from the point of view of cryogenics. The detector went smoothly into operation with all the subsystems performing according to specifications. Cosmic-ray runs were taken in order t o study the features of the reconstruction and analysis programs, and to test and optimize the event simulations. The run period lasted 104 days including the start up and shutdown phases of 36 days. During the 68 days of detector lifetime about 30000 cosmic ray events were collected and their analysis is currently in progress. As an example, a multi-track and an electromagnetic shower events are shown in Fig. 2.

3. Outlook As mentioned above, after the commissioning of the T600 module in the Hall B of the LNGS, the next phase of the ICARUS project will be the extension of the detector mass up to 3000 ton by cloning the basic T600 unit. An artist view of the final T3000 detector is shown in Fig. 3. It is composed of the T600, of two additional T1200 modules, schematically made up of two T600 detectors on top of each other with a single thermal shielding for the four cryostats, and of a muon spectrometer needed to detect the muons produced in the interaction of neutrinos from the CNGS beam. The details of the design and the main physics goals can be found in the Pro-

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Run 308 Event 332 Collection view

wire coordinate

Figure 2. Multi-track (top) and electromagnetic shower events (bottom) induced by cosmic rays in the T300 detector.

posal '. The mass of 3000 ton will allow to collect a large event statistics to perform experiments with astrophysical neutrinos (solar, atmospheric and from Supernovae), to search for the proton decay with high sensitivity, and to search for neutrino oscillations in the CNGS beam. Concerning the proton decay search, given the high detection efficiency and the low background, ICARUS should be able, already with an exposure of a few ktonxyear, to provide sensitive limits in the range of a few years, with an approach complementary to that of SuperKamiokande, that features a larger mass but a lower detection efficiency in specific decay channels. Also atmospheric neutrinos will be looked at with different methods respect to SuperKamiokande, which focuses on single-ring events and relies on Monte Carlo simulations for other channels. ICARUS will look at atmospheric neutrino interactions with a rather unbiased and systematic-free way, by exploiting the good energy and angular resolution and its imaging capabilities. Improvements are expected in the domain of low energy, electron and neutral current events. Already in one year running of the T600 detector one should be able to collect (in presence of oscillations) about 100

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Figure 3. Artist view of the future T3000 detector (3000 ton of liquid Argon), composed of the T600 detector, of two T1200 modules and of a muon spectrometer.

high-quality events. As a last example, it is worth mentioning the search for vp-vToscillations with the CNGS beam starting from 2006. ICARUS will look for this process in the parameter region indicated by the SuperKamiokande and K2K experiments in T appearance mode, by exploiting in particular the 'gold plated' T decay into electron. Assuming the nominal CNGS operation and a five year running of the T3000 detector, one should be able to unambiguously detect the oscillations in I h e whole parameter range indicated by the atmospheric signal. About 17 r events are expected with a background of 0.7 if oscillation occur with parameter values: Am2=3 eV2 and full mixing. With the same five year exposure in the CNGS high energy beam ICARUS will also be able to set a (90% CL) limit to the 813 mixing angle of about 6 degrees. A factor of five more sensitive limit could be achieved by maximizing the neutrino beam flux in the range 0-2.5 GeV, as shown in Fig. 4. In conclusion, I like to emphasize that with the forthcoming commissioning for physics of the T600 at LNGS and the progressive installation of the following modules, a new, performing astro-particle observatory will become fully operational by 2006. The detector will look at all 'hot' physics subjects with improved potentialities thanks t o its innovative imaging technology and, in addition, will also be ready to meet the challenge of the future

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Figure 4. Sensitivity of ICARUS and of other experiments to the measurement of the 813 mixing angle.

neutrino Super Beams and, eventually, Neutrino Factories. Acknowledgments

I warmly acknowledge Prof. Y. Suzuki for the kind invitation, and the local Committee members for the excellent organization of the Workshop. References 1. C. Rubbia, CERN-EP/77-08, (1977). 2. P. Benetti et al., Nucl. Instr. and Meth. A332 (1992) 395. 3. The ICARUS Web Page: http://www.cern.ch/icarus. 4. F. Arneodo et al., Nucl. Inst. Meth., A498 (2002) 292. 5. The ICARUS Collaboration, LNGS - 95/10, (1995). 6. The ICARUS Collaboration, LNGS-P28/2001. 7. The ICARUS Collaboration, LNGS-94/99 I&II. 8. The ICARUS Collaboration, CERN/SPSC 2002-027; SPSC-P-323.

OFF-AXIS EXPERIMENT IN THE NUMI BEAM AT FERMILAB STANLEY WOJCICKI Stanford Universify Varian Physics Building Stanford, CA 94305-4060 E-mail: [email protected] The NuMl neutrino beam at Fermilab will provide the most intense high energy neutrino beam in the world. We describe briefly the NuMl beam and its current status, a possible detector for an off-axis experiment, and the potential sensitivity for v,,-+v, oscillations. It is shown that with a low Z 50 kt detector, one can improve on the current limit from CHOOZ in a 5 year run by a factor of about 20.

1. Introduction The last decade has seen a remarkable progress in the field of neutrino physics. Solar neutrino deficit and atmospheric neutrino anomaly, have both been shown to almost certainly be due to oscillations, the relevant mass squared values have been determined to better than a factor of two, and the general features of the neutrino mixing matrix, the PMNS matrix, have been roughly determined. The next generation of experiments, K2K in Japan, MINOS at Fermilab, and the CNGS program in Europe, should further elucidate the situation in the atmospheric mass squared region. In addition, the MiniBoone experiment at Fermilab should be able to resolve the LSND puzzle. On the assumption that MiniBoone experiment will not validate LSND results, the most pressing questions to address next will be: a) observation of the vp+v, transition in the region corresponding to atmospheric mass squared region and hence obtaining some information on the range of 813. Currently there is only an upper limit on its value, the best limit coming from the CHOOZ [ 11 experiment. b) Determination of the mass hierarchy, i.e. whether m3>m2,mIor m3<m1,m2. c) Search for and study of CP violation in the lepfonic sector. The rate for v+v, transition depends not only on the value of 8 1 3 but also on mass hierarchy, value of CP violation parameter 6, and the value of 023. If one ignores matter effects and CP violation, to a very good approximation the rate for vp-+v,, in the L/E range where solar mass range transitions can be neglected, can be written as: P (vp+ve) = sin2OZ3x sin22OI3x sin2 (1.27 x Am213x L / E) (1) where L is the source to detector distance in km,E the neutrino energy in GeV, and Am213the mass squared difference between mass states 1 and 3. 139

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Introduction of matter effects increases (decreases) the neutrino (antineutrino) transition rate for a given value of OI3 and for normal hierarchy. The opposite is true for the inverted hierarchy. This effect grows with the energy of the neutrinos studied. The relationship between value of 013,matter effect and value of CP violation parameter 6 can best be represented in a biprobability space characterized by the v+v, transition rate for neutrinos on one axis and antineutrinos on the other axis. This representation [ 2 ] is displayed in Fig. 1 for a MINOS source to detector distance L of 732 km, and at the first oscillation minimum. As can be seen, the CP violation effects transform a predicted point in this space into a locus of points forming an ellipse. The magnitude of CP violation effects depends also on the values of €lI2 and Am212. We have used in Fig.1 the current best estimate of these two parameters [ 3 ] . =

L

1.5 GeV

= 732. k q

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&me< 0

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t I

2e..= -- I"

o.oia

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1.w

Id

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k 3.=,O.lO

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x

Fig. 1. Bi-probability plots for different values of €Il3. Note that linear scale is used in the left part of the figure, logarithmic in the right one.

Fig. 1 illustrates the challenge of extracting OI3 from experimental measurements. It requires knowledge of the other mixing angles and solar mass squared value and the uncertainties in those parameters will reflect themselves in worse determination of OI3 [4]. It also illustrates the need for more than one experiment searching for vp->v, transition, The experiments would ideally have different values of L and E and run with both neutrinos and antineutrinos IS]. If €lI3 is in a range that is accessible to next generation superbeam or reactor experiments, 2 or 3 different ones will probably be necessary to unravel the important physics. If OI3 is lower, so that it is inaccessible to those experiments, a neutrino factory will have to resolve the issue.

141

2.

NuMlBeam

The neutrino beam at Fermilab is currently under construction. The proton source is the 120 GeV Main Injector accelerator. One bunch in the machine will be used for antiproton production and the remaining 5 will be extracted into the NuMI beam line. The layout of the beam line is illustrated in Fig.2.

Target Shaft Area

I

MINOS ShaA Ares

Fig.2. Layout of the NuMI beam, plan view on the top and elevation view on the bottom. The distances are indicated in feet.

The proton beam strikes a thin carbon target located in front of a two-horn magnetic focusing system. The two horns are operated in series and the design value for the pulsed current is 200 kA.Both the target and the second horn can be moved with respect to the first horn. This flexibility allows one to vary the spectrum of the produced neutrinos. Three configurations, referred to as low, medium and high energy, are being planned. Initially we plan to optimize the neutrino flux in the low energy region, following Am223indications from SuperKamiokande [6] and K2K [7]. Moving only the target downstream results in a flux at higher energies that is about 20-30% less than the optimized one for that energy obtained by also moving the second horn. The target hall region is followed by a 2m diameter, 675m long decay pipe that will be held under vacuum. The decay pipe is followed by hadron absorber and further downstream by three muon monitoring stations to monitor the beam on a pulse to pulse basis. The experimental hall, which will house the near detector, is another 300 m downstream of the absorber. The main underground excavation is now completed and the current work focuses on construction of the two associated buildings, one above the target

142

hall, the other near the detector hall, and on outfitting the surface buildings and the underground facilities. The first beam is anticipated in December 2004. The currently projected proton intensity available for NuMI is 2.5 x lOI3 protons every cycle, i.e. 2 sec, which would give an estimated 2.5 x 10” protons per year. There are active studies going on aimed at significantly increasing the proton intensity with time, with an optimistic goal of obtaining 2.5 x protons in an integrated 5 year long MINOS run. 3.

Offaxis Experiment In NuMI Beam Line

Neutrino flux and the total neutrino interaction rate is maximum at 0’ with respect to the meson direction where the neutrino energy is highest and center of mass to laboratory solid angle transformation most favorable. The neutrino spectrum there is quite broad, mirroring the focused meson spectrum, since each neutrino emitted in forward direction carries about 43% of the pion energy. An interesting phenomenon [8] occurs at a laboratory angle which corresponds roughly to the 90’ center of mass decay of the pions with energy near the center of the focused pion spectrum. At that angle the neutrinos from a wide band of pion energies have similar energy, i.e. the rate of change of neutrino energy with pion energy is rather small. Thus a relatively monochromatic beam of pions can be obtained with an energy roughly a factor of 2 smaller than one would have from those pions in the forward direction. The number of neutrino interactions is approximately a factor of 8 smaller (factor of 2 from neutrino energy and a factor of 4 from solid angle transformation) but the flux is concentrated in a narrow energy band and there one can increase the flux compared to the forward direction case. The lower total interaction rate is frequently an added advantage because of the lower background. To exploit this general feature in the NuMI beam for exploration of the atmospheric mass squared region one can place a detector transversely to the beam near MINOS location, or move to closer or hrther locations, effectively looking at neutrinos emitted at an angle in the vertical plane. For in the 2.2 - 3.0 x eV2 range, the optimum neutrino energy for the NuMI offaxis beam is between 1.5 and 2.0 GeV, corresponding to the transverse distance from the forward beam direction in 8-12 km range, and the possible source to detector distances of about 550 to 900 km. The NuMI medium energy beam configuration maximizes the flux in that energy range, although the degradation as one goes to the low energy beam is not very significant.

143

4.

Off-Axis Detector

Since the physics that will be investigated with the NuMI beam and an off-axis detector centers around measuring the rate of the v,,+v, process (and its charge conjugate) the detector should be optimized for detection of v, CC interactions. In addition, since the rates to be searched for can be quite low, the detector should be as massive as possible. Thus the main challenges are construction of a massive detector for reasonable price, one that has good efficiency for detecting electrons and rejecting backgrounds. Our conclusion is that an optimum detector would be a low Z tracking calorimeter, consisting of slabs of inert material of low Z followed by an active detector, either scintillator or RPC’s. The water Cherenkow counter does not give good enough rejection for 7~’’s above 1 GeV and liquid argon requires significant R&D before a detector of sufficient mass could be built economically. The current plan calls for construction of a 50 kt detector, with transverse dimensions large enough (in 20 x 25 x 140 m range) so that a 40 kt fiducial volume can be obtained. The likely inert absorber would be particle board with a density of about 0.7 glcc. The active detector would be segmented into longitudinal strips, with width in the 3-6 cm range. The exact parameters will be determined based on ongoing simulation studies. The choice of active detector will be determined based on performance, cost, ease of construction and reliability. The main advantage of WC’s is the ability to read both dimensions in one plane (which translates into cost savings for an equivalent performance). The scintillator has a potential of providing energy resolution if analogue readout is used. Also, very importantly, the experience of MINOS with scintillator has been very positive.

5. Backgrounds and Potential Sensitivity We are currently actively involved in an extensive effort to determine the potential sensitivity of the experiment and the optimum parameters of the detector. The results presented here should hence be viewed as highly preliminary and will undoubtedly be modified as a result of hrther work. The experimental challenge is demonstrated in Fig. 3 , where we show the visible energy spectrum of CC interactions of the oscillated v, events, the signal, superimposed on the two principal backgrounds, NC events and beam v, CC interactions. The latter can only be rejected by the total energy cut and thus they constitute at some level an irreducible background. One wants to design the detector and analysis so that the other main background, the NC events, contribute less than the beam v, events. The other two potential backgrounds, misidentified v,, CC interactions, and T-+e decays, give a much smaller

144

contribution, the latter because our central beam energy is below z production threshold.

E (GeV) Fig.3. Visible energy for NC events, beam V, CC events, and oscillated V, CC events for a NuMI medium energy offaxis beam with the detector at 735 !an and 10 km away from the beam axis. The signal is taken as being 5 times below the CHOOZ limit.

The characteristic signature of the electrons is that their tracks are “fuzzy” i.e. several neighboring strips in the same plane have hits, due to accompanying electromagnetic radiation. On the other hand muon tracks are much “cleaner”. By restricting oneself to events with high fraction of energy taken by the electrons (low y events) one can gain significantly in the signal to background ratio. The NC events with a z0 can frequently be rejected because of a gap between the neutrino vertex (if there exists a clearly identifiable other vertex) and the start of the track andor presence of an additional electron-like track in the vicinity. The total visible energy cut is also powerful in rejecting this background as can be seen from Fig.3. We have focused our current studies on longitudinal granularity of 25-50% of radiation length (r.1.) and strip width of 3-6 cm. As a measure of quality of a given configuration we use Figure of Merit (FOM), number of signal events divided by the square root of the background events. This assumes that the backgrounds can be measured in the Near Detector and extrapolated to the Far Detector so that the main uncertainty is the statistical fluctuation in the number of background events in the Far Detector. We feel that this is a good assumption and systematic uncertainty will be smaller. In this assumption FOM squared is inversely proportional to the fiducial mass of the detector.

145

For 35% r.1. longitudinal granularity and strip width of 5 cm we obtain energy resolution dE/E of 15%/sqrt(E). In Table 1 we show the results of a recent simulation (30% r.1. longitudinal granularity and 3 cm detector strip width) and its comparison with the JHF proposal [9]. Table 1. Comparison of performance of the potential NuMI Offaxis beam with the JHF to Kamioka proposal. The signal estimate is for oscillation probability of 5%, i.e. around the CHOOZ limit. NuMI Off-axis 5 years, 4x I 02' pot/y All vp CC (no osc)

NC Beam v, Signal (Am213=2.8/3 x NuMI/JHF) FOM (signal/l/bckg)

After cuts

JHF to SK Phase I, 5 years All

After cuts

28348

6.8

10714

8650

19.4

4080

604

31.2

292

1.8 9.3 11

867.3

307.9

302

123

40.7

26.2

6. Site Issues There is some flexibility in choosing an optimum site for a given value of AmZl3.Firstly, the transverse distance is not rigorously fixed. As one moves closer to the forward direction, flux increases and the mean energy of the neutrinos also increases. Thus the basic issue here is how much one can increase the flux while keeping the background sufficiently low. Secondly, there is flexibility in the distance away from the source. Besides the signal to background criterion, the other relevant point here is that increasing the longitudinal distance increases the sensitivity to matter effects and thus makes the NuMI experiment more complementary to the proposed experiment at JPARC [91. One possible site for the location of the detector is the old LTV mine at a distance of about 712 km from Fermilab. The site is large enough so that there is considerable flexibility in the transverse distance. The alternatives are further north at progressively larger distances. The furthest feasible site is east of Kenora in Ontario, Canada, alongside the trans-Canada highway. It is at about 980 km from Fermilab and thus would be very attractive for values of

146

around 2.2 x eV2 or below. Clearly, practical issues like accessibility, availability of utilities, proximity to housing and stores, will have to be given important consideration. It is planned to site the detector on the surface. The short beam spill (-10 psec every 2 sec), directionality constraint, and relatively high energy appear sufficient to reject all the cosmic ray backgrounds.

7. Time scale The Collaboration is planning to submit a proposal to Fermilab at the end of 2003 for support of construction of a Near Detector using the chosen technology and design. This detector would be a useful prototype for understanding all the construction details. Construction of the Far Detector could begin in 2006 and sufficient mass be available by 2008 to start data taking. In parallel there will be concerted efforts to increase the available proton intensity.

Acknowledgements This work was supported by a National Science Foundation grant 0089 1 16. The NuMI beam line work is supported by the US.Department of Energy.

References 1) M. Apollonio et al., Phys. Lett. B 466 (1999) 415; see also F. Boehm et al, Phys. Rev. D 62 (2000) 072002. 2) H. Minakata and H. Nunokawa, JHEP 0110 (2001) 001. 3) Q. R. Ahmad et al., Phys. Rev. Lett. 89 (2003) 01 1301; K. Eguchi et al., Phys. Rev. Lett. 90 (2003) 021802. 4) M. Freund, P. Huber, and M. Lindner, Nucl. Phys. B 615 (2001) 331. 5) P. Huber, M. Lindner, and W. Winter, Nucl. Phys. B 654 (2003) 3.; H. Minakata, H. Nunokawa, and S. Parke, hep-ph/0301210. 6) S. Fukuda et al., Phys. Rev. Lett 85 (2000) 3999. 7) M. H. Ahn et al., Phys. Rev. Lett. 90 (2003) 041801. 8) BNL E889 Collaboration, BNL52459, April 1995. 9) Y. Itow et al., The JHF-Kamioka neutrino project, hep-ed0106019.

JHFNU (PHASE I) NEUTRINO OSCILLATION EXPERIMENT

A. K. ICHIKAWA IPNS, KEK, 1-1 Oho, Tsukuba,Ibaraki 305-0801 Japan E-mail: [email protected] FOR JHF-SK NEUTRINO EXPERIMENT COLLABORATION The JHF-Kamioka neutrino experiment is a next-generation long baseline oscillation experiment to explore the physics beyond the Standard Model. The experiment will use high intensity proton beam from the J H F 50 GeV proton synchrotron, and Super-Kamiokande as a far detector. The baseline length is 295 km. High intensity neutrino beam is produced in an off-axis configuration. The peak neutrino energy is tuned to the oscillation maximum. The experiment aims to discover v,, 4 v, at Am2 3 x 10-3eV2 down to sin22013 N 0.006, to measure oscillation parameters in up disappearance down to b(Am;3) = l o p 4 eV2 and b(sin2 2 8 2 3 ) = 0.01, and to search for a sterile component in up disappearance by detecting neutral current events.

-

1. Physics Motivation Studies of atmospheric and solar neutrinos have shown that neutrinos have masses and have large mixing. The confirmation of the existence of neutrino oscillations by the first generation experiments must be followed by precision measurements of the neutrino oscillation parameters. Appearance of different kind of neutrino as a result of neutrino oscillation has not yet been observed directly. The next generation experiments aim to discover the appearance. Comparison of neutrino and anti-neutrino oscillations are the only possible way to search for the leptonic CP violation with presently available technologies. The lepton mixing is described by a unitary 3x3 matrix (MakiNakagawa-Sakata (MNS) matrix) that is defined by a product of three rotation matrices with three angles ( 4 2 , 4 2 3 , and 813) and a complex phase (6) as in the Cabibbo-Kobayashi-Maskawa matrix With the two Am2 values suggested by solar and atmospheric neutrino measurements (including the recent Kamland results); Am:, = Am:o, 2 (6 N 9) x lop5 or

147

148

(1.3 2 . 0 ) ~ 1 O - ~ eand V ~ Am:, 21 Am:, Am:,, = (1.6 4) x10V3 eV2, and for an oscillation measurement with E, Y Am:, . L , the oscillation probabilities can be approximately expressed by two mixing angles; N

N

P(vp-+ v p ) = 1- sin2 2823 . c0s4 813 . sin2(1.27Ami,L/E,)

(1)

P(up+ v,) = sin2 2OI3 . sin2 8 2 3 . sin2(1.27Am;,L/E,)

(2)

The most stringent constraint on 6’13 comes from reactor 0, disappearance experiments. The current limit is sin2 2813 5 0.12 for Am;, N 3 x lo-, eV2 at 90 % C.L ,. 2. Overview of the experiment

The experiment will use high intensity proton beam from the JHF 50 GeV proton synchrotron (JHF PS), and Super-Kamiokande as a far detector. The baseline length is 295 km. The beam power of JHF PS is capable of delivering 3.3 x 1014 50 GeV protons every 3.5 seconds (0.75 MW). The far detector, S~per-Kamiokande~>~3~>~, is located in the Kamioka Observatory, Institute for Cosmic Ray Research (ICRR), University of

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Figure 1. Layout of JHF.

149

Tokyo. It is a 50,000 ton water Cerenkov detector. Cerenkov rings produced by relativistic charged particles are detected by PMT's. The pulse-height and timing information are fitted to reconstruct the vertex, direction, energy, and particle identification. The Cerenkov ring shape, clear ring for muons and fuzzy ring for electrons, provides good e / p identification. The e's and p's are further separated by detecting decay electrons from the p decays. The layout of JHF facility is drawn in Fig. 1. The protons are extracted toward the inside of the PS ring, and are bent t o Super-Kamiokande (SK) direction. The secondary pions (and kaons) from the target are focused by horns, and decay in the decay pipe. The length of the decay pipe is 130 m. We adopt the off axis beam (OAB) configuration. The OAB is a method to produce a narrow neutrino energy spectrum *. The axis of the beam optics is displaced by a few degrees from the far detector direction (off-axis). With a finite decay angle, the neutrino energy becomes almost independent of parent pion momentum due to characteristics of the Lorenz boost, thus providing the narrow spectrum. The peak neutrino energy can be adjusted by choosing the off-axis angle. Figure 2(a) shows expected neutrino energy spectra of charged current interactions at SK. The OAB is roughly a factor of three more intense than possible momentum selected beam. The energy spectrum of the Y, contamination is plotted in Fig. 2(b). At the peak energy of the up spectrum, the Y , / Y ~ratio is as small as 0.2%. This indicates that

I

E, (GeW

Figure 2. (a) Neutrino energy spectra of charged current interactions. Thick solid, dashed and dash-dotted histograms are O A l O ,OA2' and OA3', respectively. (b) Comparison of v, and v p spectra for OA2". Solid (black) histogram is v p and dashed (red) one is v,. Hatched area is contribution from K decay. The low energy v, component is due to p decay.

150

beam u, background is greatly suppressed by applying an energy cut on the reconstructed neutrino energy. For the reconstruction of neutrino energy at near and far detectors, events produced by the quasi-elastic interaction (CCQE) will be used. Below 1GeV, the charged current interaction is dominated by this interaction. For this interaction, the neutrino energy can be calculated by a formula:

where mN and ml are the masses of the neutron and lepton (=e or p ) , El, pl and 81 are the energy, momentum, and angle of the lepton relative t o the neutrino beam, respectively. The near detector hall will be located at 280 m from the target as shown in Fig. 1. The role of the near detectors is to provide predictions of the expected neutrino at the far detector. The near detector is required to have a capability of identifying event type (CCQE, up and u, inelastic events, neutral current events) and should be able to measure the neutrino spectrum at the near location. By comparing the observables at a near detector and far detector, many of systematic errors cancel out. Systematic uncertainty, however, remains due t o the difference of spectra and detector. In Figure 3, spectra at the

Ev (GeV)

Figure 3. Calculated energy spectrum of the neutrino flux at Super-Kamiokande (solid) and at 280 m (dashed) and 1.5 km (dotted) distances from the neutrino production target for the 2 O off-axis beam.

151

far and near sites are compared. The peak position is shifted t o higher energy at the far site than at the near site. The sources of this far/near difference are the difference in the solid angle between far and near detectors and the finite length of the decay pipe. At distances longer than one km or more from the target, the far/near ratio becomes flat. We propose to construct a water Cerenkov detector at intermediate position t o cancel detector systematics as much as possible.

3. Physics sensitivity 3.1. High precision measurement of Am:, and disappearance

023

with up

The neutrino energy can be reconstructed through quasi-elastic (QE) interactions (Eq. 3) for fully contained single ring muon-like events at SK. The neutrino energy spectrum is extracted by subtracting the contribution from non-QE background events. Full SK Monte Carlo events are generated. The ratio between the “measured)) spectrum at SK and the expected one without oscillation, after subtracting the non-QE contribution, is fitted by P(vp + vp) in Eq. 2. The obtained survival probability of P(v@+ v p ) is shown in Fig. 4, in which the oscillation pattern is clearly seen. Assuming 10% systematic uncertainty in the far/near ratio, 4% uncertainty in the energy scale, and 20% uncertainty in the non-QE background

t

0

I I

I

1000

2000

1 3000

00

Figure 4. The ratio of the measured spectrum with neutrino oscillation to the expected one without neutrino oscillation after subtracting the contribution of non QE-events. The fit result of the oscillation is overlaid.

152

subtraction, the total systematic error is estimated t o be less than 1 % for sin’ and less than 1 x lop4 eV2 for am;,.

3.2. u, appearance search

The JHF neutrino beam has small v, contamination (0.2% at the peak energy of OAB) and the v, appearance signal is enhanced by tuning the neutrino energy at its expected oscillation maximum. The appearance signal is searched for in the CCQE interaction, for which the energy of neutrino can be calculated. The signal has only a single electro-magnetic shower (single ring e-like). The criteria t o select single ring e-like events is single ring, electron like (showering), visible energy greater than 100 MeV, and no decay electrons. Reduction of number of events by this “standard” 1 ring e-like cut for charged and neutral current events are listed in Table 1. The remaining background events at this stage are predominantly from single 7ro production through neutral current interactions and from v, contamination in the beam. Table 1. Number of events and reduction efficiency of “standard” lring e-like cut and T O cut for 5 year exposure (5 x loz1 p.0.t.) OA2”. For the calculation of oscillated v e , Am2 = 3 x 10V3 eV2 and sin’ 28,, = 0.05 is assumed. OAB 2O Generated in F.V. 1 R e-like e/TO separation 0.4 GeV< E,,, < 1.2 GeV

v, C.C.

up N.C.

10713.6 14.3 3.5 1.8

4080.3 247.1 23.0 9.3

Beam v, 292.1 68.4 21.9 11.1

Oscillated v, 301.6 203.7 152.2 123.2

For further reduction of background events, cuts are applied for (1) angle between v and e, (2) invariant mass of 2 photons, (3) difference between double and single ring likelihoods and (4) energy fraction of lower energy ring ( E(7:$)(T21). Table 1 lists the number of events after this e / r 0 separation. An order of magnitude extra rejection (23/247.1) in the v p neutral current background is achieved with 152.2/203.7=75% in the signal acceptance. Figure 5 (left) shows the reconstructed neutrino energy distributions for 5 years. The oscillation parameters of 4m2 = 3 x lop3 eV2 and sin22&3 = 0.1 are assumed. A clear appearance peak is seen at the oscillation maximum of E, -0.75 GeV. The right plot of Figure 5 shows 9O%C.L. contours for 5 year exposure of OA2” assuming 10% systematic uncertainty in background subtraction.

153 90% C.L. sensitivities

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3.3. Search for sterile neutrinos (us) in up disappearance

Neutral current (NC) events represent the sum of up -+ u e , u p , and u, oscillations. Therefore, NC measurement combined with v p -+ u, and up + up measurements provide indirect measurement of the up + u, and up + us oscillation. In the JHF sub-GeV neutrino beam, the dominant detectable NC interactions are single T productions. Among those, single 7ro production process is selected t o study NC events, because of a unique signature. The expected numbers of events as a function of Am2 are shown in Fig. 6. The expected numbers of events for up +- u, and for v p + us are clearly separated if the Am2 is larger than 1 x 4. R&D items and Summary

In the JHF-Kamioka experiment, we already have a excellent far detector, Super-Kamiokande. In order to achieve the experimental goal, however, neutrinos has to be produced with the highest intensity proton beam in the world in this energy region. Equipments such as the production target, horns, decay volume and beam dump have t o be developed with sufficient cooling power and strength against the shock waves due t o radiation heating. The R&D has already started and the experiment is planed to start in 2007.

154

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References 1. Z. Maki, M. Nakagawa, S.Sakata, Prog. Theor. Phys. 28,870 (1962) 2. M.Kobayashi, T. Maskawa, Prog. Theor. Phys. 49,652 (1973) 3. CHOOZ: Apollonio M. et al., Phys. Lett. B466 (B1999) 415. Palo Verde:F. Boehm et al., Nucl.Phys.Proc.Supp1. 91:91(2001) 4. Super-Kamiokande collaboration, Nucl. Instrum. Meth. A 501,418 (2003) 5. Super-Kamiokande collaboration, Phys.Rev.Lett. 81,1562 (1998) 6. Super-Kamiokande collaboration, Phys.Rev.Lett.85,3999 (2000) 7 . The Super-Kamiokande collaboration, Phys. Rev. Lett.86,5651 (2001), Phys. Rev. Lett.86,5656 (2001) 8. D. Beavis, A. Carroll, I. Chiang, et al., Proposal of BNL AGS E-889 (1995).

PRECISE MEASUREMENT OF sin2 2913 USING JAPANESE REACTORS *

F.SUEKANE: K.INOUE, T.ARAKI AND K.JONGOK Research Center for Neutrino Science, Graduate School of Science, Tohoku University, Sendai, 980-8578, Japan http://www. awa. tohoku. ac.jp

After the KamLAND results, the remaining important targets in neutrino experiments are to measure still unknown 3 basic parameters; absolute neutrino mass scale, CP violation phase 6 c p and last mixing angle 813. The angle 813 among them is expected to be measured in near future by long baseline accelerator experiments and reactor experiments. In this paper, a realistic idea of high sensitivity reactor measurement of sin2 2813 is described. This experiment uses a giant nuclear power plant as the neutrino source and three identical detectors are used t o cancel detector and neutrino flux uncertainties. The sensitivity reach on sin2 2813 is 0.017 0.026 at 3 x 10W3eVZ,which is five to seven times better than the current upper limit measured by CHOOZ. N

N

1. Introduction The year 2002 was a fruitful year for neutrino physics. The SNO group showed that the solar neutrino deficit is due to neutrino transformation'. The KamLAND group observed large deficit in reactor neutrinos and excluded all the solar neutrino solutions except for LMA2. K2K group confirmed3 SuperKamiokande (SK) results of atmospheric neutrino oscillation4. From these observations, four out of seven elementary parameters of neutrinos have been measured. The measurements of remaining parameters, such as mixing angle 013, absolute scale of neutrino mass and CP violating phase S c p are the next crucial issues. *The theoretical working group members are H.Minakata, 0.Yasuda and H.Sugiyama; Dept. of Physics, Tokyo Metropolitan Univ. tspeaker; [email protected]

155

156

The mixing parameter sin2 2QI3 can be measured by disappearance of reactor pe at energylbaseline range to be around Am:,, as shown below.

-

The current upper limit of sin22Q13was measured by CHOOZ group using reactor fle to be 5 0.12 if Am:, 3 x 10-3eV2 5. In order to improve the sensitivity, a realistic idea of new-generation reactor experiment is being investigated It uses a giant nuclear power plant of multi reactor complex as the neutrino source. Identical detectors axe placed at approximately oscillation maximum baseline and near the reactors. The data from those detectors are compared to cancel systematic uncertainties when extracting the disappearance rate. This nearlfar detector strategy was originally proposed by Kr2Det group7. Together with optimized baselines, detector improvements and farlnear strategy, our experiment can improve the sensitivity for sin2 2813 significantly better than the CHOOZ experiment.

‘.

2. Physics Motivations There is a number of reasons why reactor Q13 measurement is important. (1) 613 is the last neutrino mixing angle whose finite value has not yet been measured. Especially it is important to know how small Q13 is, while other two mixing angles are large unlike quark sector. (2) The size of 813 is related to the detectability of leptonic S c p in future long baseline (LBL) accelerator experiments. The sensitivity to b ~ p changes rapidly at around sin2 2QI3 0.02 and the knowledge of sin2 2QI3 down to this range will give important guideline to make strategies for future LBL b ~ experiments p (3) The reactor measurement of sin2 2813 is complementary measurement to LBL sin2 2813 experiment which measures u, appearance probability in up beams; P(up -+ u,) The probability at E,/L = Am&/27r is expressed in eq.(2). (For simplicity, the matter effect is ignored.)

-

‘.

P(vp-+ v,)

2

M sin2 2813 sin Q23

Using best fit oscillation parameters measured by SK and KamLAND, the coefficient for sin 2QI3sin S c p in the 2nd term is calculated to be around

157

0.04. Because sinScp is totally unknown, the 2nd term becomes full ambiguity when determining sin2 2OI3. Moreover, there is degeneracy of 6'23. That is, even if sin226'23 is determined by P ( v p -+ vp) measurements, there are two solutions for sin2 6'23 if sin2 26'23 is not unity. Namely, if sin2 26'23 = 0.92, which is the current lower limit from SK, sin2 6'23 = 0.64 or 0.36. These circumstances are described in detail in the referencesg. Fig.-1 shows the relation of the appearance probability and sin2 26'13, taking into account these ambiguities. The sensitivity of the JHF experiment, for example, on sin226'13 is limited to ~ 0 . 0 2 5( ~ 0 . 0 1 5 depending ) upon possible 6'23 degeneracy is (is not) taken into account lo.

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Figure 1. The relation between sin2 2813 and v p + v, appearance probability at Am:, energy-distance range. The matter effect is ignored for simplicity. Two bands which corresponds to two 823 solutions for sin2 2823 = 0.92 are displayed. The width of each band is due to unknown sin 6 c p . Even if appearance probability is precisely measured, there are intrinsic ambiguities on sin2 2813.

On the other hand, the reactor experiment is pure sin226'13 measurement and by combining reactor data and LBL data, there is a possibility to resolve ambiguities of 6'23 degeneracy and Am;, hierarchy and even access to sin6Cp6.

3. The Experiment In this experiment, three identical detectors are build in the site of Kashiwazaki-Kariwa nuclear power plant (NPP) which is operated by Tokyo Electric Power Company. The Kashiwazaki NPP has 7 reactors, producing total thermal energy of 24.3GW. This is the most powerful NPP in the world. Using large-power nuclear power plant is profitable for not only obtaining high event rate but also realizing low background to signal

158

ratio at a given depth underground. The relative locations of reactors and detectors are shown in the fig.-2. Although, the far/near distance ratios between the reactors and detectors are not unique, the uncertainty introduced from the variations of the distances are estimated to be only 0.2%. The

Reactor and Detector Locations

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15m

Relative Position (m)

Figure 2. Reactor (circles) and detector (squares) relative locations. There are 7 reactors in Kashiwazaki-Kariwa nuclear power plant, producing 24.3GW maximum thermal power. Reactor #1 through #4 form a cluster and #5 through #7 form another cluster. The two clusters separate about 1.3km apart. Two near detectors will be placed at around 300 to 350m from each cluster. The far detector will be placed at around 1.3km from all the reactors.

detector is CHOOZ like detector as shown in the fig.-3. The central part; the ve target is 8.5 ton Gadolinium loaded liquid scintillator. The component of the liquid scintillator is the PaloVerde type, which was proven to be stable in an acrylic container". The Gd concentration is 0.15% which is 1.5 times higher than that of CHOOZ scintillator. The higher Gd concentration is intended to increase the neutron absorption efficiency on Gd and to reduce the systematic uncertainty associating with the inefficiency. Our preliminary study shows that the scintillator is stable with 0.15% Gd concentration. The reactor Ve is detected by the following inverse /3 decay reaction. ge+ p + e+

+n

(3)

The positron annihilates with electron within a few nano seconds after slowing down in the scintillator material, then produces two 0.511MeV 7's. These process produces a prompt signal, whose energy is between 1MeV and 8MeV. On the other hand, the produced neutron is thermalized quickly and absorbed by Gd, producing y rays whose total energy amounts

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ZM

Figure 3. Schematic view of the detector. The V;. target is 8.5ton Gd loaded liquid scintillator. The re target is surrounded by 70cm thick y catcher scintillator. The y catcher scintillator is surrounded by 60cm thick buffer scintillator with very slight light output. The outer most layer is muon anti-counter made of the same scintillator as the buffer region. The far detector will be placed at the bottom of 200m shaft hole with diameter 6m. The near detectors will be placed a t the bottom of 70m depth shaft hole.

to 8MeV. The neutron absorption occurs typically 20ps after the prompt signal. By requiring the timing correlations between the positron signal and the neutron signal, backgrounds can be severely suppressed. The 2nd layer is unloaded liquid scintillator whose light output is adjusted to be

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the same as the Ve-target scintillator. This layer works as y-ray catcher. When neutrino events occur near the detector edge, y-rays from positron annihilation and neutron absorption may escape from the detector. The y-ray catcher is used to catch such y-rays and to reconstruct the original energy. The energy threshold for prompt signal is set to be below minimum positron energy (1.022MeV). In this way no systematic ambiguities associated with threshold cut is introduced. The fiducial volume is defined by the existence of correlated signals. That is, when 8MeV of energy deposit is observed after associating prompt signal whose energy is greater than lMeV, this event is considered to be lie event, regardless the positions of prompt and delayed signals. As no position cut is necessary, this method is free from position reconstruction error. The total volume of the liquid scintillator in the acrylic vessel can be measured precisely from the liquid level in the thin calibration pipe even if there is a distortion of the vessel after the installation. The 3rd and 4th layers are also liquid scintillator which has a very slight scintillation light output. These layers work as a shield of gamma rays and as cosmic ray anti-counters. The slight light output is to detect low energy muons whose velocity is below the Cherenkov threshold. Intense calibration work will be essential in this experiment to monitor the detector condition change. The whole detector will be placed in the bottom of the shaft hole with 6m diameter and 200m depth (far detector) and 70m depth (near detectors). Digging such shaft holes can be done using existing 6m diameter vertical drilling machine. The background rate is expected to be less than 2%. The major component of the background comes from fast neutrons produced in nuclear interaction caused by cosmic rays going through the rock near by. The visible energy distribution of the prompt signal in the fast neutron backgrounds was measured to be flat by CHOOZ group at the energy range below 30MeV5 and this kind of background rate can be estimated by using the event rate within non-reactor-v, energy range, such as below 1MeV and beyond 10MeV. The systematic error in CHOOZ experiment was 1.7% (detector associated) @ 2.l%(neutrino flux associated). By improving the detector system as described above, the detector associated systematics will reduce to 1.1%. When the far and near detectors are compared the ambiguity in neutrino flux mostly cancels. Even without cancellation of the detector associate systematics, the systematic error at this stage can be reduced to 1.1%. Prediction of how good the detector systematics cancellation will be is difficult. However, in Bugey case, their systematic error reduced to be half of the original error after comparing three detectors 12. If the same ratio

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is applied to this case, the detector associated systematics is expected to be reduced to 0.5% after taking near/far ratio. All these considerations are summarized in the table-1 and the the total systematic error will be 0.5-1010, where -1% is for the case that the detector cancellation does not work so well. In two years of operation, 40,000 neutrino events will be recorded in far detector and ten times more in each near detector. The statistic error will be 0.5%. The 90% CL sensitivity of this experiment is shown in the fig.-4. At Am2 3 x lOP3eV2,the sensitivity of 0.017-0.026 is expected. This is five t o seven times better limit than CHOOZ and comparable to the LBL sensitivity on sin2 2 0 ~ ~ .

-

Table 1. systematic error (%) at each stage. Detector

Flux

Total

(1) Original (CHOOZ)

1.7

2.1

2.7

(2) Detector Improvement

1.1

2.1

2.4

1.1

0.2

(3) Far/Near V;: flux Cancellation

(4)Far/Near Detector Cancellation

0.5~1

0.2

1.1 0.5-1

4. Summary and Discussions

The reactor measurements of sin22013 is important because it is a pure sin2 2813 measurement and plays complimentary role to LBL experiments. The Kashiwazaki experiment is realistic. By comparing 3 improved CHOOZ like detectors placed at appropriate locations from multi reactors, it is possible to measure sin2 2813 down to 0.017 to 0.026. If this experiment observe positive result, the accessibility t o sin 6 c p is high for future LBL experiment. Also there is a chance to determine 023 degeneracy, Amg3 hierarchy, by combining with LBL data, and even to obtain a clue to nonzero sin 6 c p before going t o i) mode. If this experiment observes negative result, it means that v3 component in v, is very small, while all other components are hundred times larger. This peculiar fact may become a key information to build unified theory of elementary particles.

Acknowledgments

FS thanks to Prof. A.Piepke for providing a sample of Gd loaded liquid scintillator and giving us precious advice of the treatment. FS thanks to Prof. H. de Karret for useful discussions about CHOOZ experiment.

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1

1.E-02 I

Expected Exclusion L=1.3km I

N40,WOevents

1

'

1

/

K2K Best fit

F

-?>,

1.E-03

0

sys=o 5%

1.E-04 0.01

0.10

1.00

sin"22ti-13

Figure 4. The expected 9O%CL exclusion region of this experiment for the case of u3,,=1% and 0.5% obtained by rate only analysis. At Am2 3 x 10W3eV2,sin2 2813 < 0.026 and < 0.017 are possible, respectively. N

References 1. 2. 3. 4.

SNO Collaboration, Phys. Rev. Lett. vol.89, 011301(2002). KamLAND Collaboration, Phys. Rev. Lett. v01.90, 021802-1 (2002). K2K Collaboration, Phys. Rev. Lett., v01.90, 041801(2003). Super-Kamiokande Collaboration, Phys. Rev. Lett. 81, 1562 (1998); Phys. Rev. Lett. 85, 3999(2000). 5. CHOOZ Collaboration, Eur.Phys.J. C27(2003) 331-374. 6. H.Minakata, H.Sugiyama, O.Yasuda, K.Inoue and F.Suekane, hepph/0211111. 7. V.Martemianov et al., hep-ex/0211070. 8. For example, JHF LoI, (http://neutrino.kek.jp/jhfnu/). 9. J. Burguer-Castell et al., Nucl. Phys. B 608, 301 (2001); H.Minakata et al., JHEPO110, OOl(2001); H.Minakata et al., NucLPhys. Proc. Suppl. 110, 404(2002); V.Barger et al., Phys. Rev. D65, 073023(2002). 10. H. Sugiyama, Talk at NuFACT03, Columbia University, June 5-11, 2003. For similar estimate, see Huber et al., hep-ph/0303232. 11. F.Bohem et al., hep-ex/0003022. 12. Achkar et al., Nucl. Phys. B434, 503-534 (1995).

THE HLMA PROJECT IN THE LIGHT OF THE FIRST KAMLAND RESULTS MEASUREMENT OF sin2 (2813) WITH A NEW SHORT BASELINE REACTOR NEUTRINO EXPERIMENT

THIERRY LASSERRE CEA/Saclay, DAPNIA/SPP 91 191 Gif-s-Yvette, France STEFAN SCHONERT Max-Planck-Institut fur Kernphysik, Saupfercheckweg 1, 0-69117 Heidelberg, Germany LOTHAROBERAUER Technische Universitat Miinchen, James-Franck-Strasse, 0-85748 Garching, Germany The year 2002 was very fruitful for low energy neutrino physics. Prior to the results of SNO and KamLAND, a few solutions were perfectly allowed by the combination of all the results of solar and terrestrial neutrino experiments. In that context, the HLMA project was originally proposed to improve the KamLAND determination of the solar mixing parameters if Am:ol 2 2 10W4e V 2 . In this article we analyse the impact of this project in the light of the first KamLAND results. Altought not new, the possibility to constraint the mixing angle between the third mass field and the electron field with a short baseline reactor neutrino experiment is explored in this article. We show that an experiment with a near detector close to a nuclear reactor and a far detector at about 2 kilometers distance could provide a limit of sin2 (2013) < 0.02 (9O%C.L.), competitive and complementary with the next generation of accelerator long baseline experiments. Nevertheless, the total systematic error uncertainty has to be reduced by a factor three with respect to the CHOOZ experiment to achieve this goal.

1. The post-KamLAND context In december 2002, the KamLAND experiment measured for the first time a deficit in the D, flux coming from surrounding nuclear reactors located at an average distance of 180 kilometers '. Among 86 events expected in the no-oscillation hypothesis only 56 have been observed, indicating that

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the MSW large mixing anlge solution (LMA) is realized in the nature. The HLMA project proposed in 2002, aimed to improve the solar mixing parameter determination in case the true Am:,, 2 lop4eV2. At these high values of Am:,, Ve oscillations are averaged at the KamLAND site because the distances between the detector and the reactors are too large. In consequence, no distorions due to neutrino oscillations are imprinted on the positron energy spectrum and consecutively, the accurate determination of the solar mixing parameters becomes impossible. By taking the KamLAND results alone, a large fraction of the HLMA region is still allowed at 95% C.L.. However, the best fit is obtained at Am:,, = 7 eV 2 , and a maximal mixing angle. Nevertheless, error on the determination of the mixing angle at KamLAND with this low statistics remains quite large, a few tens of percent. On the other hand, the combination of all the solar and terrestrial neutrino experiments allow to restrict the parameter space to two solutions, named low-LMA (at roughly the same position as the best KamLAND fit) and high-LMA, with a Am:,, 1.5 - 3 e V 2 at 99% C.L. The low-LMA is more favored by the present KamLAND data, but the high-LMA solution should not be neglected a priori. In that context, the future goal of the next experiments is to isolate one of the two islands and t o do a precise measurement of the solar mixing parameters. If the true solution is the low-LMA, it is highly probable that the best measurement will be done by the KamLAND experiment. Another experiment could certainly improve the determination of the mixing angle by having a detector at the first minimum of oscillation, which is around 70km for this particular solution (the measurement could be pushed down to the systematic error uncertainty limit of approximatly 2%.) If the solution is high-LMA, then preliminary estimation shows that even with 5 times the kamLAND published sensitivity l, no unique solution can be isolated. In that case, it is likely that another reactor experiment with a shorter baseline is needed to pin down the right solution and the solar mixing parameters. It is worth noting the a measurement of those parameters with a precision of less than 10% is mandatory to interpret the data of the future generation of accelerator long baseline experiments.

>

-

2. The HLMA project

2.1. The HLMA project at Heilbronn As discussed in the previous section, if Am:,l 2 2 . lop4 eV2 (HLMA region), a new medium baseline reactor neutrino experiment (- 20 km) will

165

be needed to measure precisely the solar mixing parameters. In that particular case, we propose to locate a detector in the Heilbronn salt mine (Germany). p, detection is done via inverse beta decay on protons ( p e p + e+n), and pe energy is derived from the measured positron kinetic energy. If the true Am:,, lies in the HLMA region, such an experiment would observe a reduction of the 0, flux coming mainly from two nuclear plants, both located at 19.5 km, as well as a strong distortion of the positron spectrum. The shape analysis allow the accurate determination of the mixing parameters (in that regime, KamLAND would only see a global rate suppression, and could only derive a lower limit on Am:,,). Including all European nuclear reactors, a detector containing 1031 free protons would detect N 1150 0, interactions per year, among which 77% originate from the two closest reactors Neckarwestsheim (6.4 GWth) and Obrigheim (1.1 GWth). Nevertheless, it is likely that the Obrigheim reactor, that was coupled to the power network in 1968, could be shut down in the coming years ; in that case, only 74% of the flux would come from the 20 km baseline, and one would then loose 11%of the total flux. With this target mass, a 10% rate suppression would be detectable a t a 30 level after one year of data taking. Preliminary simulations indicate that Am:,, can be recontructed at 5% (10 error) in the HLMA area while the error on sin2 20,,1 would be a few percent, depending on the solar mixing angle (Fig. 1.) At the considered baseline, both V , oscillations due to Am:,, and Am2,,, can develop without being averaged if Am:,, 6 Am:,, and Ue3 # 0. The envelop of the positron spectrum is roughly given by the two-neutrino solar mixing, whereas ripples are imprinted with the “atmospheric” frequency and an amplitude proportional t o (Ue312. This would allow a lo3’ free protons scale experiment to put additional constraint on lUezl down to a few percents. The proposed detector is a PXE based scintillator contained in a vessel surrounded by ultra-pure passive water shielding, viewed by a PMT-sphere ( r > 5m, 30% optical coverage) mounted on an open structure which separates optically the outer part of the detector that is used as a muon veto. This design allows the background rate (primordial -and man-made g/g radioactivity) t o be less than 1 event/year, if U, Th, K 5 5 x for the water buffer and U, Th 5 g / g for the PXE sintillator. At the salt mine depth (480 mwe to 640 mwe), cosmic ray muons dominate the trigger rate (76 (36)/h/m2). Fighting the correlated and uncorrelated muon induced background (interactions in the detector or in the surrounding rocks) would be the challenge of the design, implying the optimisation of the water shielding, as well as the pulse shape discrimination techniques N

166

in order to stop or tag muon induced events with a very high efficiency.

r

~LMA Hellbmnn: 1151 3 y (201

*asno osc) E-nu s1.8 MeV (averaged)

_I

N2 U

.................

..............

Q ..... . . & .....:. .... ...............:.

...........

10'

0.5

0.6

0.7

0.8

0.9 1 sin2(2 q2)

Figure 1. Preliminary estimation of the sensitivity of the HLMA project at the Heilbronn salt mine site. One considers a detector containing 115 tons of PXE liquid scintillator, running for 3 years (assuming 100% life time for the reactor, and 100% detection efficiency). Sensitivity to perform a good determination of the mixing parameters starts just below Am:,1 2 . lop4 eV2, which is not optimal to probe the high-LMA solution. However, a good sensitivity is obtained for Am:ol ;L 2 . l o p 4 eV2.

-

2.2. The H L M A at Boulby Originaly the HLMA project baseline of 20 km was chosen to start to be sensitive to spectrum distortions exactly when KamLAND stop to be sensi2 . lop4 eV2. But according to the first tive. This corresponds to Am:,, KamLAND results, the high-LMA solution is at Am:,, 1.5 -3.10W4 eV2,

-

N

167

not optimum neither for KamLAND nor for the HLMA a t Heilbronn (the baseline is a little bit too short to perform a precise Am:,, measurement.) Therefore, an experiment at a around 50 kilometers would provide excellent results to pin down the solar mixing parameters. However, since the no-oscillation flux decreases with the square of the distance it is preferable to have a closer detector t o keep the target size as small as possible. The minimum baseline to obtain a good sensitivity in the high-LMA region is 25 km (sensitivity to Am:,, would then start at 1.2 . lop4 eV2.) It turns out that there already exists a site located at this precise distance from a nuclear power plant: the Boulby mine in UK ‘. The Boulby mine is already used for physics activities. At a depth of 1100 meter rocks, it is well shielded for cosmic ray muons (attenuation of roughly one million.) Detector design constraints could then be relaxed with respect to the Heilbronn salt mine case, since the latter site is much shallower. The Hartlepool reactor (AGR type, 3.1 GWth) located at 25 km from the Boulby site would provide 81% of the total flux in the no-oscillation case. Among the surrounding nuclear power plants 6% of the flux would come from the Heysham reactor (- 150 km, 5.9 GWth). The rest of the f i e flux is shared by all other european nuclear plants, mainly in UK and France. A detector containing a target volume of 500 tons of PXE liquid scintillator and taking 3 years of data (we consider for simplicity that both reactor and detector work with 100% efficiency) would lead to 2000 events in the no-oscillation case. Precision of the solar mixing parameter detecrmination are shown on Fig. 2; this shows that at the Boulby site, one has not only the possibility to discriminate between the low-LMA and high-LMA solutions, but also to measure the mixing parameter values within the latter solution at the level of 5% percent ( 1 ~ ) .

-

-

-

3. Measurement of sin2 (2&) neutrino experiment

with an optimum reactor

Altough not innovative, the idea to get a strong constraint on sin(2813)’ with a new short baseline reactor neutrino experiment has been growing all around the world since a few months. The best limit is still the property 2 of the CHOOZ experiment with the upper bound sin(2813) _< 0.14, at 90% C.L., for Am:,, = 2.5. 10W3 eV2. To obtain this limit, the CHOOZ experiment was looking at the disapearance of reactor 0, coming from a two core power plant located at about 1 km from a 5 tons Gd-loaded liquid scintillator based detector. It now appears that 1 km is not the optimum

168

Boubly: 5OOt 3 y (2000 evts no osc) E-nu 21.8 MeV (averaged)

Nz

I

U

...................

(;..:,,.$&&:)

...............

..........

Q .>........... ......... 10-

0.5

0.6

0.7

0.8

0.9

1

sin2(2 CI,~)

Figure 2. Preliminary estimation of the sensitivity of the HLMA project at the Boulhy mine site. One considers a detector of 500 tons of PXE liquid scintillator, running for 3 years (assuming 100% life time for the reactor, and 100% detection efficiency). Sensitivity starts at Am:ol N 1.2 . l o p 4 eV2, which is sufficient to discriminate between the lowLMA and high-LMA solutions, hut also t o probe the value of the mixing parameters within the high-LMA solution.

baseline to perform such a measurement; indeed, for the best value of the atmospheric mass splitting Am:,, N 2.5 . lop3 eV2, the optimum baseline would be 1.8 km (at the first minimum of the atmospheric oscillation to maximize the total rate suppression for a given value of sin (2OI3)'.) It is worth noting that an experiment at this optimum baseline is rather insensitive t o variations of the Am:,, value, compared to shorter baseline such as CHOOZ or Krasnoyarsk for instance. The sin (2613)' parameter, which plays a very important role for the future neutrino oscillation experiments,

169

can also be measured by accelerator neutrino long baseline experiment. In such a case, one has to detect u, appearance in an almost pure up beam. Altough the observation of an excess of u, would already be a major result, the interpretation of the Superbeam experimental results would be very difficult. Indeed, on the top of both statistical and experimental errors, there are degeneracies due to the lack of knowledge concerning the neutrino mass hierarchy (the electron field being the heaviest or the lightest), the octant in which lies the atmospheric mixing angle 023 (if non maximum), and the 6-CP phase that prevent t o pin down the sin (21913)~value. For instance, the JHF to Superkamiokande experiment sensitivity would be sin(2fi$3)2 5 0.006 at 90% C.L. by neglecting all the degeneracies, but only sin (2813)~ 0.017 at 90% C.L. if one includes this lack of knowledge in the analysis g . On the other hand, since reactor neutrino experiment is a disapearance experiment type, the 6-CP phase value has absolutely no impact on the measurement. Furthermore, since Ve produced by reactors have only a few MeV energy, and the baseline is only a few kilometers, the matter effects can be safely neglected; indeed, they contribute at the level of 10W4. To summarize, the reactor experiment measurement gives a clean constraint on sin (2013)’; unfortunatly, low sin (2813)2 values are difficult to detect since a reactor experiment look for a disapearance of the fie predicted flux (the integrated reactor V , rate is known with an error of 2%.) The total CHOOZ systematic error was 2.8% (dominated by the reactor flux uncertainty). To be as sensitive as the future generation of accelerator neutrino experiments, one has to lower this global systematic error by a factor 3 (this contains errors on the reactor flux, on the detector design, on the backgrounds control, and on the V , tagging efficencies). This is only possible by using a set of two detectors. The principe is simple, the first detector is located close to the nuclear power plant (< 500m) to monitor the flux while the second detector is located at 1.8 km, to detect a small neutrino oscillation effect. To reduce the value of the systematic error, both detector should be identical, and ideally, they should have roughly the same signal to background ratio. Analysis is done by comparing energy spectra of both detectors (bin by bin) in order to detect a total rate suppression and a spectral shape distortion. Even if the near and far detector are identicals, the calibration procedure would be crucial to demonstrate that one controls the overall systematics at the level of the percent. One could also consider to have a far detector that could be moved close to the near detector for calibration purpose (on a railway for instance.) Beside the statistical error uncertainties, the statistics should be also increased to at least 40000 events

<

N

170

(0.5% error). For example, this corresponds to a detector of 20 tons, located at 2 km from a reactor of 10 GWth, taking 5 years of data (assuming a 70% overall efficiency). As usual for this kind of project, the first most serious problem is to find a place to do the experiment. It is even more difficult in the case under study, since one has many requierements: one needs two cavities, located underground, and the near detector cavity has to be very close to the nuclear core(s). In addition, in order to decrease the muon induced backgrounds, the far detector has to be protected be at least 300 mwe, while the near detector site has to be located roughly between 100 and 300 mwe, depending on its position with respect t o the nuclear plant. To control the backgrounds, two different cases have to be considered: the single nuclear core experiment, as the Kr2Det project ', where one can measure in situ the backgrounds during the reactor off periods (but the signal to noise ratio is rather low, typically a few tens), and the multi-cores experiment, where on/off measurement is impossible, but a very high signal to noise ratio can be achieved. For instance, with a signal to noise ratio of 100, a 10% knowledge of the backgrounds leads to a 0.1% additional systematic error. To answer all these questions, an european working group has been formed in 2002. The goal is to address the feasibility of such an experiment and t o look for potential sites. To be competitive a reactor neutrino project needs to start roughly at the same time as the next generation long baseline neutrino experiments, around 2008. Nevertheless, if a positive signal is detected by accelerator appearance experiments, any reactor neutrino result (positive or negative) would allow a better interpretation and constraint on the sin (2813)~- 6 - 823 - sign(Am:,,) parameter space. References 1. K. Egushi et al. (KamLAND), Phys. Rev. Lett. 90, 021802 (2003), hepex/0212021. 2. S. Schonert, T. Lasserre, L. Oberauer, Astropart. Phys. 18, 565 (2003), hepex/0203013. 3. G.L. Fogli et al., hep-ph/0212127. 4. http://hepwww.rl.ac.uk/ukdmc/boulby/boulby.html 5. M. Apollonio et al. (CHOOZ), Phys. Lett., B466, 415 (1999), hepexp/9907037. 6. V. Martemyanov et al., hep-exp/0211070. 7. Y.Itow et al., Nucl. Phys. Proc. Suppl., 111, 146, (2001). 8. P. Huber et al., hep-ph/0303232.

USING REACTORS TO MEASURE

eI3

M. H. SHAEVITZ AND J. M. LINK COLUMBIA UNIVERSITY, DEPT. OF PHYSICS NEW YORK, NY 10027, USA A next-generation neutrino oscillation experiment using reactor neutrinos could give important information on the size of mixing angle 813. The motivation and goals for a new reactor measurement are discussed in the context of other measurements using off-axis accelerator neutrino beams. The reactor measurements give a clean measure of the mixing angle without ambiguities associated with the size of the other mixing angles, matter effects, and effects due to CP violation. The key question is whether a next-generation experiment can reach the needed sensitivity goals to make a measurement for sin2 2013 at the 0.01 level. The limiting factors associated with a reactor disappearance measurement are described with some ideas of how sensitivities can be improved. Examples of possible experimental setups are presented and compared with respect to cost and sensitivity.

1. Motivation and Goals of a Next-Generation Reactor

Oscillation Experiment Information on the masses and mixing angles in the neutrino sector is growing rapidly and the current program of experiments will map out the parameters associated with the solar, atmospheric, and LSND signal. With the recent confirmation by KamLAND and isolation of the Amzozarin the LMA region, the emphasis of many future neutrino oscillation experiments is turning t o measuring the last mixing angle, 613 and obtaining better precision on Amzozar and Am:,, (along with checking LSND). A road map for future, worldwide neutrino oscillation measurements can be considered as connected stages. Stage 0 includes the current program with K2K, CNGS, and NuMI/Minos probing the Am:,, region with the goal of measuring Am;, to about 10%. MiniBooNE over this time period will make a definitive check of the LSND anomaly and measure the associated Am2 and mixing if a signal is observed. A next step, Stage 1, would have the goal of measuring or limiting the value of 613. At this stage, experiments could possibly see the first indications of C P violation and matter effects if 013 is large enough. For

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013, the NuMI/Minos on-axis experiment has sensitivity for sin2 2813 > 0.06 at 90% CL. Better sensitivity experiments are being proposed for this stage including the NuMI and JHF off-axis experiments along with two detector reactor experiments. The combination of off-axis and reactor measurements is a powerful tool for isolating the physics. In the end, these experiments need to provide information on sin22013 > 0.01 a t the 3a measurement level as a prerequisite for building the expensive Stage 2 experiments. The goal of Stage 2 would be to observe C P violation and matter effects. One component of this stage will be high intensity neutrino sources combined with large detectors (> 500 ktons) at long baselines. Due to ambiguities in how the various physics processes manifest themselves, the program is best accomplished using a combination of high statistics neutrino and antineutrino measurements at various baselines combined with high statistics reactor measurements. If Stage 2 is successful, a Stage 3 would use a muon storage ring, neutrino factory to map out C P violation in the neutrino sector and make measurements with a precision one to two orders of magnitude better than Stage 2. For measuring 6'13, reactor measurements are an important ingredient if the required sensitivity can be reached. Reactors are a very high flux source of antineutrinos and have been used in the past for several neutrino oscillation searches and measurements (Bugey, CHOOZ, Palo Verde, and KamLAND) . Currently, several groups are considering new reactor oscillation experiments with the primary goal of improved sensitivity to the MNS mixing angle, 013. To improve sensitivity, the new experiments will use a comparison of detectors a t various distances from the reactor thus minimizing the uncertainties due to the reactor neutrino flux. 2. Appearance versus Disappearance Measurements An appearance measurements of 613 can be accomplished by observing an excess of v, events in fairly pure up beam. The measurement is difficult since the signal is a small number of v, events over a comparable background. The proposed new JHF-SuperK' and NuMI off-axis2 experiments are t o use far detectors placed off-axis with respect t o the neutrino beam direction. Due to the kinematics of pion decay, the off-axis setup gives a beam with a sharp energy spectrum which minimizes neutral current 7ro backgrounds and allows the energy to be tuned t o the first oscillation maximum. The off-axis experiments measure the v, + v, transition probability as given in Eq. 1 (where sin023 = * '-

2

and Aij = Am??L/(4E)=

173 NuMI

JHF - 295 km

Figure 1. Ambiguity bands for interpreting the vI14v, transition probability in terms of sin2 6’13 for the NuMI (712 km), left, and the JHF (295 km), right. The main part of the bands on the left are due to the value of 6 and that on right from whether Q23 < ~ / 4 or > ~ / 4 .(From Ref. 3)

( m l - m?)L/(4E) ). This transition probability is mainly proportional t o sin2 2OI3 but has ambiguities from the knowledge of sin’ 623 as well as matter and CP violation effects. The ambiguities can enhance or reduce the oscillation probability as shown i.n Fig. l3where the bands reflect the uncertainties in 6 and 023.

On the other hand, a reactor disappearance measurement looks for indications of a reduced rate of V , events in a detector at some distance from the source. The disappearance measurement directly measures sin2 2613 without ambiguities from CP violation and matter effects.

P(V, + pe) = 1 - sin2 2613 sin2 A31 - ...

(2)

Thus, an unambiguous measurement of 613 using reactors can be a powerful tool when combined with off-axis measurements to probe for CP violation and the neutrino mass h i e r a r ~ h y .The ~ ’ ~ question is whether a next generation reactor experiment can reach the required sensitivity. In a disap-

174

pearance measurement, one needs to be able to isolate a small change in the overall rate which can be difficult due to uncertainties in reactor flux, cross sections, and detector efficiencies. As stated above, sensitivities in the range of sin’ 2813 M 0.01 should be the goal. 3. Limiting factors in a reactor disappearance measurement

Previous reactor disappearance experiments used a single detector at a distance of about 1 km from the reactor complex. Antineutrinos from the reactor were detected using the inverse &decay reaction followed by neutron capture on hydrogen or gadolinium. -

v, + p

+

e+

+n

(3)

L n + p ( G d ) + 2.2(8) MeV The two component coincidence signal of an outgoing positron plus gammarays from the neutron capture is powerful tool to reduce backgrounds and isolate reactor antineutrino events. The major systematic uncertainty was the 2.8% uncertainty associated with the reactor flux. The CHOOZ experiment6 used a five ton fiducial volume detector under 300 mwe of shielding at 1 km from two 4.25 GW reactors. The event rate was -2.2 events/day/ton with 0.2 to 0.4 background events/day/ton. The other recent experiment to probe this region was the Palo Verde experiment7 which used a 12 ton detector under on 32 mwe of shielding at an average baseline of 850 m from three 3.88 GW reactor. For Palo Verde the event rate was -7 events/day/ton over a large background rate of 2.0 events/day/ton. Improvements to these previous experiments can be accomplished in several areas. Higher statistics are needed which demands larger detectors in the 50 ton range and/or larger power reactors. To reduce the dominant reactor flux spectrum and rate uncertainty, a next generation experiment would need two detectors at near and far locations. The observed rate in the near detector can then be used to predict that in the far detector where oscillation effects are to be probed. Making the near and far detectors identical will reduce relative efficiency uncertainties. In addition, providing the capability to move the far detector to the near site allows a direct cross calibration of the two detectors using the high rates available at the closer distance. Accurate knowledge of background rates especially in the far site are necessary. To accomplish the needed uncertainty level demands a combination of shielding, background measurements, and an excellent veto

175

system. The spectrum of reactor antineutrinos has a broad distribution peaking near an energy of 3.5 MeV. For a Am2 = 2.5 x lop3 eV2, there is a broad optimum for the position of the far detector between about 1 and 2 km. For smaller Am2 = 1x lop3 eV2, the sensitivity degrades by about a factor of two as the optimum position is pushed out toward 3 km. As an example experiment, we consider two 50 ton detectors located for three years near a 3 GW reactor with the near detector at 150 m. The statistical sample in a far detector at 1to 2 km would range from 23,000 to 92,000 events leading to a statistical error, &sin22013 0.003 - 0.007 Ct 90% CL. Assuming an overburden, of 300 mwe and 0.2 background events/kton/day gives 9000 background events in the far detector. The background rate can be measured to 3% during reactor off periods at a single reactor site leading to measurement uncertainty of 6 sin2 2OI3 = 0.004. At multiple reactor sites, there typically is no time when all reactors are off. Extrapolations using partial shutdowns lead to large background uncertainties corresponding to &sin22013 in the 0.01 - 0.02 range. As discussed below, the effective background rate can be substantially ( x 10) reduced by using an extensive veto system combined with passive shielding. With such a system, the measurement uncertainty can be reduced to the level of a single reactor site. The final major uncertainty is associated with the near to far comparison. With identical detectors, relative efficiency errors of 1 to 2% should be obtainable leading to measurement uncertainties for sin2 2013 in the 0.02 range. If the far detector can move to the near detector site, a cross calibration could reduce this uncertainty by a factor 2 to 4 depending on the detailed scenario. Extrapolating from the previous CHOOZ and KamLANDs detectors, a next generation detector could be improved in several ways. These detectors used liquid scintillator with buffer regions to cut down backgrounds from radioactive decays and cosmic ray muons. Possible improvements include low activity photomultipliers, an improved veto and shielding system, and capability to move detectors for cross calibration. Adding gadolinium to enhance the neutron capture signal is being considered but may effect the long term stability. As stated previously, electron antineutrino signal events are isolated using a coincidence requirement of an outgoing positron followed by a neutron capture. Background events that mimic these requirements can be divided into two types, uncorrelated and correlated. The uncorrelated background involves two independent events that randomly occur in close proximity

176

in time and space. This type of background can be minimized with low activity passive shielding and be measured t o high precision by swapping the order of the components of the signal definition. The correlated backgrounds, where both components come from the same parent event, are more problematic. Examples of this type of background are two spallation neutrons from the same cosmic ray muon or a proton recoil produced by a fast neutron. Several methods are available to mitigate the effects of these correlated backgrounds. Shielding is an effective method to reduce the cosmic ray rate. For example, the background rate for a detector at a depth of 300 (600) mwe is 0.2 (0.1) events/ton/day. One can also create an effectively larger depth by using a high efficiency veto system to detect and cut out the cosmic-ray muon events that might initiate these backgrounds. Initial studies indicate that such a system might reduce the effects of the above background rates by an order of magnitude to a very low level. The surviving background rate will still need to be measured but now a t only the 25% level. This can be achieved by using vetoed events to study distributions and extrapolate into the signal regions.

4. Examples of possible measurements and comparisons From the discussion above, the requirements for a next generation reactor experiment would include a high power, probably multi-reactor site with the ability to construct halls and possibly tunnels for the detectors. Hill or mountains near the site allow more cost effective tunnelling. The ability to move the far detector t o the near site is very desirable and may be crucial to obtain sensitivities for sin2 2813 down to 0.01. Many single and two reactor sites exist in the U.S. with average thermal power in the 3 to 3.5 GW range per reactor. As an example, the Diablo Canyon site has an average thermal power of 6.1 GW. There are good access roads and nearby hills that would allow horizontal tunnelling for a far site at 1.2 km with over 600 mwe of shielding. A three year run of two 50 ton fiducial volume detectors would provide about 120,000 events in the far detector over a background of 4900 events and lead t o a sensitivity of eV2 as shown in Fig. 2. sin2 2813 = 0.01 Q 90% CL for Am2 = 2.5 x Comparisons of various reactor experimental setups are listed in Table 1. The examples assume three years of data with two 50 ton detectors at 150m and 1200m from one or two 3 GW reactors. The cost basis uses a MiniBooNE cost model for the detector and estimates from a Fermilab NuMI engineer for the tunnels and halls. The cost inputs were $5M for the

177

10

-4

I

' ' l l l m '

10 -z

I

I

10

1

Sensitivity at Diablo Canyon (6.1 GW, 50 tons, 3 yean)

sin%,,

Figure 2. Sensitivity of a n oscillation experiment at the Diablo Canyon site with two 50 ton detectors at 150m and 1200m running for 3 years. T h e far detector is at a depth of 600 mwe and the uncertainties in the relative near t o far detector efficiency and far background rate are assumed t o be 0.16% and 3.5% respectively.

detector, $2-3M for a detector hall and $15-17M for a 1 km tunnel a t 300600 mwe depth. Tunnels were only included for the movable far detector scenarios. Table 1. Comparison of various reactor oscillation experiment scenarios. T h e sin' 2813 column gives the sensitivity at 90% CL for Am2 = 2.5 x eVZ. The background contamination is 10,000(5,000) for 300(600) mwe which is assumed t o be measured with a n uncertainty of 3.5% Source One Reactor

Depth(mwe) 300 600

Two Reactors

300 600

Detector Fixed Movable Fixed Movable Fixed Movable Fixed Movable

Events Far

Rel. Norm Err.

Cost ($M)

sin' 2013

64,000 57,000 64.000 57,000 128,000 115,000 128,000 115,000

0.008 0.0023 0.008 0.0023 0.008 0.0016 0.008 0.0016

14 25 16 27 14 25 16 27

0.022 0.017 0.020 0.014 0.018 0.011 0.017 0.010

178

5 . Summary

A next generation reactor experiment could reach a sensitivity to oscillaeV2 at the 90% CL. The tions with sin2 2OI3 = 0.01 and Am2 = 2.5 x timescales appear reasonable as a complement to the expected appearance measurements and the cost are not prohibitive. Reactor experiments can be combined with neutrino only running of off-axis appearance experiments to isolate CP violation and matter effects. To design a reactor experiment with 3a sensitivity down to sin2 2813 = 0.01 will require improvements to the background measurement along with the substantial betterments of the near to far detector comparison. If a suitable site can be found and if these improvements can be made, a reactor disappearance measurement will become a key ingredient to the understanding of neutrino masses and mixing angles. Several groups around the world are considering this possibility and expected to submit proposal over the next year. References 1. “Letter of Intent: Neutrino Oscillation Experiment at JHF”, http://neutrino.kek.jp/jhfnu/loi/loi-JHFcor.pdf . 2. “Letter of Intent to build an Off-axis Detector to study v p + ve oscillations with the NuMI Neutrino Beam”, http://www-numi.fnal.gov/other/newinitiatives /loi-6.0O.ps . 3. P. Huber, M. Lindner, and W. Winter, NudPhys., B654, 3 (2003) hepph/0211300 . 4. H. Minakata et al. , hep-ph/0211111. 5 . P. Huber, M. Lindner, T. Schwetz, and W. Winter, hep-ph/0303232 6. M. Apollonio et al. (CHOOZ Collab.), Eur.Phys.J., C27 (2003) hepex/0301017. 7. F. Boehm et al. (Palo Verde Collab.), Phys.Reu., D64, 112001 (2001) hepex/0107009 8. K. Eguchi et al. (KamLAND Collaboration), Phys. Rev. Lett. 90, 021802 (2003) hep-ex/0212021. 9. See for example: http://home.fnal.gov/4ink/theta-l3/,

http://kmheeger.lbl.gov/thetal3/, http://nuspp.in2p3.fr/Reactors/thetal3~parissummary.htm, hep-ex/0211070, hep-ph/0211111.

IMPACT OF U a ON NEUTRINO MODELS

M. TANIMOTO Department of Physics, Niigata University, Ikarashi 2-8050, 950-2181 Niigata, J A P A N E-mail: tanimoto @muse.sc. niigata-u. ac.jp We have discussed the impact of Ue3 on the model of the neutrino mass matrix. In order to get the small Ue3, some flavor symmetry is required. Typical two models are investigated. The first one is the model in which the bi-maximal mixing is realized at the symmetric limit. The second one is the texture zeros of the neutrino mass matrix.

1. Introduction In these years empirical understanding of the mass and mixing of neutrinos have been advanced 1 , 2 , 3 . The KamLAND experiment selected the neutrino mixing solution that is responsible for the solar neutrino problem nearly uniquely 4 , only large mixing angle solution. We have now good understanding concerning the neutrino mass difference squared and neutrino flavor mixings A constraint has also been placed on the mixing from the reactor experiment of CHOOZ These results indicate two large flavor mixings and one small flavor mixing. It is therefore important to investigate how the textures of lepton mass matrices can link up with the observables of the flavor mixing. There are some ideas to explain the large mixing angles. The mass matrices, which lead to the large mixing angle, are “lopsided mass m a t r i ~ ” “democratic ~, mass matrix” and “Zee mass m a t r i ~ ” ~These . textures are reconciled with some flavor symmetry. We have another problem. Is the small Ue3 always guaranteed in the model with two large mixing angles? The answer is “No”. There are some models to give a large Ue3. The typical one is “Anarchy” mass matrix l o , which gives a rather large Ue3. Another example is the model, in which the large solar neutrino mixing comes from the charged lepton sector while the large atmospheric neutrino mixing comes from the neutrino sector. In this model Ue3 = 1 / 2 is predicted.

‘.

*

179

180

In order to get the small Ue3, some flavor symmetry is required. Typical two models are investigated in this talk. The first one is the model in which the bi-maximal mixing is realized at the symmetric limit. The second one is the texture zeros of the neutrino mass matrix. 2. Deviation from the Bi-Maximal Mixings

We consider the symmetric limit with the bi-maximal flavor mixing at which Ue3 = 0 as follows 11: (0)ui u, = Uai

,

(1)

where

One can parametrize the deviation U ( l )in u, = [U(')+ U(o)],iui as follows: ~ ( 1= )

(=

-ci3si2

c:3c:2

s1 23 51 13c1 12 ei4

c:3s:2

ci3ci2- s123 5113 3112 ei4

31

e-i4

)

4 3 4 3 (3) ci3si3s&ei4 4l 33 4 3 where s:j sin8ij and cij = cos8ij denote the mixing angles in the bimaximal basis and is the CP violating Dirac phase. The mixings s i j are expected to be small since these are deviations from the bi-maximal mixing. Here, the Majorana phases are absorbed in the neutrino mass eigenvalues. Let us assume the mixings s i j to be hierarchical like the ones in the quark sector, si2 >> si3 >> s&. Then, taking the leading contribution due to s&, we have S;~S&

-

- c;3si3cizei4

-s;,&

-

which lead to

Thus, the solar neutrino mixing is somewhat reduced due to si2. By using the data of the solar neutrino mixing, we predict the small Ue3 such as

which is testable in the future experiments. In the next section, we present another approach, texture zeros.

181

3. Texture Zeros of Neutrino Mass Matrix

The texture zeros of the neutrino mass matrix have been discussed to explain these neutrino masses and mixings l 2 > l 3 , l 4 Recently, . Frampton, Glashow and Marfatia l5 found acceptable textures of the neutrino mass matrix with two independent vanishing entries in the basis of the diagonal charged lepton mass matrix. The KamLAND result has stimulated the phenomenological analyses of the textlure zeros 16,17,18)19. These results favour texture zeros for the neutrino mass matrix phenomenologically. There are 15 textures with two zeros for the effective neutrino mass matrix Mu, which have five independent parameters. The two zero conditions give 3

(Mv)ab

=

3

UaiUbiXi

=0

,

( M v ) a p= E U a i u p i X i = 0

i= 1

, (7)

i=l

where X i is the i-th eigenvalue including the Majorana phase, and indices (ab) and (ap) denote the flavor components, respectively. Solving these equations, the ratios of neutrino masses m l , m2, m3, which are absolute values of Xi's, are given in terms of the neutrino mixing matrix U 2o as follows:

Then, one can test textures in the ratio R,,

which has been given by the experimental data. The ratio R, is given only in terms of four parameters (three mixing angles and one phase) in

u=

(

c13c12 -C23S12 -

s23s13c12eis

s 2 3 s 1 2 - c23s13c12ei6

c13s12 c23C12

-s23c12

- s23s13s12ei6 - c23s13s12ei6

s13e@ s23c13

c23c13

1

(10)

where cij and sij denote cos8ij and singij, respectively. Seven acceptable textures with two independent zeros were found for the neutrino mass matrix 15, and they have been studied in detail 17,18.Among them, the textures A1 and A2 15, which correspond to the hierarchical neutrino mass spectrum, are strongly favoured by the recent phenomenological analyses l6>l7,l8. Therefore, we study these two textures in this paper.

182

= 0 and

In the texture A l , which has two zeros as the mass ratios are given as

In the texture Az, which has two zeros as mass ratios are given as

= 0,

= 0 and

= 0, the

+ slse-is

If 812, 023, 013 and 6 are fixed, we can predict R, in eq.(9), which can be compared with the experimental value Am~,,/Am~t,. Taking account of the following data with 90% C.L. 5 , sin2 2Bat, 2 0.92 ,

Am:,,

= (1.5

-

0.67 ,

Am:,,

= (6

8.5) x 10V5eV2,

tan2 B,,

= 0.33

-

-

3.9) x 10-3eV2

, (13)

5 0.2, we predict R,. In Fig.1, we present the scatter plot

with sinB,,,,,

A1

0.3

R"

.

I

.:;I

..:. .. : ..y : ...

.

;

0.2

0.1

0.05

0.1

0.15

0.2

Figure 1. Scatter plot of R, versus sin013 for the texture A1. The unknown phase 6 is taken in the whole region -7r T . The gray horizontal band is the experimental allowed region. N

183

of the predicted R, versus sin813, in which 6 is taken in the whole range -7r 7r for the texture A1. The parameters are taken in the following rangesin812 = 30" 39", 823 = 37" 53", 813 = 1" 12" a n d 6 = -7r 7r with constant distributions those are flat on a linear scale. It is found that many predicted values of R, lie outside the experimental allowed region. This result means that some tunings among four parameters are demanded to be consistent with the experimental data. We get sin613 2 0.05 from the experimental value of R, as seen in Fig.1. In order t o present the allowed region of sin 613, we show the scatter plot of sin813 versus tan' 812 and tan2 823 in Fig.2 and Fig.3, respectively, for the texture Al. For the texture A2, the numerical results is similar with the one in the texture A1 because those are obtained only by replacing tan823 in A1 with - cot 823. The allowed regions in Fig.2 and Fig.3 are quantitatively understandable in the following approximate relations:

-

N

N

N

N

for the texture A l , and

for the texture AZ, respectively, where the phase 6 is neglected because it is a next leading term. As tanO12 increases, the lower bound of IUey increases, and as tan823 decreases, it increases. It is found in F i g 2 that the lower bound IUe31 = 0.05 is given in the case of the smallest tan2&2, while IUe31 = 0.08 is given in the largest tan'812. On the other hand, as seen in Fig.3, the lower bound IUe31 = 0.05 is given in the largest tan' 823, while JUe31= 0.08 is given in the smallest tan' 823. In the future, error bars of experimental data in eq.(13) will be reduced. Especially, KamLAND is expected to determine Am:, precisely. Therefore, the predicted region of lUe31 will be reduced significantly in the near future. Above predictions are important ones in the texture zeros. The relative magnitude of each entry of the neutrino mass matrix is roughly given as follows: O

M u - (0 A

O

A

1 1) 1 1

forA1,

(i 1 u)

for A2

,

(16)

where X !Y 0.2. However, these texture zeros are not preserved to all orders. Even if zero-entries of the mass matrix are given at the high energy scale,

184

0.5

1

1.5

2

2.5

3

tan2e12

Figure 2.

Scatter plot of sin 813 versus ta n 2 812 for the texture A1.

0.5

1.5

2.5

tan2e,, Figure 3.

Scatter plot of sin 6'13 versus tan2 823 for the texture A1

non-zero components may evolve instead of zeros at the low energy scale due to radiative corrections. Those magnitudes depend on unspecified interactions from which lepton masses are generated. Moreover, zeros of the neutrino mass matrix are given while the charged lepton mass matrix has off-diagonal components in the model with some flavor symmetry. Then, zeros are not realized in the diagonal basis of the charged lepton mass matrix. In other words, zeros of the neutrino mass matrix is polluted by the small off-diagonal elements of the charged lepton mass matrix. Therefore, one need the careful study of stability of the prediction for Ue. because this is a small quantity. In order to see the effect of the small non-zero components, the conditions of zeros in eq.(7) are changed. The

185

two conditions turn t o

where 6 and w are arbitrary parameters with the mass unit, which are much smaller than other non-zero components of the mass matrix. These parameters are supposed to be real for simplicity. For the texture A l , we get

m3

U I ~ U I ~ U I ~-UUZ I Z U I ~ U ~ ~U12U22E U ~ ~ + U12U125 Ul2 u12 Ull U2l - Ul 1Ull u12 u 2 2

where and 5 are normalized ones as ? = E /A3 and w = w/XQ, respectively. We obtain approximately

where

tij = tan6ij.

The JUe3)= sin613 is given as

It is remarked that the second and third terms in the right hand side could be comparable with the first one. In order to estimate the effect of 5 and E , we consider the case in which the charged lepton mass matrix has small off-diagonal components. Suppose that the two zeros in eq.(16) is still preserved for the neutrino sector. The typical model of the charged lepton is the Georgi-Jarlskog texture ’l, in which the charged lepton mass matrix M E is given as

(

d

0

d

m

m

0

d%K) ,

(21) 0 JEFG mr where each matrix element is written in terms of the charged lepton masses, and phases are neglected for simplicity. This matrix is diagonalized by the unitary matrix U E , in which the mixing between the first and second families is 2: 0.07 and the mixing between the second and third

ME=

6

m,

186

0.2

0.175 0.15 0.125

sine,,

0.1

0.075 0.05 0.025 0.5

1

2

1.5

3

2.5

tan2eI2 Figure 4.

Scatter plot of sin 813 versus tan2 8 1 2 in the case of K. = 2W = 0.07.

I

...,

I 0.5

1

2.5

1.5

tm2e23 Figure 5.

Scatter plot of sin813 versus tan'

families is

E 0.02.

823

in the case of

tc

= 2W = 0.07.

Since the neutrino mass matrix is still the texture

A l , it turns to

in the diagonal basis of the charged lepton mass matrix. Here only the leading mixing term of tc = By using the texture of the neutrinos in eq.(22), we show our results of the allowed region of sin 813 versus tan' 012 and tan2 6'23 in Fig.4 and Fig.5, respectively. These results should be compared with the ones in Fig.2 and Fig.3. It is noticed that the lower bound of sin 6'13 considerably comes down

187

due to the correction K. The small

Ue3 of

5 x lop3 is allowed.

4. Summary

We have discussed IUe31 in the models, in which the samll IUe3(is predicted. The first one is the model in which the bi-maximal mixing is realized at the symmetric limit. The second one is the texture zeros of the neutrino mass matrix. In the first model, lUe31 = 0.03 0.2 is predicted. In the second model, the lower bound of lUe31 is given as 0.05, which considerably depends on tan2 OI2 and tan2 OZ3. We have investigated the stability of these predictions by taking account of small corrections, which may come from radiative corrections or off-diagonal elements of the charged lepton mass matrix. The lower bound of IUe31 comes down significantly in the case of w >> 0.01, while ? is rather insensitive to JUe31. The measurement of lUe31 will be an important test of the texture zeros in the future. N

This talk is based on the reserach work with M. Honda and S. Kaneko. The research was supported by the Grant-in-Aid for Science Research, Ministry of Education, Science and Culture, Japan(No.12047220). References 1. Super-Kamiokande Collaboration, Y. Fukuda et al, Phys. Rev. Lett. 81 (1998) 1562; ibid. 82 (1999) 2644; ibid. 82 (1999) 5194. 2. Super-Kamiokande Collaboration, S. Fukuda et al. Phys. Rev. Lett. 86, 5651; 5656 (2001). 3. SNO Collaboration: Q. R. Ahmad et al., Phys. Rev. Lett. 87 (2001) 071301; nucl-ex/0204008, 0204009. 4. KamLAND Collaboration, K. Eguchi et al., hep-ex/0212021. 5. G. L. Fogli, E. Lisi, M. Marrone, D. Montanino, A. Palazzo and A.M. Rotunno, hep-ph/0212127; J. N. Bahcall, M. C. Gonzalez-Garcia and C. Peiia-Garay, JHEP 0302 (2003) 009; M. Maltoni, T. Schwetz and J.W.F. Valle, hep-ph/0212129; P.C. Holanda and A. Yu. Smirnov, hep-ph/0212270; V. Barger and D. Marfatia, hep-ph/0212126. 6. CHOOZ Collaboration, M. Apollonio et al., Phys. Lett. B466 (1999) 415. 7. J. Sato and T. Yanagida, Phys. Lett. B430 (1998) 123; C.H. Albright, K.S. Babu and S.M. Barr, Phys. Rev. Lett. 81 (1998) 1167; J. K. Elwood, N. Irges and P. Ramond, Phys. Rev. Lett. 81 (1998) 5064; M. Bando and T. Kugo, Prog. Theor. Phys. 101 (1999)1313. 8. H. F'ritzsch and Z. Xing, Phys. Lett. B372 (1996) 265; ibid. B440 (1998) 313; M. Fukugita, M. Tanimoto and T. Yanagida, Phys. Rev. D57 (1998) 4429;

188 M. Tanimoto, Phys. Rev. D59 (1999) 017304;

M.Tanimoto, T. Watari and T. Yanagida, Phys. Lett. B461 (1999) 345. 9. A. Zee, Phys. Lett. B93 (1980) 389; B161 (1985) 141; L. Wolfenstein, Nucl. Phys. B175 (1980) 92; S.T. Petcov, Phys. Lett. B115 (1982) 401; C.Jarlskog, M. Matsuda, S. Skadhauge and M. Tanimoto, Phys. Lett. B449 (1999) 240; P. H. Frampton and S. Glashow, Phys. Lett. B461 (1999) 95. 10. L. J. Hall, H. Murayama and N. Weiner, Phys. Rev. Lett. 84 (2000) 2572; N. Haba and H. Murayama, Phys. Rev. D63 (2001) 053010. 11. C. Giunti and M. Tanimoto, Phys. Rev. D66 (2002) 053013; ibid. 113006. 12. H. Nishiura, K. Matsuda and T . Fukuyama, Phys. Rev. D 6 0 (1999) 013006. 13. E. K. Akhmedov, G. C. Branco, M. N. Rebelo, Phys. Rev. Lett. 84 (2000) 3535. 14. S.K. Kang and C.S. Kim, Phys. Rev. D63 (2001) 113010. 15. P.H. Frampton, S.L. Glashow and D. Marfatia, Phys. Lett. B536 (2002) 79. 16. Z. Xing, Phys. Lett. B530 (2002) 159. 17. W. Guo and Z. Xing, hep-ph/0212142. 18. R. Barbieri, T. Hambye and A. Romanino, hep-ph/0302118. 19. M. Bando and M. Obara, hep-ph/0212242, 0302034. 20. Z. Maki, M. Nakagawa and S. Sakata, Prog. Theor. Phys. 28 (1962) 870. 21. H. Georgi and C. Jarlskog, Phys. Lett. B86 (1979) 297.

CP VIOLATION IN JHFv (PHASE-11)

T . NAKAYA FOR JHF-SK NEUTRINO WORKING GROUP Faculty of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, JAPAN E-mail: [email protected]

A future extension of the JHF-Kamioka neutrino experiment to search for CP violation in neutrino oscillation is presented. With an upgraded 4 MW J-PARC accelerator and a Megaton-class water Cerenkov detector, Hyper-Kamiokande, the CP asymmetry between up --t ve and Pp Ve will be measured. The experiment has a sensitivity on the CP violation phase, 6 , in the MNS matrix down to 10' 20' at three sigma discovery level. The experiment has a great potential for the discovery of CP violation in the neutrino sector. --f

1. Introduction

C P violation is one of the most fascinating phenomena, which explores deep implications in fundamental physics, such as origin of flavors. It is also observed in the baryon asymmetry of the universe. Large C P violation is recently measured in the B meson system, which has firmly established the CKM model of C P violation in the quark sector. Since C P violation in the CKM matrix is not sufficient to explain the baryon asymmetry of the universe, another C P violation is expected. It is a natural way to look for CP violation in the lepton sector. Leptogenesis, in which C P violation originates from the lepton sector, is one of the popular ideas to explain the baryon asymmetry. A large C P violation effect may be observable in the lepton mixing (MNS) matrix. In measuring the C P asymmetry in the lepton sector, vp H v, oscillation is known to provide the best chance. Because the leading term of up +-+ u, oscillation is highly suppressed due to the small value of Am'&, the subleading terms, such as 013 related and C P violating terms, give leading

189

190

controbutions: Ther appearance probability is expressed as

where Sij (Czj) stands for sinezj (cos8ij) and @ij s Am$L/4EV = 1.27Am~j[eV2]L[km]/Eu[GeV]. The first term has the largest contribution. The second c o d term is generated by the CP phase 6 but C P conserving. The third sin6 term violates CP. The fourth term, which is the solar neu2 Amz L trino term, is suppressed by sin &: . The matter effect is characterized by

a = 2 h G ~ n , E , = 7.6 x 10-5p[g/cm3]E,[GeV]

[eV2],

(2)

where GF is the Fermi constant, ne is the electron density and p is the earth density. The probability P(pp -+ f i e ) is obtained by replacing a -+ -a and 6 -+ -6 in Equation. (1). The C P asymmetry in the absence of matter effect is calculated as be) - 1.27Amf2L sin2812 .-. sin6 (3) E sin 813 P(vp ve) P ( 5 p Ve) With the JHF neutrino beam of E, 0.75 GeV and the baseline of 295 km, the C P asymmetry can be large. For example, taking recent results by Super-Kamiokande, KamLAND and SNO for the values sin22812 = 0.93 and Am:, = 6.9 x eV2, and the value sin22813 = 0.01 (1/10 of CHOOZE limit) and the value 6 = 7r/2 (the maximum CP effect), ACP becomes as large as 50%. The low energy neutrino beam makes the fake asymmetry by matter effect small since the asymmetry increases linearly with the neutrino energy as shown in Equation (2). Figure 1 shows oscillation probabilities of vp -+ ve(black) and pp --+ D,(red) for a typical set of the parameters mentioned above except for the value 6 = 7r/4 (half of the maximum C P violation effect). ACP =

p ( v p -+ ve) - P ( g p -+ -+

+

-+

N

2. The JHF-Kamioka neutrino experiment

A detailed description of the JHF-Kamioka neutrino experiment is reported in the other part of the NOON2003 proceedings ’. Therefore, essential elements upgraded for a C P violation search are described here. The sensitive

191 h0.009 .?Of

008

Z O . 007

$0.006 a0.005

0

20.004

0.003

s o . 002

-4

4Jo .001 (d

r rl

l

o

-40.001

u

m 0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

E, ( GeV)

Figure 1. Oscillation probabilities of v p 4 v,(black; lower line) and ep 4 ve(red; upper line). The solid curves includes matter effect. For the dashed curves, the matter effect is subtracted and the difference between v p --t v,(black) and G p + C,(red) are all due to CP effect.

search for CP violation is conducted with a new far detector of WMton mass and together with an upgrade of the J-PARC accelerator (JHF) to 4 MW power. The Megaton-class water Cerenkov detector, Hyper-Kamiokande 3 , is currently under design and R&D. A possible site for Hyper-Kamiokande is 10 km south from Super-Kamiokande. A fiducial volume of HyperKamiokande is designed to be 0.54 Mton. Hyper-Kamiokande is designed to have the same performance as Super-Kamiokande. The upgrade of the JHF is also considered by increasing the harmonics, increasing the repetition rate, and adapting the barrier bucket scheme to run more protons in the ring. The neutrino beam line and the target have to be upgraded to accommodate the power and the radiation of the 4 MW beam. In a CP violation search, an anti-neutrino beam is produced by reversing the polarity of the magnetic field of the horns. The anti-neutrino flux is estimated to be 15% lower than the neutrino flux, and the total number of anti-neutrino events result in one third of neutrino events because of the smaller cross section. The beam exposure is assumed for two years for neutrinos and for 6.8 years for anti-neutrinos to collect the equal numbers of statistics. In addition, neutrino detectors at the near and at the intermediate locations are necessary to measure the neutrino flux and to study neutrino

192

interaction, which shoiild reduce a possible systematic uncertainty to level for the CP violation search.

N

2%

3. Sensitivity on CP Violation

With the experimental condition described in Section 2, the same selection criteria for a v p + v, search are applied in this analysis. We used a GEANT based Monte Carlo simulation for the neutrino and anti-neutrino beams, the Super-Kamiokande Monte Carlo simulation for neutrino interaction and detector response, and the Super-Kamiokande analysis code to reconstruct neutrino events. The reconstructed neutrino energy of the v, and 0, candidate events are shown in Figure 2 with expected background events. The numbers of expected signal and background events are sum-

p goo

v, Beam

(u

c

$00 E

D

L

D (u

1

500 z

600

; ~

400

300

400

~

200

200 100

0

02 04 06 08

1

12 14 16 18 Reconstructed E, (Ge\

0.2 0 4 0.6 0 8

1

1 2 1 4 1.6 1.8 Reconstructed E, (GeV

Figure 2. The reconstructed neutrino energy of the ve (left) and Ye (right) candidate events with expected background events. The signal events are estimated with the value sin2 2813 = 0.02. The background events from up (black), ijp (red), ue (purple) and Y e (pink) are overlaid.

marized in Table 1. The effect of CP violation is observed as the asymmetry of the number of events between u, and 0,. The numbers including the background events are shown in Figure 3 as a function of the CP violating phase 6. The sensitivity of ACP depends on the estimated accuracy of the background events. In Table 1, we find that the signal to background ratio is around 0.5 with the value sin2 2013 = 0.01. Taking the background estimation into account, the

193 Table 1. The number of expected signal and background events with the standard v,, + ue selection criteria. The number of signal events is calculated with parameters; Am:, = 6.9 x eV2, Am& = 2.8 x eV2, 812 = 0.594, 023 = ~ / 4and sin22813 = 0.01. The signal is shown in the case of no CP violation (a = 0) and in the case of maximum CP violation (6 = ~ / 2 ) . signal 6 = ~ / 2 total 536 229 913 536 790 1782

6 =O v,,

+ ve

C,,

4

Ve

background Pw Ve 450 370 66 399 657 297 L J ~

fie

26 430

-

+

1300

8

Y

2 1200 1100

1000

900

800

700

Figure 3. The numbers of ve and Ve appearance events including background are shown as an ellipse of green as a function of the parameter 6 with the unit of a degree. The two ellipses correspond to the sign (positive and negative) of Am'& due to the matter effect. The circles with the same center indicate the 30 contour (blue; outer) and the 90% confidence level contours (red; inner) with and without a 2% systematic uncertainty.. Four sets of circles with different centers are with and without the matter effect.

sensitivity of 6 extracted from ACPis shown in Figure 4 as a function of the value sin2 2813. In Figure 4, we do not consider the uncertainty of the other neutrino oscillation parameters; 012, and Aml,. In Figure 4, it is notable that the sensitivity on sin6 is almost independent of the value of sin2 2013 if the value of sin2 2813 is larger than 0.01 and the number of background

194

JHF-HK CPV Sensitivity 5? N% 0.14 C .-u)

0.12

0.1

0.08 0.06 0.04 0.02

0 Figure 4. The sensitivity of the CP violation parameter 6 as a function of sin2 2013 with background events. The values Am:, = 6.8 x lop5 eV2 and 812 = 7r/4 are assumed. The sensitivity depends on the uncertainty of the signal efficiency and the accuracy of the background estimation. From the right line in the figure, the uncertainties of the signal efficiency and the background estimation are assumed t o be 10, 5, 2 ,0% and no background, respectively.

events is well estimated with an accuracy of 2% level". By assuming that uncertainties of the signal efficiency and the background estimation are 2%, we expect that we discover CP violation with the values sin6 above 0.28 (S > 16 degrees), Am:, = 6.8 x eV2 and 612 = 7r/4. Since the sensitivity linearly depends on the values Am:, and 612 as shown in Equation (3), the sensitivity on 6 lies in 10" - 20" at three sigma discovery level. 4. Summary

We present a possibility to search for CP violation in neutrino oscillation in the JHF-Kamioka neutrino experiment phase-11. The sensitive search is possible to probe the CP violation phase 6 down to 10 - 20 degrees. "Please note that ACP in Equation (3) is inversely proportional to 813, and the statistics of the number of events is proportional t o 813. Both effects are canceled without background.

195

At NOON2003 workshop, another approach is proposed t o measure 613 by using reactor anti-neutrinos, which can predict the first term in Equation (1). If information of 613 by reactors is available, we can extract the C P effects by subtracting the leading (first) term in Equation (1). In this case, we need only a neutrino beam and significantly reduce the running period of the experiment. With current knowledge of the experimental results, there is no constraint on CP violation in neutrino oscillation. Therefore, we may find larger C P violation than the expectation by the MNS matrix if new physics exists behind neutrino oscillation. It is worthwhile t o look for CP violation in neutrino oscillation. References 1. B. Richter, SLAC-PUB-8587 (hep-ph/0008222), 2000 and references there in. 2. A.K. Ichikawa, presentation at NOON2003 and proceedings for NOON2003, 'JHFnu (Phase-I) neutrino oscillation experiment', February 10-14, 2003,

Kanazawa Japan. 3. M. Koshiba, Phys. Rep. 220, 229 (1992); K. Nakamura, talk presented at Int. Workshop on Next Generation Nucleon Decay and Neutrino Detector, 1999, SUNY at Stony Brook; K. Nakamura, Neutrino Oscillations and Their Origin, (Universal Academy Press, Tokyo, 2000), p. 359.

LONG BASELINE NEUTRINO OSCILLATIONS: PARAMETER DEGENERACIES AND JHF/NUMI COMPLEMENTARITY*

HISAKAZU MINAKATA Department of Physics, Tokyo Metropolitan University 1-1 Minarni-Osawa, Hachioji, Tokyo 192-0397, Japan Email: [email protected] HIROSHI NUNOKAWA Instituto de Fisica Tedrica, Universidade Estadual Paulista R u a Pamplona 145, 01405-900 SaXo Paulo, SP Brazil Email: [email protected] STEPHEN PARKE+ Theoretical Physics Department, Fermi National Accelerator Laboratory P. 0.B o x 500, Batavia, IL 6051 0, USA Email: [email protected]

A summary of the parameter degeneracy issue for long baseline neutrino oscillations is presented and how a sequence of measurements can be used to resolve all degeneracies. Next, a comparison of the JHF and NuMI Off-Axis proposals is made with emphasis on how both experiments running neutrinos can distinguish between the normal and inverted hierarchies provided the E/L of NuMI is less than or equal to the E/L of JHF. Due to the space limitations of this proceedings only an executive style summary can be presented here, but the references and transparencies of the talk contain the detailed arguments.

1. Parameter Degeneracies: Overview The probability of up + u, depends on 0 1 3 , 6 c p , 8z3 and sign of 6mil. Untangling the degeneracies associated with these parameters is the subject of this section, see Ref. [1]-[4]. ~

* http://www-sk.icrr.u-tokyo.ac.jp/noon2003/transparencies/ll/parke.pdf tPresenter at NOON 2003.

196

197

1.1.

013

and 6 c p Degeneracy

If the probabilities P ( v p + v,) and P ( o p + De) are precisely determined by long baseline experiments then in general there are four solutions of parameters ( 0 1 3 , S c p ) for a fixed value” of 8 2 3 . This is shown on the right biprobability diagram (see Ref. [5]) of Fig. 1 where the four ellipses intersect at a single point. Two of these ellipse are assuming normal hierarchy and the other two are the inverted hierarchy. Note, that the values of sin’ 2 8 1 3 varies significantly between the ellipses of the same hierarchy.

Energy = 0.6 GeV

Energy = 0.8 GeV

K h

I aa A

I

0

1

2

3

4

5

JHF P(v, -> v e ) %

0

1

2

JHF P ( u ,

3

4

5

6

-> v e ) %

Figure 1. The allowed region in the bi-probability plot at oscillation maximum (left panel) and at 30% above oscillation maximum (right panel) for v p + v, verses U p + Ue for J H F at 295 km. The ellipses are for fixed sin2 2013 but allowing 6 c p to vary from 0 to 27r. Except where noted the other mixing parameters are fixed to be IArn?, I = 2.5 x lop3 eV2, sin2 2823 = 1.0, Am:, = $7 x l o p 5 eV2 and sin2 2012 = 0.85. The electron density for J H F is fixed t o be Yep = 1.15 g cmp3 (for NuMI we will use 1.4 g cm-,).

The left hand panel of Fig. 1 shows that these four ellipses collapse to a line at the energy that corresponds to oscillation maximum and that the value of sin2 2 8 1 3 can be determined precisely at this special energy, see Ref. [3]. For a given hierarchy, the complicated ( 8 1 3 , 6 c p ) degeneracies factorizes into a fixed value for 013 and a ( S c p , 7r - 6 c p ) degeneracy. In general, the hierarchy degeneracy still exists unless nature has chosen one of the edges of the allowed region in bi-probability space represented in Fig. 1. aThe ambiguity in 023 will be discussed in the next section.

198

In Fig. 2 we have plotted the fractional difference in the allowed values of 8 1 3 for the same hierarchy in the left panel and different hierarchies in the right panel. This fractional uncertainty in the allowed value grows as 8 1 3 gets smaller but for values of 8 1 3 not too far below the current Chooz bound of sin2 2OI3 < 0.1 the fractional uncertainty is less than say 20%. A0/8 (%) for L =295 km, E = 0.8GeV

6 5 4

3 2

1

0. 0.

1

2

3

4

5

0.

1

JHF P(v,+v,) Figure 2. The fractional difference in the values of panel) and different hierarchy (right panel).

1.2.

023

2

3

4

5

6

% 6'13

for the same hierarchy (left

Degeneracy

In general, 823 is determined from ufi + vfi disappearance experiments. Unfortunately in the disappearance probability 8 2 3 appears as sin2 2823. If sin2 2823 differs from 1 by t2 then the two solutions for sin2 6'23 are (1 .5)/2. Since the appearance probability for up + u, depends on sin2 8 2 3 this ambiguity leads an ambiguity in the determination of 813. However, the quantity (sin 823 sin 8 1 3 ) can be determined accurately from the appearance experiments. See Fig. 3. In Fig. 3 we have assumed that sin2 2823 = 0.96 = 1- (0.2)2 and drawn the bi-probability ellipses for (2 sin2 8 2 3 sin2 2OI3) = 0.02, 0.05 and0.09. In the right panel the energy is chosen at 30% above oscillation maximum and the four ellipses (two different 823 times the two hierarchies) are approximately, but not exactly, degenerate. The left panel is at oscillation maximum and the degeneracy of the four ellipse is nearly exact.

199

Energy

= 0.6

1

3

E n e r g y = 0.8 GeV

GeV

6 5

4

3 2

1 0

0

2

4

5

0

1

-> v e ) %

JHF P(v,

2

3

4

5

6

JHF P(u, -> v e ) %

Figure 3 . The bi-probability plots at oscillation maximum (left) and at an energy 30% above oscillation maximum (right) assuming that 8 2 3 differs from 7r/4 for constant values of (sin 823 sin 813). Here, sin2 2823 = 0.96 giving two solutions for sin2 = 0.4 and 0.6.

E ,,,

0

EJHF = 0.8 GeV, ,E,

= 0.6 GeV, ENuM, = 1.88 GeV

1

2

3

4

5

0

JHF P(v,

1

2

3

= 2.5 GeV

4

5

6

+ v,) %

Figure 4. Allowed region in the bi-probability plane for J H F vfi t v, verses NuMI U p t U , at 915 km with represented ellipses for fixed values of sin2 2813. The left panel is both experiments at oscillation maximum while the right panel is both experiments 30% above oscillation maximum.

200

Thus the ambiguity in the determination of 6 2 3 leads t o an ambiguity in the determination of 813 in long baseline oscillation experiments. However, the quantity (sin 6 2 3 sin 813) can be precisely determined especially at oscillation maximum. To break the degeneracy in 6 2 3 ; (sin 623 sin 813) and (cos 823 sin 6 c p ) can be measured at oscillation maximum then (cos 623 cos 6 c p ) can be determined above oscillation maximum. The combination of these measurements leads to a determination of cos 823, breaking this 623 degeneracy. JHF (L=295km) neutrino vs. NuMl (L=915 km) neutrino

6

5 4

3

3 2 1 0

0

1

2

3

4

5

0

1

2

3

4

5

6

JHF P(vK+ ve) % Figure 5. Allowed region in the bi-probability plane for JHF uw + u, verses NuMI vw -+ v, with represented ellipses for fixed values of sin2 26'13. The top (left) two panel are J H F (NuMI) at oscillation maximum while the bottom (right) panel are J H F (NuMI) at 30% above oscillation maximum. The ellipse are for sin2 2813 = 0.02, 0.05 and 0.09.

2. JHF/NuMI Complementarity Detailed discussions can be found in references [ 6 ] , [7] and [8].

201

2.1. Neutrino-Antineutrino Fig. 4 represents the allowed region in bi-probability space for one experiment neutrinos and the other anti-neutrinos. Note the similarity between this plot and the plots where both the neutrino and anti-neutrino probability are from the same experiment (Fig. 1 for example).

2 . 2 . Neutrino-Neutrino Fig. 5 represents the allowed region in bi-probability space for both experiments neutrinos. The allowed regions are narrow ‘‘pencils” which grow in width as the energy of either or both experiments differ from oscillation maximum. The ratio of slopes of these pencils increases (decreases) as the energy of the experiment with smaller (larger) matter effect increases. For JHF/NuMI this means that the best separation occurs when

The top right panel of Fig. 5 violates this condition and there is substantial overlap between the two allowed regions, see Ref. [8]. 3. Conclusions

The eight fold parameter degeneracy in v p + v, can be resolved with multiple measurements in the neutrino and anti-neutrino channel. A neutrino as well as an anti-neutrino measurement at oscillation maximum plus a neutrino measurement above oscillation maximum is sufficient if chosen carefully. Exploitation of the difference in the matter effect between JHF and NuMI can be used to determine the mass hierarchy provided that the E/L of NuMI is smaller than or equal to the E/L of JHF. References 1. J. Burguet-Castell, M. B. Gavela, J. J. Gomez-Cadenas, P. Hernandez and 0. Mena, Nucl. Phys. B 646,301 (2002). 2. V. Barger, D. Marfatia and K. Whisnant, Phys. Rev. D 65,073023 (2002). V. Barger, D. Marfatia and K. Whisnant, Phys. Rev. D 66,053007 (2002). 3. T. Kajita, H. Minakata and H. Nunokawa, Phys. Lett. B 528,245 (2002). 4. H. Minakata, H. Nunokawa and S. Parke, Phys. Rev. D 66,093012 (2002). 5. H. Minakata and H. Nunokawa, JHEP 0110, 001 (2001). H. Minakata, H. Nunokawa and S. Parke, Phys. Lett. B 537,249 (2002). 6. V. Barger, D. Marfatia and K. Whisnant, Phys. Lett. B 560,75 (2003). 7. P. Huber, M. Lindner and W. Winter, Nucl. Phys. B 654,3 (2003). 8. H. Minakata, H. Nunokawa and S. Parke, arXiv:hep-ph/0301210.

USING

YE

+Y

~ GOLDEN :

AND SILVER CHANNELS AT THE NEUTRINO FACTORY

A. DONINI* Institlito Fisica Tedrica C - X V I , Universidad Autonoma Madrid Cantoblanco, E-28049, Madrid, Spain E-mail: [email protected]

I briefly review the source of the so-called intrinsic ambiguity and show how the combination of “golden” and “silver” channel at the Neutrino Factory can solve the problem, in the absence of other sources of degeneracies. I then relaxed the hypothesis 6’23 = 45O and show how the different dependence of the two channels on 6’23 can help in solving the intrinsic and 6’2s-octant ambiguity at the same time.

The most sensitive method to study leptonic CP violation is the measure of the transition probability ve(tie)+ ~ ~ ( 0 , )In. the framework of a Neutrino Factory-based beam this is called the “golden channel” : being an energetic electron neutrino beam produced with no contamination from muon neutrinos with the same helicity (only muon neutrinos of opposite helicity are present in the beam), the transition of interest can be easily measured by searching for wrong-sign muons, i.e. muons with charge opposite to that of the muons in the storage ring, provided the considered detector has a good muon charge identification capability. The transition probability v, + v, is also extremely sensitive to the leptonic CP-violating phase S. We can indeed look for muonic decay of wrong-sign T ’ S (the so-called “silver channel”, due to its lesser statistical significance with respect to the “golden channel”) in combination with wrong-sign muons from ve -+ vw to improve our measurement. The transition probability (at second order in perturbation theory in

*Work supported by the Programa Ramon y CajAl of the Ministkrio de Ciencia y Tecnologia of Spain.

202

203

813, A,

/ Aatm,A,

/ A and A, L ) is

41516

:

p$(813,6) = X* sin2(2613)+~*cos(813)sin(2813)cos (1) and

pk,(813,6) = XI sin2(2613)-~*COs(813) sin(2813)cos (2) where f refers to neutrinos and antineutrinos, respectively. The parameters 613 and 8 are the physical parameters that must be reconstructed by fitting the experimental data with the theoretical formula for oscillations in matter. The coefficients of the two equations are:

with A = fiGFn, (expressed in eV2/GeV), B, = JA?Aaatm)(with T referring to neutrinos and antineutrinos, respectively) and Aatm= Am;,/2EV, A, = Amf2/2E,. The parameters in X , Y , Z have been considered as fixed quantities, supposed to be known by the time when the Neutrino Factory will be operational with good precision: we put 812 = 33" and Am;, = 1.0 x 10W4 eV2; 823 = 45" and Am;, = 2.9 x lop3 eV2, with Am;, positive (for 823 = 45" the 023-octant ambiguity is absent); A = 1.1 x 10W4 eV2/GeV (a good approximation L < 4000 Km). We have not included errors on these parameters since the inclusion of their uncertainties does not modify the results for 013 and 6 significantly '. Eqs. (1) and (2) lead t o two equiprobability curves in the (813,S) plane for neutrinos and antineutrinos of a given energy:

P$(813,6) = P$(013,4;

p2(813,6)= p & ( 0 1 3 , S ) .

(4)

Notice that X y and 2' differ from the corresponding coefficients for the Y, + v p transition for the cos823 e sin023 exchange, only (and thus for 023 = 45" we have X = X ' , Z = Z T ) . The Y* term is identical for the two channels, but it appears with an opposite sign. This sign difference in the Y-term is crucial, as it determines a different shape in the (813, S) plane for the two sets of equiprobability curves.

204

-200”

-2

-1

0

1

2

A0 Figure 1. Equiprobability curves for neutrinos i n the (A0,S) plane, for 613 = 5 O , 6 = 60°, E , E [5,50] Ge V and L = 732 K m for the u, -+ up a n d u, -+ ur oscillation. A0 is the difference between the input parameter &3 and the reconstructed parameter 813, A0 = 013 - & 3 .

In Fig. 1equiprobability curves for the v, + u p ,v, oscillations at a fixed distance, L = 732 Km, with input parameters 813 = 5” and 6 = 60” and different values of the energy, E, E [5,50] GeV, have been superimposed. The effect of the different sign in front of the Y-term in eqs. (1) and (2) can be seen in the opposite shape in the (013,S) plane of the v, + v, curves with respect to the v, + v p ones. Notice that both families of curves meet in the “physical” point, 013 = g13, S = 8, and any given couple of curves belonging to the same family intersect in a second point that lies in a restricted area of the (Ad, S) plane, the specific location of this region depending on the input parameters (&,8) and on the neutrino energy. Using a single set of experimental data (e.g. the “golden” muons), a x2 analysis will therefore identify two allowed regions: the “physical” one (i.e. around the physical value, &,8) and a “clone” solution, spanning all the area where a second intersection between any two curves occurs. This is the source of the so-called intrinsic ambiguity When considering a t the same time experimental data coming from both the “golden” and the “silver” channels, however, a comprehensive x2 analysis of the data would result in the low-x2 region around the physical pair, only 3, since “clone” regions for each set of data lie well apart. This statement is only true if the statistical significance of both sets of experimental data is sufficiently high. The golden channel has been

‘.

205

180

90

' 0 0

-90

-180 0

-180

3 013

180

90

r

o

o

-90

-180

-3

-2

-1

A0

0

1 $13

Figure 2. Equiprobability curves for neutrinos and antineutrinos (left) and the corresponding outcome of a f i t (right) for golden channel only (above) and including both the golden and the silver channel (below). The input parameters are 813 = 1'; 8 = 90'. The golden signal is obtained at a realistic 40 Kton M I D and at an ideal 2 Kton ECC. The results are substantially unchanged when considering a realistic ECC of doubled size of 4 Kton.

thoroughly studied considering a 40 Kton magnetized iron detector (MID) located at L = 3000 Km. A dedicated analysis of the silver channel at an OPERA-like Emulsion Cloud Chamber (ECC) detector has been recently performed l o to substantiate the results on the impact of the silver muons when combined with golden muons based on the OPERA proposal. In Fig. 2 we present equiprobability curves and the outcome of the fit when only golden muons (above) or both golden and silver muons (below) are considered, for input parameters &, = 1";s= 90". The golden muon signal is measured a t a 40 Kton MID, with realistic efficiency and background '; the silver muon signal is measured at an ideal 2 Kton ECC with spectrometers following the OPERA proposal These results do not change when including efficiency and backgrounds if considering a doubled-

'.

206

size ECC of 4 Kton. Notice that the scanning power needed to take full advantage of a 4 Kton detector is considered to be easily under control by the time of the Neutrino Factory lo. In order to study the effect of the Oz3-octant ambiguity, we now relax the hypothesis on the value of 0 2 3 = 45" (for which no ambiguity was present).

180

Lo

90

0 0

1

0.5 Ae

1.5

2

0

0.5

1

1.5

2

ne

Figure 3. The trajectory i n the (A8,6) plane of the clone regions for 8 = as a function of 813 for the SPL at L = 130 Km and the Neutrino Factory at L = 732,3000 Km. I n the case of the Neutrino Factory, both the golden and the silver channel are considered. T h e thick dot is the true solution, located at A8 = O', 6 = 6 = 90'. The two plots represent: 023 = (left); 8 2 3 = 50' (right).

It is possible to compute the analytical location of the clones by solving eq. (4) for 0 1 3 and 6 as a function of the input parameters &3,8, after convoluting over the flux and the neutrino-nucleon cross-section and integrating over the neutrino energy. In Fig. 3 we present the trajectory of the intrinsic clone region for 8 = 90" for the different channels, beams and baselines in the (Ad, 6) plane as a function of 813 E [0.01", lo"] for the two cases of &3 = 40" (left) and 653 = 50" (right). The thick dot is the true solution, A0 = 0",6= 8. In Fig. 3 (left, 0 2 3 = 40°), the isolated line going down represents the displacement of the intrinsic clone for the SPL beam l1 for the CERN-Frejus baseline, L = 130 Km. The cluster of lines moving towards larger values of 6 and A0 represent the displacement of the intrinsic clone for the golden channel at the Neutrino Factory beam, for 4 different energy bins (in the neutrino energy range E, E [lo, 501) and two baselines, L = 732 and L = 3000 Km. Finally, the cluster of lines moving towards smaller values of 6 and larger values of A0 represent the displacement of the intrinsic clone for the silver channel at the Neutrino Factory beam, again for 4 different energy bins and two baselines. Notice that the qualitative behaviour of golden and silver trajectories is substan-

207

tially independent of the neutrino energy and of the considered baseline. In Fig. 3 (right, 023 = 50") the SPL trajectory moves up and the golden and silver cluster are interchanged with respect to the previous case, due to the interchange of cos023 +) sin023 in the X and Z coefficients of eqs. (1) and (2). For decreasing values of &, the clones move away from the thick dot, the physical point. Notice that for large &3, all lines are relatively near the physical input pair: this reflects the fact that for $13 large enough degeneracies are not a problem 12, being A0/013 always small. For small values of &3, any combination of experiments (golden and silver at the Neutrino Factory, or any of the two in combination with the SPL superbeam 13) would result in killing the intrinsic degeneracy, provided that statistics of the considered signals is large enough. Regarding the 023-octant ambiguity it seems reasonable to expect that the combination of the golden and silver channels would help in solving the ambiguity, due to the different behaviour of the respective clones depending on the value of 023. This seems indeed to be the case from a preliminar analysis of our data l 4 for &3 2", with a loss of sensitivity below this value due t o the extremely poor statistics in the silver channel.

>

References 1. A. Cervera et al., Nucl. Phys. B 579 (2000) 17 [Erratum-ibid. B 593 (2001) 7311; Nucl. Instrum. Meth. A 472 (2000) 403. 2. M. Apollonio et al., arXiv:hep-ph/0210192. 3. A. Donini, D. Meloni and P. Migliozzi, Nucl. Phys. B 646 (2002) 321; arXiv:hep-ph/0209240. 4. J. Burguet-Castell et al., Nucl. Phys. B 608 (2001) 301; J. Burguet-Castell and 0. Mena, arXiv:hep-ph/0108109. 5. M. Freund, Phys. Rev. D 64 (2001) 053003. 6. H. Minakata, H. Nunokawa and S. Parke, Phys. Lett. B 537 (2002) 249. 7. V. Barger, D. Marfatia and K. Whisnant, Phys. Rev. D 65, 073023 (2002). 8. A. Cervera, F. Dydak and J. Gomez Cadenas, Nucl. Instrum. Meth. A 451 (2000) 123. 9. M. Guler et al., OPERA Collaboration, CERN/SPSC 2000-028, SPSC/P318, LNGS P25/2000, CERN-SPSC-2001-025. 10. D. Autiero et al., arXiv:hep-ph/0305185. 11. M. Mezzetto, arXiv:hep-ex/0302005. 12. P. Huber, M. Lindner and W. Winter, Nucl. Phys. B 654 (2003) 3. 13. J. Burguet-Castell et al., Nucl. Phys. B 646 (2002) 301. 14. 0. Mena, arXiv:hep-ph/0305146.

PARAMETER DEGENERACY AND REACTOR EXPERIMENTS *

OSAMU YASUDA Department of Physics, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo 192-0397, Japan E-mail: [email protected]. ac.jp

Degeneracies of the neutrino oscillation parameters are explained using the sin2 2013-s;~ plane. Measurements of sin2 2OI3 by reactor experiments are free from the parameter degeneracies which occur in accelerator appearance experiments, and reactor experiments play a role complementary to accelerator experiments. It is shown that the reactor measurement may be able to resolve the degeneracy in 823 if sin2 2013 and cos2 2023 are relatively large.

1. Introduction

Thanks t o the successful experiments on atmospheric and solar neutrinos and KamLAND, we now know approximately the values of the mixing angles and the mass squared differences of the atmospheric and solar neutrino oscillations: (sin2 2812, Am;,) = (0.8,7 x lOP5eV2) for the solar neutrino and (sin2 2823, IAm&l) = (1.0,3 x lOP3eV2) for the atmospheric neutrino. In the three flavor framework of neutrino oscillations, the quantities which are still unknown to date are the third mixing angle 813, the sign of the mass squared difference Am:, of the atmospheric neutrino oscillation, and the CP phase 6. Among these three quantities, the determination of 813 is the next goal in the near future neutrino experiments. In this talk I will first explain briefly the ambiguity due to the parameter degeneracies, which occur in the long baseline experiments, using the sin2 2813& plane, and then I will show that reactor experiments will play a role complementary to accelerator experiments, and it may resolve a certain degeneracy when combined with an accelerator experiment. This talk *This work is supported in part by the Grant-in-Aid for Scientific Research in Priority Areas No. 12047222 and No. 13640295, Japan Ministry of Education, Culture, Sports, Science, and Technology.

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209

is based on the work', in which references on the subject can be found.

2. Parameter degeneracies

It has been realized that we cannot determine the oscillations parameters 63k, Am:k, 6 uniquely even if we know precisely the appearance probabilities P(up -+ y e ) and P(fip-+ f i e ) in a long baseline accelerator experiment with an approximately monoenergetic neutrino beam due to so-called parameter degeneracies. There are three kinds of the parameter degeneracies: the intrinsic (013,S) degeneracy, the degeneracy of Am& c-) -Am:,, and the degeneracy of 023 H 7r/2 - 623. Each degeneracy gives a two-fold solution, so in total one has eight-fold solution if the degeneracies are exact. When these degeneracies are lifted, there are eight solutions for the oscillation parameters such as 013 etc., and it will be important in future long baseline experiments to discriminate the real solution from fake ones. To explain the parameter degeneracies, let me consider the contours which are given by P = P(vp -+ y e ) and P E P(pp 4 V e ) at the same time in the sin2 2&3-S& plane. If there were no matter effect A = ~ G F N=, 0, if the mass squared difference Am;, of the solar neutrino oscillation were exactly zero, and if 023 is exactly ~ / 4 then , we would have one solution with 8-fold degeneracy as is shown in Fig.l(a). If we lift the conditions in the order ( A = 0, Am;, = 0,023 - 7r/4 = 0) + ( A = 0, Am:, = 0,023 - 7r/4 # 0) --+ ( A = 0, Am;, # 0,023 - 7r/4 # 0) ( A # 0, Am;, # 0,023 - 7r/4 # 0), then the exact degeneracies are lifted as is depicted in Figs.l(a) (one solution with %fold degeneracy) -+ (b) (two solutions with 4-fold degeneracy) (c) (four solutions with 2-fold degeneracy) + (d) (eight solutions without any degeneracy). Furthermore, if we assume the neutrino energy to be approximately monoenergetic and to satisfy the oscillation maximum condition lAm&L/4EI = 7r/2 as is the case at the JHF experiment, then the contours look like Fig.l(e) and in this case only ambiguity which causes a problem is the 023 degeneracy, since the intrinsic (613,s) degeneracy is exact and there is little ambiguity due to the sgn(Am&) degeneracy because IAL/2/ << 1. Here let me explain briefly the behaviors of the contours in Fig.l(e), which is shown in Fig.2 in detail. Using the analytic approximate formulae3 in the case of the oscillation maximum, -+

-

+ y2g2, P = x 2 p + 2xyfg sins + y2g2,

P

= x2f2 - 2xyfg

sin 6

210

m

NN v)

0.5

C

sin22e13

0

sin22813

m

NN v)

0.5

0

sin22e13

0

sin22813

p are known. The eight-fold parameter degeneracy is lifted as t h e small parameters are switched on: (cos’ 2023, lAm:,/Am;,l, AL)

Figure 1. Contours which are given when both P and

(a)(= 0, = 0 , = 01, 0, = 0, = O), (c)(# 0, # 0, = 01, (d)(# 0, # 0, # 01, (e)(# 0, 0, a t the first oscillation maximum). The solid (dashed) line stands for the case for Am;, > 0 (Am;, < 0), respectively, (a),(b),(c). P = P ( P > P ) is assumed in (a), (b) and (c) ((d) and (e)), respectively.

# 0, #

21 1

Pz0.025, P=0.035, Am$,
--

i i

I

Sin22el3 (Am$,>O) sin22e13(Am&cO)

sin22013

The contours which are given by both P and P for Am:, > 0 (the solid thick line) and for Am;, < 0 (the dashed thick line) a t t h e oscillation maximum IAmilL/4EI = ~ / 2 . These lie in t h e overlap of t h e region which is given by P only (the area which is bound by t h e thin black solid (dashed) line for Am:, > 0 (Am;, < 0)) and t h e region which is given by P only (the area which is bound by the thin gray solid (dashed) line for Am:, > 0 (Am;l < 0)).

Figure 2.

where z = ~23sin2813, (f,!) = cos(AL/2)/(1 FALIT), g sin(AL/2)/(AL/.ir), x 3 ~23sin2813, y ~~23sin2812and ( A m z l / A m ~ l (one , can show for any given value of si3

=

=

=

if 1AL/2) << 1. Therefore the thick solid and thick dashed lines are close to each other in Fig.2 because the matter effect and E are both small. Notice that J P- PJcould be large if E were large even if JAL/2)<< 1. One can also show

N

1 -

€2

( 2 1 ~ )-AL ~ (P-P)

sin22e12

.ir

(3)

212

large in Fig.2 because a small quantity AL(P - P ) is enhanced by a large factor 1 / ~ ' . In the case of the JHF experiment, which has L=295km, A -1/(1900km), E = 1/35, if P=0.025 and P=0.035, then the right hand side of (2) N 5 x lop4, and the right hand side of (3) N 0.3.

3. Reactor measurements of 013 In the three flavor framework the disappearance probability of the reactor neutrinos with a baseline less than l0km is given by

to a good approximation. Hence reactor measurements are free from the ambiguity due to the matter effect, the CP phase b and 023. It has been shown that a reactor measurement at the Kashiwazaki-Kariwa nuclear power plant potentially has sensitivity down to sin' 2813 0.02.

-

I

I

0

sin22013

I

I

0

sin22013

Figure 3.

Situations of the long baseline accelerator experiment at the oscillation maximum (lAmz,L/4EI = 7 ~ / 2 )(a) : the case with 823 N 7r/4, (b) the case with 823 # ~ / 4 .

4. Resolution of the 023 ambiguity by the LBL and reactor experiments Once we have the results from, say, the phase 2 of the JHF experiment on P(vp --t ve) and P(Gp -+ G e ) and the reactor measurement of P(Ge -+ f i e ) , there are two possibilities. One is the case where sin' 2 8 2 3 is close to 1, as is shown in Fig.S(a). In this case one could not resolve the ambiguity within

213

P=0.025, e=0.035, Am$ >O P=0.025, PzO.035, Am$
---

0.12

sin2 2813

P=0.025, r=0.035, Am:, >O P=0.025, PsO.035, Am& CO

Figure 4.

---

Resolution of the 623 degeneracy by combining the results of the reactor and the long baseline accelerator experiments at the oscillation maximum: (a) the case with 823 < a/4, (b) the case with 6 2 3 > 7r/4. The shaded region stands for the error in sin2 2613 of the reactor experiment.

214

osys= 2%, lOt-yr, 1d.o.f.

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.-c

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-- -

~ 0 . 0 2 8sin220 , -0.09 ~=0.028,sip220~~=0.03 E=o.12, sin 20 -0.09 2 13~=0.12,sin 2Ol3=O.06 e=0.12, sin22~,,=0.03 - - I.................

m

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0.6

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.-ca

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0.06

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0.92

0.96

sin22OI3

1.00

0.96

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sin2202,

Figure 5.

(a) Errors in the reactor experiment. (b) Ambiguities due to the 823 degeneracy in the long baseline accelerator experiment at the oscillation maximum, where the horizontal l A m ~ l / A m ~ l l = 0 . 0 2is8 the axis is defined in such a way that it is near in sin22823. E best fit case for the solar and atmospheric neutrino data where 6d,(sin2 2813)/ sin2 2813 is approximated by (1-tan2 6’231 for almost all the values of sin2 2813, while c = 0.12 is the most pessimistic case within the 9O%CL allowed region for the solar and atmospheric neutrino data, for which approximation by 11 - tan2 8231 is not good.

the experimental error nor would one have to worry about the ambiguity, as the difference is small. On the other hand, if sin’2823 turns out to be away from 1 as is depicted in Fig.S(b), then the reactor result may enable us to resolve the 823 ambiguity. As is shown in Fig.4(a) and (b), if the ambiguity bde(sin22813) = I sin’ 28i3 - sin2 28131 due to the degeneracy, where 813 and 8i3 stand for the values of 813 for the real and fake solutions, is larger than the error &,(sin2 281~)of the reactor measurement, then we can resolve the 823 ambiguity. &,(sin’ 2813) can be computed from the equation (26) in Ref.4, and we obtain Sd,(sin2 2e13) sin2 2e13 c2

sin2 2e13

tan2(aL/2)

UL

1

[I - (1r)2] sin2 2e12 . (5)

( ~ L / T ) ~

Hence &,(sin2 2813)/ sin2 2013 can be approximated by 11 - tan2 8231 un-

215

less E is large such as 0.1. As for the error of the reactor measurements, we have S,,(sin226'13) I I0.018 for any value of sin226'13 in the case with the systematic error 0.8% and 40t.yr. &,(sin2 26'13)/ sin2 26'13 and &,(sin2 26'13)/ sin2 26'13 are shown in Fig.5(a) and (b), and from these figures one can read off the region where the 6'23 ambiguity is resolved. In general the 6'23 ambiguity is resolved if sin2 26'13 and 1- sin2 26'23 are both large. 5 . Summary

In this talk I have shown that the %fold parameter degeneracy in long baseline experiments can be visualized in the sin2 26'13-~;~plane. I have demonstrated that one may be able to resolve the 6'23 ambiguity by combining the results of the JHF experiment at the oscillation maximum and a reactor experiment whose sensitivity for sin2 26'13 is 0.02, if sin2 26'13 and cos2 26'23 are both relatively large. This scenario offers one of the strategies which are expected to resolve the ambiguities due to the parameter degeneracies." References 1. H. Minakata, H. Sugiyama, 0. Yasuda, K. Inoue and F. Suekane, arXiv:hepph/0211111. 2. F. Suekane, talk at The 4th Workshop on "Neutrino Oscillations and Their Origin", February 10-14, 2003, Kanazawa, Japan (http://www-sk.icrr.u-tokyo.ac.jp/noon20O3/transparencies/l1/Suekane.pdf) . 3. A. Cervera, A. Donini, M. B. Gavela, 3. J. Gomez Cadenas, P. Hernandez, 0. Mena and S. Rigolin, Nucl. Phys. B 579,17 (2000) [Erratum-ibid. B 593, 731 (200l)l [arXiv:hep-ph/0002108]. 4. V. Barger, D. Marfatia and K. Whisnant, Phys. Rev. D 6 5 , 073023 (2002) [arXiv:hep-ph/Ol12119] ; 5 . S. Parke, talk at The 4th Workshop on "Neutrino Oscillations and Their Origin", February 10-14, 2003, Kanazawa, Japan (http://www-sk.icrr.u-tokyo.ac.jp/noon2003/transparencies/l l/Parke.pdf). 6. A. Donini, talk at The 4th Workshop on "Neutrino Oscillations and Their Origin", February 10-14, 2003, Kanazawa, Japan (http://www-sk.icrr.u-tokyo.ac.jp/noon2003/transparencies/11/Donini.pdf) .

"As other alternatives to resolve the ambiguities, Parke5 proposed to measure both P(up 4v,) and P(Gp 4 3,) at JHF off the oscillation maximum and at NuMI at the oscillation maximum, whereas Donini6 discussed the measurements of the golden channel P ( Y , + up) and the silver channel P(Y, + vT) at a neutrino factory.

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Session 3

Atmospheric Neutrinos

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RESULTS FROM L3+C

P. LE COULTRE LHP-ETH Hoggerberg CH-8093 Zurich, Switzerland E-mail: Pierre.Le. [email protected] A short description of the L3+C detector is given. A precision measurement of the muon muomentum spectrum between 20 and 2000 GeV is presented together with it's zenith angular dependence and the charge ratio. Other results related to cosmic rays and astro-particle physics are mentioned.

1. The L3+C detector In order t o run the L3 detector installed at LEP, CERN, also as a cosmic ray muon telescope (L3+C) some 202 m2 of timing plastic scintillator tiles have been installed on top of the huge solenoidal magnet with it's volume of 1000 m3 and it's field of 0.5 T, see Figure la. Drift chambers installed inside allow for a precise measurement of the muon momentum (5.5 % at 100 GeV) and direction (the pointing precision is 0.1 "). The geometrical acceptance ranges up to 200 m2 sr. The energy threshold for cosmic muons is 15 GeV, since the detector is located only below 30 m of molasse. The geographic coordinates are 6.02 E , 46.25 "N and 450 m a.s.1. Data taking with an L3-independent trigger and readout system started in 1999 and stopped in Nov. 2000. A total of 1.2 . lo1' muon triggers have been collected during an effective live-time of 312 days. On the roof of the surface building (30 x 54 m2) an air shower scintillator array (Figure l b ) composed of 47 plastic scintillators (0.5 m2 each) has been installed. It allows to estimate the shower size associated with the muons measured underground. This part of L3+C was running in parallel with the underground spectrometer in 2000, and the events were time stamped with a common GPS clock.

219

220

b

8.) The L3 detector covered with timing scintillators, b.) the extensive air shower scintillator array.

Figure 1.

2. Physics Topics

The muon momentum mectrum: The muon spectrum is related to the muon neutrino spectrum since there exists a ”one t o one” relation between muon and muon neutrino fluxes (same parents !). Using the L3+C precision measurement of the muon spectrum (with a total error of less than 3 % at 100 GeV/c), the angular dependence and the charge ratio will reduce the uncertainty of the calculated neutrino spectrum above 20 GeV. A further motivation is to get constraints on the parameters entering the cascade calculation in the atmosphere: the primary composition and the inclusive cross-sections at high energies Figure 2a shows the absolute differential vertical spectrum compared to other absolute measurements, figure 2b the charge ratio as a function of energy and figure 3 the corresponding angular dependences. Anti-proton to proton ratio around 1 TeV: Data are available up to 40 GeV/c and are in agreement with secondary production models. L3+C is able to give a very reliable upper limit in the energy region between 500 GeV and 1 TeV. The method is to observe the ”moon shadow”: protons are deviated by the earth magnetic field to the east. High energy muons produced in the air shower keep nearly the original direction of the proton. Protons hitting the moon will be absorbed and a lack of muons pointing to the west side of the moon will be observed. The lower the energy, the further out the shadow will be. Anti-protons would produce a shadow on the opposite side of the moon. Figure 4 shows the observed shadow for two different muon energy ranges. From the absence of a similar shadow on the opposite side of the Moon an upper limit on the

22 1

I 8

L3+C preliminary

0.6

8 L3+C preliminary

a.) The vertical differential muon momentum spectrum compared to other absolute experimental results. The inner error bar denotes the statistical error, the full bar the total error. b.) The charge ratio as a function of the muon momentum.

Figure 2.

1.4 1.2

..................................

................................

1.2

1 0.8

0.6

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1 -

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cos(e)

Figure 3 . The zenith angle dependence of the momentum spectrum a.) and of the charge ratio b.). The histograms show the Target 2.1 transport code simulation with Target 2.1 (solid), SIBYLL 2.1 (dotted) 5 , and QGSJETOl (dashed) as interaction models (primary flux model according to ').

anti-proton to proton flux ratio of 0.15 with a 90 % CL could be extracted. Bursts from point sources: In a first search the sky has been subdivided in cells of 1" x I", 2" x 2 " , 3" x 3" , to record for each day, month or year period the number

222

Figure 4. The moon shadow seen underground through missing muon events.

The moon is supposed to be in the center and the selected muon energies are between 65 and 100 GeV in the first case and above 100 GeV in the second. Plotted is the significance of the signal (in units of us, see scale on the right hand side of the plot) as a fct. of the deflection from the moon’s position, after correcting for the earth magnetic field effect on the proton’s trajectory for given moon positions in the sky.

of muons collected in each cell along its track across the sky, and to look for an excess for different muon energy thresholds (20, 30, 50, 100 GeV). No excesses have been found and upper flux limits between and 10-8cm-2s-1 could be set. This search is presently being continued for shorter time windows. For a set of known point sources (Mrk 421, Mrk 501, Crab, Geminga, Cyg X-1, Cyg X3, Her X-1, 3-C 273, lES1426+428, 1ES2344f514) a dedicated signal search has also been performed, again without success. A second independent method with weaker event selection criteria for an all sky survey has also been tried. For one particular region near Pollux, a dc excess has been found with a chance to be a statistical fluctuation of only iO-5.5. Solar anisotrow: As a complementary research a study has been completed about the anisotropy of cosmic rays. The achieved sensitivity on the anisotropy amounts t o lop4, which is a quite good result, given the short data taking period and it is in agreement with other experimental data for muon energies above 100 GeV (corresponding roughly to primary protons of 1 TeV). No significant deviation from isotropy has been found. For muons above 20 or 30 GeV a significant departure from isotropy has been found for the second harmonic at solar frequency. In this case the structure of the anisotropy function is similar in shape to the one reported by the GRAND experiment at 0.1 GeV threshold, but with a smaller amplitude l o .

223

Search for GRB signals: There exist experimental hints from other experiments, that very high energy gammas are also present in gamma ray bursts (GRB); according to the HEGRA collaboration eventually up t o 16 TeV 1 2 . For such cases L3SC may have a chance to detect a few muons. Several models also predict these numbers. According to E. Bugaev 1 3 , assuming that the gamma ray spectrum gets flatter at high energies, one may observe up to 5 muons in one sec in our detector, against a very low background. 8 BATSE GRBs were in the field of view during stable data taking periods. As a conclusion about the present status of the GRB search the statement is that no signal from 8 selected BATSE GRBs has been found and the flux limits obtained are around 3 . lop5 cm2 s-l. A full sky survey is in progress. Muons associated with air showers: The cosmic ray composition above 100 TeV is still uncertain. The L3+C experiment consisting of a muon spectrometer and an EAS scintillator array samples both the muon and the electromagnetic component of EAS needed for the study of this question. About 25 showers per day were recorded by the L3+C air shower array with an estimated energy of 1015 eV (knee region of the primary spectrum). Muon spectra, as well as multiplicity- (with chosen energy thresholds) and pseudorapidity distributions as a function of the shower size have been obtained and compared to CORSIKA simulation l4 results. The fact that the CORSIKA simulation used here does not reproduce the single muon high energy momentum spectrum implies that one cannot trust conclusions about the primary composition from the mentioned distributions . Solar Flare of July 14, 2000: There is a considerable interest in identifying solar flares with particles accelerated to GeV and even higher energies in order to better understand the acceleration processes occurring at the Sun. Several experiments have reported observations of possible correlations between the flux of high energy muons and intense solar flares 1 5 . The exceptional solar flare of July 14, 2000, offered a unique opportunity for the L3+C experiment to search for a correlated enhancement in the flux of high energy muons. A faint signal of muons between 15 and 25 GeV, with a probability of 2.7. lop3 to be a background fluctuation, has been recorded at the time of the flare. Correlations over Large Distances: Two groups have claimed to have observed coincident events over large distances 16,and 17: A first trial has been performed for a one weak common running of H1 (DESY) and L3+C. No coincident events have been found.

224

Six months of d a t a , taken in parallel with CosmoALEPH (at 6 k m distance) in 2000, a r e presently being analyzed with respect to a coincidence of events within a time window of 0 to 100 psec and to t h e arrival direction. Other topics: We simply mention here meteorological effects, t h e measurement of t h e temperature coefficient as a function of t h e muon energy and the search for exotic events.

3. Conclusions

As presented in this report t h e L3+C experiment is delivering results on very different topics related to cosmic ray a n d astroparticle physics. Acknowledgements T h e L3+C group would like to express their thanks to CERN, to Edgar Bugaev, John Ellis, Andreas Engel, Anatoly Erlykin, Paolo Lipari, T h o m a s Gaisser, Morihiro Honda, Vadim Naumov, Leonidas Resvanis, and Todor Stanev for helpful discussions and their continuous support.

References 1. L3 detector: B.Adeva et al., NucJ.1nstr. Meth. A289 (1990) 35 2. L3+C detector: 0. Adriani et al., Nucl.Instr.and Meth. A488 (2002) 209 3. E.V. Bugaev et al., Phys.Rev. D58 (1998) 054001; G. Fiorentini, V.A. Naumov, F.L. Villante, Phys.Lett. B510 (2001) 173 and hep-ph/0201310; V.Agrawa1, T.K. Gaisser, P. Lipari and T. Stanev, Phys. Rev. D53 (1996) 1314; R. Engel, T.K. Gaisser, T. Stanev, Proc. ICRC 2001, vo1.3, p. 1029 4. R.Enge1 et al, 2001, Proc. 27th ICRC, 1381 5. R.Engel et al, 1999, Proc. 26th ICRC, 415 6. N.N.Kalmykov et al. 1997, Nucl. Phys. B (ProcSuppl.), 7 7. T.K.Gaisser and M. Honda, Ann. Rev. of Nucl. Part. Sci. 52 (2002) 153 8. R. Ramelli, Ph.D thesis, ETH Zurich, June 2002 9. F. Halzen et al., Phys.Rev. D55 (1997) 4475 10. J. Poirier and C.D’Andrea, Proc. XXVIIth ICRC, Hamburg, 2001, SH3.04 11. S.P. Ahlen et al. [MACRO collab.] Astr0phys.J. 412 (1993) 301 12. L. Padilla et al. [HEGRA collab.] A & A 337 (1998) 43 13. E. Bugaev, L3+C internal note (August 2000) 14. D. Heck, et al., FZKA-6019, Forschungszentrum Karlsruhe, 1998 15. S.N. Karpov et al., Nuovo Cim. 21 C, N.5, (1998) 551 16. 0. Carrel and M. Martin, Phys. Lett. B325 (1994) 526 17. N. Ochi et al., Proc. XIth ISVHECRI, NucLPhys. B(Proc.Supp1.) 97 (2001) 165, 169, 173; N. Ochi et al., Proc. 27th ICRC, (2001) paper No.219

A MEASUREMENT OF MU, P AND HE ENERGY SPECTRA AT THE SMALL ATMOSPHERIC DEPTH. *

K. ABE t for the BESS Collaboration$ Department of Physics, Graduate school of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

The cosmic-ray proton, helium, and muon spectra at small atmospheric depths of 4.5 28 g/cm2 were precisely measured during the slow descending period of the BESS-2001 balloon flight. The variation of atmospheric secondary particle fluxes as a function of atmospheric depth provides fundamental information to study hadronic interactions of the primary cosmic rays with the atmosphere. ~

1. Introduction Primary cosmic rays interact with nuclei in the atmosphere, and produce atmospheric secondary particles, such as muons, gamma rays and neutrinos. It is important to understand these interactions to investigate cosmic-ray phenomena inside the atmosphere. For precise study of the atmospheric neutrino oscillation [2], it is crucial to reduce uncertainties in hadronic interactions, which are main sources of systematic errors in the prediction of the energy spectra of atmospheric neutrinos. At small atmospheric depths below a few ten g/cm2, production process of muons is predominant over decay process, thus we can clearly observe a feature of the hadronic interactions. In spite of their importance, only a few measurements have been performed with modest statistics because of strong constraints of short observation time of a few hours during balloon ascending periods from the ground to the balloon floating altitude. *Work supported by grant 12047206 of the Ministry of Education, Culture Sports, Science and Technology (MEXT). tpresent address: Kobe University, Kobe, Hyogo 657-8501, Japan XBESS Collaboration formed with The University of Tokyo, High Energy Accelerator Research Laboratory (KEK), Kobe University, NASA Goddard Space Flight Center, University of Maryland, and The Institute of Space and Astronautical Science.

225

226

In 2001, using the BESS spectrometer, precise measurements of the cosmic-ray fluxes and their dependence on atmospheric depth were carried out during slow descending from 4.5 g/cm2 to 28 g/cm2 for 12.4 hours. The growth curves of the cosmic-ray fluxes were precisely measured. The results were compared with the predictions based on the hadronic interaction models currently used in the atmospheric neutrino flux calculations. 2. BESS spectrometer The BESS (Balloon-borne Experiment with a Superconducting Spectrometer) detector [3, 4, 5, 6, 71 is a high-resolution spectrometer with a large acceptance t o perform precise measurement of absolute fluxes of various cosmic rays [8, 9, 101, as well as highly sensitive searches for rare cosmicray components. Figure 1 shows a schematic cross-sectional view of the BESS instrument. In the central region, a uniform magnetic field of 1 Tesla is provided by a thin superconducting solenoidal coil. The magnetic-rigidity ( R = Pc/Ze) of an incoming charged particle is measured by a tracking system, which consists of a jet-type drift chamber (JET) and two innerdrift-chambers (IDC’s) inside the magnetic field. The deflection ( E l ) is calculated for each event by applying a circular fitting using up-to 28 hitpoints, each with a spatial resolution of 200 pm. The maximum detectable rigidity (MDR) was estimated to be 200 GV. Time-of-flight (TOF) hodoscopes provide the velocity ( p ) and energy loss (dE/dz) measurements. A 1/p resolution of 1.4 % was achieved in this experiment. For particle PRESSURE

AEROGEL

\ L e a d plate/ 0

05m

lm

Figure 1. Cross sectional view of the BESS detector.

227

identification, the BESS spectrometer was equipped with a threshold-type aerogel Cherenkov counter and an electromagnetic shower counter. The refractive index of silica aerogel radiator was 1.022, and the threshold kinetic energy for proton was 3.6 GeV. The shower counter consists of a plate of lead with two radiation lengths covering a quarter area of the lower TOF counters, whose output signal was utilized for e / p identification.

3. Balloon flight

-

The BESS-2001 bal40 loon flight was carried out at Ft. SumData acquisition time ner, New Mexico, 7 10 USA (34"49'N, 6 6 10 hL'/4' ' ' 1 6 " / 8 "j0 " 2 2 "i4' 104"22'W) on 24th Local timefhour) September 2001. Throughout the flight, the vertical geomag-40 netic cut-off rigidity was about 4.2 GV. k-6024 Altitude(km) The balloon reached Flgure 2. Altitude during the BESS-2001 balloon flight exat a floating periment(top). Temperature and residual atmosphere as a altitude Of 36 km function of altitude(bottom). at an atmospheric depth of 4.5 g/cm2. After a few hours, the balloon started to lose the floating altitude and continued descending for more than 13 hours until termination of the flight. During the descending period, data were collected at atmospheric depths between 4.5 g/cm2 and 28 g/cm2. The atmospheric depth was measured with accuracy of f 1 g/cm2, which comes mainly from an error in absolute calibration of an environmental monitor system. Figure 2 shows a balloon flight profile during the experiment.

--

4. Results and discussions

The proton and helium fluxes in energy ranges of 0.5-10 GeV/n and muon flux in 0.5 GeV/c-10 GeV/c, at small atmospheric depths of 4.5 g/cm2 through 28 g/cm2, have been obtained from the BESS-2001 balloon flight. The overall errors including both statistic and systematic errors are less than 8 %, 10% and 20 % for protons, helium nuclei and muons, respectively. The obtained proton and helium spectra are shown in Fig. 3 .

228

Around at 3.4 GeV for protons and 1.4 GeV/n 4 4 for helium nuclei, a I 4 44 geomagnetic cut-off ef**** 44 ! fect is clearly obh'4 ** A served in their spec++ ** I tra. Figure 4 shows ++ * I I the observed proton ++++ and helium fluxes as a function of the atmospheric depth. Below 0l- 1 1 ' A 26.4g/cmZ 2.5 GeV the proton 13.6g/cm: fluxes clearly increase 4.6g/cm as the atmospheric depth increases. It is because the secondary protons are Figure 3 . The observed proton and helium spectra. The error bars include statistical error only. In the proton specproduced in the at- tra, atmospheric secondary components are clearly observed mosphere. In the below 2.5 GeV in the BESS results. primary fluxes above the geomagnetic cutoff, the fluxes attenuate as the atmospheric depth increases. In this energy region, the production of the secondary protons is much smaller than interaction loss of the primary protons. This is because the flux of parent particles of secondary protons is much smaller Atm. depth (g/crn2) Am. depth (g/crn2) due to the steep spectrum Of primary COS- Figure 4. The observed proton and helium fluxes as a function of atmospheric depth. mic rays. Figure 5 show the observed muon spectra together with theoretical predictions.

' ,

I

*

P

229 2

The predictions were -110 made with the hadronic interaction model, u DPMJET-I11 [ll],which c, u was used for the eval* uation of atmospheric >L neutrino fluxes [ E l . ?@ s 10 The obtained proton 2fluxes were used t o re3 produce the primary i3: cosmic-ray fluxes in the calculation. Figure 6 shows the ob11 - DPMJET-ZZZ~ 4.6&m2 served muon fluxes as 1 ' 1 10 1 10 a function of atmoMomentum(GeV/c) Momentum(GeV/c) spheric depth together with the calculated Figure 5 . The observed negative muon spectra. The fluxes. The calcu- solid lines show theoretical predictions calculated by using DPATJET-111. lated fluxes show good agreement with the observed data. Further detailed study of the hadronic interaction models will be discussed elsewhere. T

2

3

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,

(

'

'

'

'

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5 . Conclusion

We made precise measurements of cosmicray spectra of protons, helium nuclei and muons at small I , / , , I I 4 10 30 4 10 0 atmospheric depths of Atm. depth (g/cm2) Atm. depth (g/crn2) 4.5 through 28 g/cm2, during a slow descend- Figure 6 . The observed negative and positive muon fluxes. ing period of 12.4 The solid lines show theoretical predictions calculated by hours, in the BESS- using DPMJET-111. 2001 balloon flight at Ft. Sumner, New Mexico, USA. I

230

In Fig. 7, obtained muon fluxes are shown as a function of atmospheric depth toget her with the previous measurements, CAPRICE98 [14] and BESS99 [13] data. We have obtained the precise muon fluxes Figure 7. The observed muon fluxes and the previous measureand spectra at ment, CAPRICE98, BESS99. Solid lines show theoretical prethe small atmo- dictions [12]. Primary fluxes in this predictions were tuned for spheric depths of 1998, thus these lines are not same as those in Figs. 5 and 6 4.5 through 20 g/cm2, where only few points of data had been available before this experiment. The results provide fundamental information to investigate hadronic interactions of cosmic rays with atmospheric nuclei. The measured muon spectra showed good agreement with the calculations by using the DPMJET-I11 hadronic interaction model. The understanding of the interactions will improve the accuracy of calculation of atmospheric neutrino fluxes. References 1. K. Abe et al., astro-ph/0304102, Phys. Lett. B in pres. 2. Y. Fukuda et al., Phys. Rev. Lett. 81 1562 (1998). 3. S. Orito, Proc. ASTROMAG Workshop,KEK Report KEK87-19, eds. J. Nishimura, K. Nakamura, and A. Yamamoto (KEK, Ibaraki, 1987) p.111. 4. A. Yamamoto et al., Adv. Space Res. 14 75 (1994). 5. Y. Asaoka et al., Nucl. Instr. and Meth. A416 236 (1998). 6. Y. Ajima et al., Nucl. Instr. and Meth. A443 71 (2000). 7. Y. Shikaze et al., Nucl. Instr. and Meth. A455 596 (2000). 8. T. Sanuki, et al., Astrophys. J . 545 1135 (2000). 9. M. Motoki, et al., Astropart. Phys. 19 113 (2003). 10. T. Sanuki, et al., Phys. Let. B, 541 234 (2002). 11. S. Roeseler, et al., SLAC-PUB-8740, hep-ph/0012252, unpublished. 12. M. Honda, et al., Proc. 27th ICRC, Hamburg, 2001, 162. and private communication. 13. T. Sanuki, et al., Proc. 27th ICRC, Hamburg, HE2.01 950 2001. 14. P. Hansen, et al., Proc. 27th ICRC, Hamburg, HE2.01 921 2001.

THE CALCULATION OF ATMOSPHERIC NEUTRINO FLUX.

MORIHIRO HONDA Institute f o r Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba 277-8582, Japan E-mail: [email protected] The processes of the atmospheric neutrino generation is overviewed. Not all the processes are well known, but some of them are remained as the uncertainties of the calculation. From the view point of the calculation, the atmospheric neutrino experiment is reviewed, and efficient determination of neutrino characteristics is discussed. A work to reduce the uncertainty using the secondary cosmic rays is introduced shortly.

1. An overview as the introduction The discovery of the neutrino oscillations and the neutrino masses using the the atmospheric neutrinos are illustrious achievements in the recent physics'. However, the uncertainty of the flux of atmospheric neutrino is a crucial for further study of the neutrino. and several experiments using accelerator neutrinos are being carried out. It is important to use the atmospheric neutrino flux properly with the knowledge of the uncertainties, and to reduce the uncertainty. lo4 Most of the calculation' of the atmospheric neu- z% trino flux is the simulation -0 of the atmospheric neu- I trino generation processes. a" 'E When high energy cosmic rays come in the atmosphere, the cosmic ray in- en teract with the air nuclei ,03 and produce many mesons. loo 10' lo2 lo3 lo4 lo5 Ek (GeV) The neutrinos are the decay product of mesons and Figure 1. Observed primary proton flux.

-

1-

231

232

the muons, which is also the decay product of the meson. The probability for mesons to decay or interact with air nuclei is determined by the meson energy and mass, decay life time, and the air density where these processes take place. The geomagnetic field sets a lower limit t o the momentum of cosmic rays t o come in the atmosphere. This is a source of directional variation of the atmospheric neutrino flux at lower energies. Thus, the primary flux of cosmic rays and the interaction model are the two major components in the calculation atmospheric neutrino flux. However, they are also the main sources of the uncertainties. The primary cosmic spectra below 100 GeV are well determined by the AMS3 and BESS4experiments. But, there are large uncertainties left above 100 GeV (Fig. 1). The situation for the hadronic interaction is similar or worse. The number of useful experiments are limited and concentrate in the lower energies (530 GeV). As the decay of main neutrino source mesons, kaons and pions, is well studied. Also the density structure of atmosphere and the geomagnetic field are monitored frequently and are known well at least as the average of a long period. The flux ratio of electron and muon neutrinos is almost free from the uncertainties of primary cosmic rays and interaction models, since it is determined by the r - p decay process. This is the main source of atmospheric neutrinos below 100 GeV. The energy differences between 3 neutrinos in the r - p decay and the steep spectra of pions give some effect on this ratio. However, even with large variation of interaction model, air density, etc, the calculation give a very close value t o the naive value, l / 2 . At energies above a few GeV, the muons tend to go into the ground before they decay. Therefore, the flux of electron neutrinos decreases more quickly than the flux of muon neutrino. The zenith angle variation of neutrino flux is related t o the production height of neutrinos. When the mesons are created at higher altitudes, the decay is more favored in the competition process of the decay and interaction than when they are created at lower altitudes, due t o the difference of air density.

233

As the first interaction point of inclined cosmic rays are higher than the vertical ones, the energy of inclined neutrinos is generally larger than that of vertical neutrinos for the same energy and same kind primary cosmic rays. Therefore, the horizontal atmospheric neutrino flux is generally larger than that of vertical ones, with the steep energy spectra of primary cosmic rays. If only the 7r - p decay is the source of the atmospheric neutrinos, there are almost no uncertainties for the zenith angle dependences. However, as the kaon is an important source of atmospheric neutrino at higher energies, the uncertainty of Kl7r-ratio causes a uncertainty for the zenith angle variation. In Fig. 2, the energy spectra of muon neutrino are depicted for different zenith angles, and the contributions from kaons and pions separately. However, it is seen that the contribution of kaons are still small at around 70 GeV. The flux ratio (vertical/horizontal) changes only 5 % by the change of 20 % change of K/.ir-ratio. The median energy of neutrinos, which cause the upward-through-going-muon events, is around 70 GeV. We often ignore the transverse momentum of the hadronic interaction, and geomagnetic filed in air, in the calculation of atmospheric neutrinos (1dimensional calculation). This is because the full treatment (3-dimensional calculation) consumes a huge computation power, and it is difficult to get a useful results within a reasonable computation time until recently. The differences of atmospheric neutrino flux calculated in l-dimensional of 3dimensional calculation are found at low energies and at the near horizontal directions. For the flux ratio, there are almost no differences. The difference disappears except for near horizontal directions at the neutrino energy above 1 GeV. The difference remains to higher neutrino energies 10 GeV due to the curvature of muons in the air. In principle, the difference can be calculated accurately, but we consider it as the uncertainty from the practical reason. Note, even in the l-dimensional calculation, the geomagnetic filed is taken into account outside the atmosphere. It is used to check if a cosmic ray can come in the atmosphere (rigidity cutoff test). It causes larger directional variation than the zenith angle variation at lower energies (21 GeV). Although there are some directional variations, there is an important symmetry for the atmospheric neutrino flux, if there are no neutrino oscillations. The neutrino flux arriving from the zenith angle 8, (0 5 8 5 90) is the same as the neutrino flux arriving from zenith angle of 180-8, (upward going) above a few GeV. This up-down symmetry is explained by the pure geometry. A t the production position, the zenith angles of both neutrinos are the same, then the zenith angle variation works the same for both neu-

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234

trinos. Also the neutrino flux is almost free from the rigidity cutoff above a few GeV. 2. Atmospheric neutrino experiments and uncertainties The neutrino events in a detector are categorized by the topology as the fully-contained-events, vertex-contained events, upward-stopping-muon events, and upward-through-going-muon events. For the fully-contained events, the neutrino energy is relatively well determined but the energy is limited to 5 3 GeV. For other type of events, it is difficult t o determine the neutrino energy, but the typical energies are estimated as 10 GeV for upward-stopping-muon events and vestex-contained events, and 70 GeV for upward through-going-muon events. We expect an up-down symmetry in the observation for fully and vertex contained events, but only upward going neutrinos are observed by upward-stopping and upward-through-going muon events observation. Here we assume the 2 component oscillations between p and r neutrinos. Starting from a u p , the probability to find the up at the distance of x is expressed by the formula,

-

N

P(u,, x) = 1 - sin2 28 sin2 Ax P ( u T z) , = sin2 28 sin2 Ax Where, 8 is the mixing angle of two neutrinos, and

Am2 lGeV E, lev2

AX = 1.27(-)(-)(-)

-

x lkm

3 x 10V3 eV, the oscillation With the rough estimation for Am2 length L = 1/1.27 . (leV2/Am2) . (E,/lGeV) km corresponding to the typical energy of neutrino experiment categories are 40 400 km for fully contained events, 2600km for upward-stopping-muon and vertex-contained events, and 18000 km for upward through going muon events. From eq. 1 and estimation of the oscillation length, the vertical down going neutrinos in the fully and vertex contained events are almost not affected by the neutrino oscillations. The oscillation length is far shorter than the diameter of the Earth for the fully and vertex contained events, and upward-stopping-muon events. We expect the phase averaged flux in neutrino oscillation, calculated by substituting sin2 Ax = 1 / 2 in eq. 1. For the upward-through-going muon events, however, the oscillation length is comparable to but longer than the diameter of the Earth.

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235

The mixing angle can be determined from the difference of expectation and observed flux for ver- 6 C tical upward neutrinos in 9 200 fully and vertex contained events, selecting a events O ii with energies above a few P GeV. The event number E 3 variation over zenith angle z is shown in Fig. 3 from SK data. The direction difference between the neutrinos

1

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and induced muons, and -1 -0.5 0 0.5 the effect of rigidity cutcos (0,) off is small for these events. The difference between ex- Figure 3. The angle dependence of event numbers. pected and experimental fluxes for upward going neutrino, then the difference between upward and downward going vertical neutrino flux are directly related to the mixing angle. Here, the uncertainties of the atmospheric neutrino does not affect much to the analysis of the mixing angle, because of the up-down symmetry of the expected atmospheric neutrino flux. The Am2 is determined by the analysis of oscillation length. Note, the distance between the neutrino production position and the detector is estimated by the formula: d = J(h2

+ 2Reh) + ( R ecos 0,)’

- Re cos 8,

,

(2)

where 8, is the arrival zenith angle of neutrino, Re 6400 km is the radius of the Earth, and h is the production height of neutrinos (10 15 km). We find the distance varies non-linearly and very quickly for cos8, = 0.1 -0.1 corresponding t o the distances from 100 to 1500km. Using the experiment category whose oscillation length is in this range, it is difficult to determine the oscillation length accurately. The neutrino direction is not determined well for neutrino energies below 1 GeV due to the large scattering angle in the detector. Also for the near horizontal directions and energies 2 1 GeV, the difference between 3-dimensional and 1-dimensional calculations is seen. It would be better not t o use the flux at near horizontal directions, until we can calculate the atmospheric neutrino flux accurately in the 3-dimensional framework. N

-

-

1

236

Therefore, the measurement of Am2 is the main task of experiment categorized as vertex-contained events, upward-stopping and upward-throughgoing muon events. Among them, the event rate is largest for upwardthrough going muon events. Therefore, we discuss this category observation here. The certainty of the zenith angle variation of the atmospheric neutrino flux is very important in this analysis. Remember, the oscillation length is longer than the diameter of the Earth, for the upward-through-going muon events, and the vari-1.0 -0.8 -0.6 -0.4 -0.2 0 ation from the no oscillacos (%I tion flux is small. Also Figure 4. Up going muon data and fit curve with free there is a large uncertainty normalization. They give almost the same ,$values. of absolute normalization expected for the atmospheric neutrino flux of this energy region. Note, the up-down symmetry of the atmospheric neutrino flux is not useful to determine the absolute normalization. This is very crucial situation to determine Am2, since we have t o assume a large uncertainty for the absolute normalization. As an example, we show a X2-test in Fig 4. Assuming the normalization is free, the x2 values are almost the same for the 3 curves. This is the main reason why the atmospheric neutrino experiment can not pin down the Am2 accurately.

3. Reduction of the uncertainties

For the the uncertainty of the primary flux above 100 GeV, we have nothing to do but wait for new results from the observation5. However, for the uncertainty of the interaction model, a calibration with the secondary cosmic rays may be useful. Here introduced is the calibration study using the muon flux observed at the balloon altitude. The 2001 BESS flight kept relatively lower altitude than the normal flight, and collected a large number of muon events. The data are very useful for this purpose. In Fig.5, we show the comparison of calculation and observation for two interaction models, which are used in the calculation of atmospheric

237

neutrino flux. It is seen that the dpmjet3 interaction model is favored by the experiment. It would be possible t o select the interaction model applying the comparisons t o all the available interaction models. More details will be published elsewhere6. 4. Summary

We have given an overview for the calculation the atmospheric neutrino flux and summarize the uncertainties. The experiments for atmospheric neutrino experiment is reviewed from the view point of the calculation and uncertainties. The mixing angle may be determined accurately by selecting a higher energy events from the fully and vertex contained events. However, the uncertainty of the absolute normalization of the atmospheric neutrino flux is crucial t o determine Am2. The reduction of the uncertainties in the absolute normalization is desired.

Acknowledgments The author is grateful for T. Kajita, K. Kasahara, S. Midorikawa, T. Sanuki, K. Abe and C. Saji for discussions. This study was partly supported by 0.3, ,

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Figure 5 . Muon flux normalized with depth at balloon altitude. Lines are calculated muon fluxes with dpmjet3, and Fritiof 1.6.

238

Grants-in-Aid, KAKENHI( 12047206), from the Ministry of Education, Culture, Sport, Science and Technology (MEXT). References 1. C.K. Jung, T. Kajita, T. Mann and C. McGrewl, Ann. Rev. Nucl. Part. Sci.

51, 451. (2001) and references there in. Also see C. Yanagisawa, this conf. 2. T. K. Gaisser and M. Honda Annu. Rev. Nucl. Part. Sci. 52, 153, (2002) and references there in. 3. J . Alcarez, et al., Phys. Lett. B490, 27 (2000) 4. T. Sanuki, et al. Astrophys. J . 545, 1135, (2000) 5. S. Haino, this conf. 6. K. Abe, ICRC2003, tsukuba.

PROGRESS IN ANALYSIS OF HIGH ENERGY PRIMARY COSMIC-RAY SPECTRA MEASURED IN BESS-02

S. HAINO f o r the BESS Collaboration * Department of Physics, Graduate school of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, J a p a n

In order to extend the energy range of primary cosmic-ray measurement up to several hundred GeV, we upgraded the BESS detector. The rigidity resolution was improved six times better than the previous detector. Balloon experiment was performed at Lynn Lake, in August 2002. The whole detector components worked as expected during the entire flight.

1. Introduction In the analysis of atmospheric neutrino oscillation, expected neutrino fluxes obtained by reliable calculations are necessary to determine the oscillation parameters in detail. Atmospheric neutrino events are observed in the Super-Kamiokande water Cherenkov detector in a wide energy range of 0.1-100 GeV. In order to calculate absolute fluxes of these atmospheric neutrinos precisely, absolute fluxes of primary cosmic rays up to around 1 TeV are indispensable, as well as detailed understanding of their hadronic interactions with the atmospheric nuclei. Although the primary fluxes in this energy region has been measured using calorimeters ', data of such experiments might have large systematic errors. Magnetic spectrometer, on the other hand, can determine the absolute magnetic rigidity of an incident particle only from its trajectory. BESS (Balloon-borne Experiment with a Superconducting Spectrometer) 2,3)4has provided proton and helium spectra up to 120 GeV and 54 GeV/nucleon (Figure 1) with the overall uncertainties below 5% and lo%, respectively, measured by the balloon flight in 1998 '. * BESS Collaboration formed with The University of Tokyo, High Energy Accelerator Research Laboratory (KEK), Kobe University, NASA Goddard Space Flight Center, University of Maryland, and The Institute of Space and Astronautical Science.

239

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Figure 1. Proton and helium fluxes measured by BESS-gs(Sanuki et a ~ ) and ~ , other experiments 1,6-16

The BESS detector is a high-resolution spectrometer with a large acceptance to perform highly sensitive searches for rare cosmic-ray components, as well as precise measurements of the absolute fluxes of various cosmic-ray particles. Taking its advantages, we upgraded the BESS detector to improve the rigidity resolution for the extension of primary spectra nearly up to 1 TeV. We call this upgraded instrument “the BESS-TeV Spectrometer,’. We performed a balloon experiment with the BESS-TeV spectrometer at Lynn Lake, Manitoba, Canada in August 2002.

2. BESS-TeV spectrometer The BESS detector is a magnetic-rigidity spectrometer which consists of superconducting solenoid, central JET-type drift chamber (JET), and two inner drift chambers (IDCs). In the bore of the solenoid, a uniform mag-

241

BESS-98

I

BESS-TeV

\

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/

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Jm

Figure 2. Cross-sectional views of BESS-98 and BESS-TeV. Thick lines represent the track length used for rigidity measurements.

netic field of 1 Tesla is provided. The magnetic rigidity is determined by a simple circular-fitting using the hit-points of drift chambers. In order to obtain higher momentum resolution, more measurement points, longer track length and better spacial resolutions are required. The BESS-TeV upgrade consists of three developments; (1) new JET and IDCs, (2) drift chambers outside of the solenoid, and (3) readout electronics of drift chambers. Figure 2 shows the comparison of the detector configurations between BESS-98 and BESS-TeV. The new J E T can measure 48 points in maximum, twice as BESS-98. Sense wires are spaced at shorter intervals for stronger electron focusing and the staggering t o resolve the left-right ambiguity becomes smaller for less electric field distortion. The spacial resolution is improved by such optimizations. To eliminate ambiguities in the alignment of J E T and IDCs, their end plates are machined in one body. Figure 3 shows a schematic view of new JET/IDCs. The comparisons of parameters of JET/IDCs between BESS-98 and BESS-TeV are summarized in Table 1. Furthermore, new drift chambers called Outer Drift Chambers(0DCs) are installed outside the solenoid. Track length becomes twice by using 4 points measured by each ODC. Figure 4 shows a schematic view of ODC. Signals from all drift chambers are read by Flash Analog-to-Digital Converter (FADC) modules. For the increased number of signals, a new FADC system is developed to operate within a limited power supply of primary batteries.

242

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Schematic view of new JET and

Table 1.

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Schematic view of ODC.

Comparison of the parameters of JET/IDCs.

I BESS-98 I BESS-TeV I

JET

Number of sense wires Max. number of hits

I 1

176 24

Wire spacing Spacial resolution

1 I

13.0 O 220 pm

I

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256 48

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14.0 O 160 pm

3. Drift chamber calibration All drift chambers are filled with the gas mixture of COz 90% and Ar lo%, called “slow gas”. Owing to its slow drift velocity and small longitudinal diffusion of the drift electrons, good spatial resolution and small Lorentz angle in a strong magnetic field can be achieved by using moderate speed readout electronics. However, the drift velocity of slow gas is relatively variable when its pressure changes. The variation is about a few % in the balloon flight and should be calibrated in the offline analysis. For cosmic-ray measurements, we can not use any absolute references for the drift chambers calibration such as beam timing, vertex position and the invariant mass which are usually used in accelerator experiments. In order to measure an absolute rigidity reliably up to 1 TV in such conditions, reliable hit reconstructions of drift chambers and deep understanding of chambers ,alignment are required. Therefore we developed a new chamber calibration procedure.

243

In this procedure, the consistency for all drift chambers is strictly required. The minimum number of parameters which should vary with the gas pressure during the flight, such as drift velocity and Lorentz angle, are calibrated. Since the gas volumes of the chambers are relatively small (40.7mxlm for JET), the uniform temperature is assumed and the common calibration parameters are used for all sense wires of each chamber. With redundant information of up to 60 hit points measured by JET/IDCs and ODCs, calibrations and position reconstructions are confidently carried out. In addition, a scintillating fiber counter system(SciFi) was installed to provide absolute position references for the calibration of ODCs. A set of SciFi consists of 2 layers of 1 mm2 square-shaped scintillation fibers which covers central one cell of each ODC (Fig. 5). Although SciFi can only measure hit positions in the accuracy of 0.5 mm, the center value of a distribution between a ODC track and hits of SciFi is an accurate position reference of an order of 10 pm when enough events are accumulated. Calibration parameters of ODCs are derived so that the center value becomes zero. 64 mm

Figure 5.

Schematic view of SciFi mounted on ODC

4. Flight

The BESS 2002 campaign was performed at Lynn Lake, Manitoba, Canada (cutoff rigidity 0.4 GV), in August 2002. The balloon launched in the evening and terminated in the next evening. The impact point was Ft. Mc-

244

Murray, Alberta, several hundreds kilometers west from Lynn Lake. Figure 6 shows a variation of the residual atmosphere during the flight. The balloon could keep stable floating altitude at the residual atmosphere around 5 g / c m 2 . We accumulated 11.8 M events during the floating period with the live time of 11.3 hours.

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'5003:00 06:OO 09:OO 12:OO 15:OO 1f 10 Local time

Figure 7. Normalized pressure, calibrated drift velocity (top) and spacial resolution (bottom) of JET at each run (shown in local time).

5. Performance of rigidity measurement Figure 7 (top) shows the pressure inside J E T normalized to 300K and the calibrated drift velocity. Because of the temperature rise inside the pressure vessel around sunrise, the variation of the normalized pressure is not so small, but the drift velocity was calibrated correctly following the variation. Figure 7 (bottom) shows the spacial resolution of J E T chamber at each run. The spacial resolution better than 160 pm was achieved during the whole flight. The performance of rigidity measurement was also evaluated from the combined fit of JET/IDCs and ODCs. Figure 8 shows the distributions of the deflection resolution of BESS-TeV and BESS-98 evaluated in the track-fitting procedure. The peak position of 0.77 TV-l corresponds to a MDR of 1.3 TV. Six times higher deflection resolution was achieved by the

245

BESS-TeV spectrometer than BESS-98. Although the designed rigidity resolution was achieved during the flight, the absolute rigidity still needs to be carefully calibrated. Especially, the alignment between J E T and ODCs is very important to determine accurately the absolute rigidity. Though the installations of drift chambers were performed with keeping a precision of 100 pm, further precise alignment needs to be obtained at an order of 10 pm by using the flight data. These analysis are now under way.

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Figure 8. Distributions of the deflection resolution of BESS-TeV and BESS-98. Each area of the histogram is normalized.

6. Prospect of the resultant primary spectra The absolute energy spectra of primary cosmic rays will be obtained with small systematic errors owing to the precise and reliable rigidity measurement enabled by the newly developed drift chambers and a calibration procedure. Although an estimated MDR of 1.3 TV was achieved, t o keep the statistic errors around 10% by using the flight data obtained during a live time of 11 hours, the energy spectrum limits for proton and helium nuclei are expected to be 600 GeV and 300 GeV/nucleon respectively. The resultant primary cosmic-ray spectra measured with BESS-TeV will be reported elsewhere in the near future. The data will help us to further understand the atmospheric neutrino oscillation phenomena and its origin.

246

7. Summary In order to extend the energy range of primary cosmic-ray fluxes up to several hundred GeV, BESS spectrometer was upgraded. We performed a balloon experiment in August 2002 and accumulated cosmic-ray data with the live time of 11 hours. Their analysis is in progress. We confirmed the designed performance of all new drift chambers during the whole flight. The experimental results of cosmic-ray proton and helium fluxes measurement in BESS-02 will be reported elsewhere in the near future.

Acknowledgment The BESS-TeV experiment has been supported by Grand-in-Aid for Scientific Research on Priority Areas (12047227 and 12047206) from the Ministry of Education, Culture, Sports Science and Technology (MEXT). We would like to thank NASA, ISAS, ICEPP, and KEK for their continuous support.

References M. J. Ryan et al., Phys. Rev. Lett. 28, 1562 (1972). Y. Ajima et al., Nucl. Instrum. Methods A 443,71 (2000). Y . Asaoka et al., Nucl. Instrum. Methods A 416,236 (1998) Y. Shikaze et al., Nucl. Instrum. Methods A 455,596 (2000) T. Sanuki et al., Astrophs. J 545, 1135 (2000). L. H. Smith et al., Astrophs. J 180,987 (1973). W. R. Webber et al., Proc. 20th ICRC(Moscow) 1 (1987) 325. E. S. Seo et al., Astrophs. J 378,763 (1991). P. Papini et al., Proc. 23rd ICRC(Ca1gary) 1 (1993) 579. 10. W. Menn et al., Proc. 25th ICRC(Durban) 3 (1997) 409 11. M. Boezio et al., Astrophs. J 518,457 (1999). 12. R. Bellotti et al., Phys. Rev. D 60,052002 (1999). 13. J. Alcaraz et al., Phys. Lett. B 490,27 (2000). 14. M. Boezio et al., Astropart. Phys. in press; astro-ph/0212253 15. J. Buckley et al., Astrophs. J 429,736 (1994). 16. J. Alcaraz et al., Phys. Lett. B 494,193 (2000).

1. 2. 3. 4. 5. 6. 7. 8. 9.

ATMOSPHERIC NEUTRINOS

CHIAKI YANAGISAWA Department of Physics and Astronomy, University at Stony Brook, Stony Brook, N Y 11794-3800, USA E-mail: [email protected] This is a review on atmospheric neutrinos based on the talk given at NOON2003, Kanazawa, Japan. First a short description of atmospheric neutrino anomaly is presented. Then further evidences of the anomaly are described in some detail. Among proposed explanations for the anomaly, explanations in terms of the most favorable one, i . e . , neutrino oscillation and of another possibility, i.e., neutrino decay are reviewed.

1. First Manifestation of Atmospheric Neutrino Anomaly

First indication of the atmospheric neutrino anomaly was observed by the IMB and Kamiokande experiments as a deviation of vP/veratio from the expected value, although statistically not significant. With much larger statistics and smaller systematic errors, the latest result (livetime 1489 days) from Super-Kamiokande on the ratio normalized to the expected value from Monte Carlo are: ( p / e ) d , t , / ( p / e ) n c = 0.638 0.016 0.05 and 0 . 6 2 9 ~f~0.092 : ~ for ~ ~sub-GeV and multi-GeV data sample, respectively A significant deviation from the expected value 1 was obtained. The past criticism that a detector with a different detector technology, namely, a detector with tracking devices did not see any deviation was found to be false as the Soudan 2 experiment also found a significant deviation in this double ratio, 0.68 f0.12 z. Furthermore, although the MACRO experiment had no capability to detect electrons and measure their energies and could not obtain the double ratio, it found a significant deviation in the ratio

+

pdata/pMC

+

'.

'.

2. Neutrino Oscillation Among several proposed solutions to the anomaly, one of the simplest and most elegant one is neutrino oscillation. It is more so, as the latest SNO and

247

248

KamLAND results are very consistent with neutrino oscillation as a cause of another anomaly in solar neutrino flux, together with the solar neutrino results from the Super-Kamiokande, Homestake, and two gallium experiments. The probability of the neutrino oscillation v p + v, is expressed by P(v, --t v,) = sin2(28)sin2(1.27Am2L/E)where Am2 is the mass squared difference between two relevant neutrino mass eigenstates in eV2, L the distance that neutrino travels in km, and E the neutrino energy in GeV. The subscript z represents a neutrino flavor other than vp. As clearly seen in this formula, the probability has a dependence on L/E. As the neutrino oscillation probability is a function of L, the neutrino travel distance, which is in turn a function of the zenith angle of the neutrino. If the anomaly is truly due to the neutrino oscillation, the zenith angle distributions we observe should be distorted from what are expected. Four left plots in Figure 1 by Super-Kamiokande show the zenith angle distributions of p- and e-like single ring events of a variety of classes: subGeV is a class of fully-contained (FC) events with visible energy less than 1.3 GeV while multi-GeV with visible energy greater than 1.3 GeV, and P C is partially contained events. While the e-like events show no significant deviations from the expected distributions, the p-like event together with P C events show significant deviations which are consistent with neutrino oscillation. The dotted (dashed) histograms are what you expect if the up + v, is (not) at work with best fitted parameter values. Two right plots in this figure show the zenith angle distributions of v, (top) and up (bottom) events by Soudan 2 and confirm the Super-Kamiokande result. MACRO also sees significant deviations from the expected in its zenith angle distribution of up events and its result is also consistent with neutrino oscillation. As mentioned earlier, since the oscillation probability actually depends on the path length L and the neutrino energy E in the form of L/E, it is more appropriate to study the ratio N,OpZ,/N;?$ as a function of L/E obs(exp)

where NPce, is the number of FC p(e)-like single ring events observed (expected). As seen in the left plot of Figure 2 by Super-Kamiokande again while the e-like events do not show any significant deviation from the expected value 1, the p-like events show more depletion of events as L/E values become larger. The histograms are what you expect if the v p v, is a t work with best fitted parameter values. The Super-Kamiokande result is confirmed by MACRO (See the right plot in Figure 2 where only v p events are used and by Soudan 2

249

... ....

MC without Y oscillation MC with vr ~ ~ c ~ i l o t ~ o n

Figure 1. Zenith angle distributions observed by Super-Kamiokande (left) and by Soudan 2 (right). In the left plots histograms are expected distributions without and with neutrino oscillation (best fit)

Figure 2.

L/E distributions observed by Super-Kamiokande (left) and MACRO (right).

If we assume that the anomaly is due to neutrino oscillation v p + v,, which is very reasonable, we can obtained a 90% C.L. contour of the allowed region in the oscillation parameter space: Am2 vs. sin220. Figure 3 shows the 90% C.L. allowed region obtained by Super-Kamiokande ', MACRO and Soudan 2 and all the results are consistent. The best values from three experiments are: (Am2(eV2),sin220)= (2.5x1OW3, 1.0) (SuperKamiokande); (7.0x1Op3, 0.98) (Soudan 2); ( 2 . 5 ~ 1 0 - ~1.0) , (MACRO). Super-Kamiokande found that the best parameter values gave the x2 = 163.2/(170 d.0.f) while that for null-oscillation hypothesis 456.5/(172 d.0.f). There is a room to add one more component to the minimum three

250

-'-

7 1 0

Vp -V, Oscillation

sin'20

Figure 3. (right).

L I E distributions observed by Super-Kamiokande (left) and by MACRO

neutrino generation scheme. This possible component is a sterile neutrino v, that was proposed to explain the LSND anomaly. Results from current analyses by Super-Kamiokande and MACRO make the pure oscillation vb + u, without involving v, very unlikely. However, us's involvement as vb +cos(v,fsin(v, is still a possibility. The existence of the v, component changes the zenith angle distributions because it introduces a suppression of the oscillation effect through matter effect and deficit in neutral current interaction events. Super-Kamiokande used this fact to set allowed regions of Am2 and sin2( as shown in Figure 4 '.

Allowed regions of Am2 and sin2<.

Now that it is established that major component of the oscillation is v, + v,, it is natural to look for a positive signal for v, appearance.

251

Super-Kamiokande analyzed the data using three defferent but somewhat correlated methods to see the signal. One method is based on event shape analysis using energy flow and on likelihood. Figure 5 is the zenith angle distribution of T candidates where the Monte Carlo predictions are for Am2 = 2.5 x l0W3 eV2 and sin'219 = 1.0. An excess from 7 events is visible in up-going events (hatched area). This analysis found the number of T produced to be 135221 with the estimated Am2 = 2.5:; x 10-3eV2 and sin220 = 1.0. Other methods found consistent results.

rn ~

...........

-1.0

Figure 5.

Data "p,e, T Monte Carlo (oscillated) V p,

Monte Carlo (oscillated)

0.0 cosine of zenith angle

Zenith angle distribution of

T

0

event candidates.

Super-Kamiokande did a neutrino oscillation analysis in a more general three-generation neutrino oscillation framework with a reasonable assumption that Am;, = Am:,, and Am:, = Amtolar. Figure 6 shows contours in Am2-sin22OI3space (left), and in sin2&3-sin2&3 space (right). The best fit corresponds to pure maximal up + u, oscillation '.

3. Neutrino Decay Although evidences for neutrino oscillation are overwhelming, it is still possible that neutrinos may decay. Using a model in which u1 u,, uw 4n19vz+cos19u3 and u3 decays to u4 that does not mix with other us (Am&=O), as shown in Figure 7, Super-Kamiokande obtained allowed regions in the parameter space, m / r vs. sin20, where m and r are the mass and the decay constant of u3, respectively '.

-

252

10

0.5

0.4 10

-0.3 m-

A

N

%

.-C

N -

E

v)0.2

10 CHOOZ PAL0 VERDE

0.1 SK 9O%C

lo 0

0.2

0.4 0.6 0.8 sin22e,,, = sin%,,

1

0

sin2e,,

Figure 6. Allowed regions in three-generation oscillation parameter space by SuperKamiokande.

- 90% C.L.

___

Figure 7.

Allowed

99% C.L. Allowed

- 90%C.L. Excluded - 99% C.L.

Excluded

Allowed regions in neutrino decay parameters by Super-Kamiokande.

References 1. J. Kameda, Talk at Moriond 2003, Les Arcs, France, Mar. 16, 2003. 2. T. Mann, Talk at Neutrino Conference 2002, Stony Brook, New Yorlc, U.S.A., Oct. 2002. 3. M. Ambrosio et al., hep-ex/0304037.

STUDY OF NEUTRINO-NUCLEUS INTERACTIONS FOR NEUTRINO OSCILLATION EXPERIMENTS MAKOTO SAKUDA KEK, IPNS Tsukuba-shi, 305-0801,Japan E-mail: makoto. sakudaekek. j p

The field of neutrino physics is developing rapidly after the atmospheric neutrino oscillations and solar neutrino oscillations are established. We review the recent progress in the calculation of neutrino-nucleus interactions which is being made for the future precise neutrino oscillation experiments.

1. Neutrino-Nucleus Interactions in the Few-GeV Region In the neutrino oscillation experiments, the measured event rate and neutrino spectrum are compared with the theoretical calculation and the neutrino oscillation parameters are determined. The theoretical calculation must be verified with experimental data of cross sections and the various distributions (q’, p,, 0,, pp, 0p). K2K experiment’ has shown that the oscillation analysis is not affected by the uncertainties in neutrino interactions at the present statistics. However, precise knowledge of neutrino-nucleus interactions will be important in the future precision experiments where measurements of Am2 at 1% level are proposed. For example, an accuracy of 1-5 MeV will be needed in E, reconstruction in the future while the present accuracy is about 20-40 MeV due to the energy calibration and nuclear effects2.Accurate measurements of charged-current cross section were performed with narrow-band beams by CDHS3/CHARM4/CCFR5 for E+20 GeV, with accuracy of 23%. Experiments below 20 GeV were performed with wide-band beams. Many processes contribute equally, with +20% errors, in this energy region. They include charged-current (CC) quasielastic scattering, CCheutral-current (NC) single pion production, CCMC multipion production, deep inelastic scattering, CCMC coherent-pion production, and NC elastic interaction. Furthermore, nuclear effects are expected to be significant in the low Q2 region, where the cross section is large. Nuclear effects include Fermi motion, Pauli blocking, nucleon binding, nuclear correlation, shadowing, the EMC effect and final-state interactions. Recent review of the neutrino-nucleus interactions can be found in Refs.6-8. Neutrino oscillation experiments ( K ~ I c ’ . ~MiniBooNE”, , MINOS’‘*12, OPERAi3, ICARUS14, JHFKamioka”) have to work in this energy region. 253

254

Further, the measurements of the neutrino-nucleus interactions provide weak nucleon form factors. Even though the vector form factors have been studied in electron-nucleon scattering experiments, very few is known on the axial form factors. Neutrino-nucleon scattering experiments can determine the axial vector form factors accurately. 2.

Recent Progress in the Calculation

Among many topics discussed at NuIntOl/NuIntO2 Workshopsf6, we explain four topics in which much progress is being made: electromagnetic form factorsf7”*,spectral function c a ~ c u l a t i o n ’ ~ ~,~single ” * ~ ’ *pion ~ ~ productionz3and deep inelastic ~cattering”.~~. There are many other interesting topicsI6 like T production and color transparency which are as important as these topics. 2.1) Nucleon Form Factors Electromagnetic current (J,ern) and weak hadronic charged current (J~~~=v;+~~-A:+~~) is written in terms of form factors: i v,F,NtQ2)+2M048qPF,N(Q’)

< N(p‘)lJ,” IN(p)>=

; ( P I )

< p(p‘)l”+’’ I n ( p )

~(p’)~.Y,F,tQ2)+q.FptQ2)3((p).

where Q2 (=-q2) is the four-momentum transfer, M is the nucleon mass, and pp and pn are the anomalous magnetic moments of the proton and neutron, respectively. F?(Q2) and FzN(Q2)are the Dirac and Pauli form factors of proton and neutron (N=p or n). They are related to the experimentally determined Sachs form factors ( GEN(Q2)and GMN(QZ) ) as G l (Q = F I N(Q I ) -rF,N (Q G,N(Q’)=F,N(Q2)+F2N(Qz)

with

7=-

Q’ 4M

G:.‘ytQ’)=,[G,P.,(Q2)-G;,ytQ’)] 1 F,“(Q*)=

GitQ’)+zG:tQ’) 1+z

and

F:tQ2)=

G: tQ’)-GitQ’) 1+T

The differential cross section for the neutrino-nucleon quasi-elastic scattering is calculated26 ,

255

where GF is the Fenni coupling constant, 0, is the Cabbibo angle, and (su)=4ME,,-Q2-m2. A(Q2), B(Q2) and C(Q2) are given by, A = 4 (m2/4M2+7) [ (1 +7)lFAI2- (1 -.r)lFIVI2 + 7 (1- T ) I F ~ ~7IReFIV*FZV ~+~ -m2/4M2(1F1V+F2v12 + IF,V+2Fp12-4( l + ~IFd2) ) ] B =-47 ReF*A(FlV+F2V), and C =1/4(IF~12+IF~V12+dF2v12), (4) where m is the lepton mass. Sachs form factors were measured in electron-proton and electron-deuteron scattering experiments in 1960s. The following dipole parametrization by Galster" has been commonly used: GEp(Q2)=D,GMP(Q2)=p+3,GM"(Q2)=p,,D.and G~"(Q~)=-~,,T/( ~+X.S)D, with D=l/( 1+Q2/Mv2)2and k5.6. (5) The vector mass Mv=0.843 (GeV/c2) is determined in the fit to the electron data. Even in 1970, it was known that the dipole parametrization was good at 10% level and failed at high Q2 region2'. An axial vector form factor was conventionally parametrized in a dipole form and the pseudo-scalar form factor is related to the axial vector form factor through PCAC as

with FA(0)=-1.2617W.OO35. While vector form factors were determined in electron beam experiments, axial vector form factor was estimated in neutrino beam experiments. In the neutrino experiments, GE"and Fp were ignored in the calculation. ddd@(v,,n3 p-p) x l U38cm2 Ratio of new dald@/old code

6

Figure 1. a) Differential cross section do/dq2(v,+n+p7p) at &=I GeV with Galster dipole form factors26and with new vector form factorsz8and (b) the ratio.

256

In the past, the nucleon electromagnetic form factors have been studied from unpolarized electron beam scattering experiments. Recently, new accurate measurements were performed with polarized electron beams. The better parametrizations for vector form factors were proposed as in Refs.29-30. Clear deviation from a simple Galster parametrization is seen for the form factors at the level of 10% and the accurate measurement of electric charge distribution of neutron, GEn(Q2),has been measured31. The effect of those new form factor, especially of GE", on the neutrino total cross sections was shown to be a few % by Budd" at NuInt02. Fig.l shows32 the differential cross section do/dq2(v,+n+p-+p) at E,,=l GeV wit dipole form factors" (GEn=O)and with new vector form factors29 and (b) the ratio. The differential cross section becomes smaller by 4-5% at Q2=0.3 (GeV/c)2 and becomes larger by 4-5% at Q2=1.5 (GeV/c)2, reflecting the change in the vector form factors. The pseudoscalar form factor contributes at the threshold of lepton production, namely at &=200-300 MeV (near muon threshold) or at 5-6 GeV (2 threshold). 2.2) Spectral Function The spectral function P(k,E) is the probability to find in a nucleus a nucleon of momentum k and removal energy E. About 70% of the spectral function is obtained mostly from (e,e'p) data while the remaining 30% of the nucleons are correlated each other and are estimated by the local density approximation (LDA)'',19. Fig.2 shows the Fermi momentum distribution of oxygen. Solid line denoted as LDA is given by the spectral function. The dotted points represents the calculation by Pieper which uses a realistic nucleonnucleon potential. Although two methods use a quite different approach, they agree each other. The flat distribution is that for a uniform Fermi-gas model when nucleons occupy plane wave states in a uniform potential. 101

-

100

0

hfontc Carlo ralriilntion (S Pit-prr e t rrlj

0

E

u3

10-1

u h

A

y

10-2 10-3 10-4

0

1

2

3

4

k [fm-'1 Fig.2 Fermi momentum distribution of oxygen'*. The solid line (LDA) represents the spectral function calculation.

257

We show in Figs. 3 a comparison of the experimental data34*35*36 of '*C(e,e') and 160(e,e') reactions with the calulation for the neutrino quasi-elastic scattering. We generate neutrino-oxygen quasi-elastic events N(ve,e-) at the same

beam energy and the same electron scattering angle, namely the same energy transfer as the existing N(e,e') experiments. The calculation was done by Nakamuram at NuInt02 workshop and is based on the relativistic Fermi-gas model by Smith-Moniz3' using the Fermi momentum distribution estimated by the spectral function. The vertical scale of the prediction is arbitrary. This figure shows that the estimation of the binding energy and the Fermi momentum distribution of the spectral function is good. Thus, (e,e') data are very useful to test the lepton energy kinematics at the level of a few MeV. Similarly , we show in Fig.4 the corresponding figure with Nuance Monte Carlo3' using a relativistic Fermi-gas model3' and a uniform Fermi-gas. The Nuance MC uses the binding energy 21 MeV and kF =225 MeVIc. 2.3) Single Pion Production Rein-Sehgal model and Schreiner-von Hippel mode141are commonly used in neutrino experiments. However, these models are based on the old data taken in 1960s and they include some obsolete parameters. It is natural that we get different distributions and different cross sections for the same MA value. trni rLJqction

50

40

20 100

200 Ebuori-kscot(MLV)

500MnV. 60deq

tbccm--tocot(hncV)

_I

# > .

-. 2

VI

Ebeom - EL.c.~:II(MoV) 73OMeV. 3 7 . 1 deq.

2

<>

7 B O M r V . 50.4drq.

g

tbcom---tsco:(McV)

700MeV. 32drq.

cj

..

,-

.....

v,

2o

> -.. lj

.L

13

c

G

,r> v,

P

C)

o

aoO

400

600'" a

Ebecm-Essot(McV) B80MeV. 32deg.

$

u

0

410 6G Fbeom--Fsco:(MsV) 1 0 8 O M e V . 32deg.

200

Fig.3 Comparison of data34*3533a and the calculation for the energy transfer (CU=E,-E&.) at the fixed scattering angle. The first enhancement is due to the quasi-elastic scattering. The solid line represents the spectral function calculation" for the quasi-elastic scattering.

258

Fig.4 Comparison of data34*35,36 and the calculation for the energy transfer (o=E,-E,.) at the fixed scattering angle. Histogram is the calculation of Nuance Monte C a r l ~ with ~ ~a uniform Fed-gas model. We proposez3 to use the following form factors. For W<1.6 GeV/c2, resonance production model with Schreiner parameters without adhoc parameters and three resonances may be used. ci A>v(Q2)=c,A,V (0)G(W,Q2 ,kF)1/2/(1+Q2/MV,A2)2, (i=3-5). (7) Pauli suppression42G(W,Q2 ,kF) is about 10-20% at low Q2 region (<0.2 (GeV/c)') and is different for different target. Non-resonant contribution,<20%, may be added. For W>1.6 GeV, deep inelastic scattering may be used. Paschos et al.43 already show that this scheme may work. We must correct CiV(Qz) with new A(1232) form f a ~ t o r s ~ ,since ~ ~ , ~they ' fall more rapidly than the elastic form factors. 3. Summary The accuracy of neutrino-nucleus (v-N) interactions at E,=O. 1-10 GeV is still poor, about 10-20% in cross section measurements. We will combine both e-N data and v-N data to understand v-N interactions better. Vector form factors are now being updated from the study of e-N scattering. It will change the quasielastic cross sections by 35% and the Q2 distributions by f5%. The calculation of resonance production is also being updated with new A(1232) form factors and the nuclear effect. Spectral function calculation which improves the old Fermi-gas model calculation is extensively studied. Transition between resonance production region (W=l.6 GeV/cz) and deep inelastic scattering (DIS) regionz4 (W>2.0 GeV/cz) is complex and involves more resonances and non-resonant contribution. Bodek's calculationz5is the first

259

trial to extrapolate DIS to the transition region. The nuclear PDF (parton distribution function in nuclei) is different from nucleon PDF, as known as EMC effect, and parametri~ed~~. The nuclear effects at high energy neutrino scattering are discussed in Ref.8 and 47. K2K near detectors (IktodSciFi) are producing new data. B o o m and an upgraded K2K detector (SciBar) will produce new data soon. MINOS near detector and ICARUS will come in operation in 2006. All these studies and development will be a step toward the precision neutrino experiments. References 1. M.H.Ahn et al.(K2K), Phys.Rev.Left.90,041801(2003);Y.Itow, NuInt02 Workshop, Irvine, December 12-15,2002. 2. C.W.Walter, NuInt02 Workshop, Irvine, December 12-15,2002. 3. P.Berge et al.(CDHS), Z.Phys. C35 (1987)443. 4. J.V.Allaby et al.(CHARM), Z.Phys. C38( 1988)403. 5 . D.B.MacFarlane et al., Z.Phys. C26(1984)1. 6. Paolo Lipari, Nucl.Phys.B(Proc.Suppl.)112,274(2002). 7. Makoto Sakuda, Nuc1.Phys.B (Proc .Suppl.) 112, 109(2002). 8. E.Paschos, Nucl.Phys.B(Proc.Suppl.)lP2, 89(2002). 9. T.Kobayashi (K2K), This Proceedings. 10. E.Zimmerman (MiniBooNE), This Proceedings. 11. M.Messier (MINOS), This Proceedings. 12. S. Wojcicki (MINOS), This Proceedings. 13. M.Nakamura (OPERA), This Proceedings. 14. A.Ereditato (ICARUS), This Proceedings. 15. A.K.Ichikawa (JHF), This Proceedings. 16. See http://neutrino.kek.jp/nuintOl/and http://www.ps.uci.edu/-nuinti 17. S.K.Singh, Nucl.Phys.B(Proc.Suppl.)ll2, 109(2002). 18. H.Budd, NuInt02 Workshop, Irvine, December 12-15,2002. 19. 0. Benhar et al., Nucl.Phys. A579,493(1994). 20. V. Pandharipande, Nucl.Phys.B(Proc.Suppl.)ll2,5l(2002). 21. H.Nakamura and R.Seki, Nucl.Phys.B(Proc.Suppl.)l12, 197(2002). 22. O.Benhar, NuInt02 Workshop, Irvine, December 12-15,2002. 23. E.Paschos et al., DOTH03001, August, 2003; M.Sakuda, NuInt02 Workshop, Irvine, December 12-15,2002. 24. A.Bodek and U-K.Yang, Nucl.Phys.B(Proc.Supp1.)112,70(2002). 25. C.Albright and C.Jarskog, Nucl.Phys.B84,467( 1975). 26. C.H.Llewellyn Smith, Phys. Rep. C3, 261(1972).

260

27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46.

SGalster et al., Nucl.Phys.B32,221(1971). M .Gourdin, Phys.Rep.C 11,29(1974). P.Bosted, Phys.Rev.C51,409(1995). E.J.Brash et al., , Phys.Rev.C65,051001(2002). H.Gao, Int.J.Mod.Phys.E12,1(2003). C.W.Walter et al., in talk at NuFact03 Workshop, May, 2003. S.C.Pieper,R.B.Wiringa and V.R.Pandharipande,Phys.Rev.C46,1741( 1992). M.Bernheim et al., Nucl.Phys.A375,381(1982). J.S.O’Connel1et al., Phys.Rev.C35,1063(1987). M.Anginolfi et al., Nucl.Phys.A602,405(1996). R.A.Smith and E.J.Moniz, Nucl.Phys.B43,605( 1972). D.Casper, Nucl.Phys.B(Proc.Suppl.)ll2, 161(2002). D.Rein and L.M.Sehgal., Ann.Phys.(N.Y.)133,79(1981). D.Rein, Z.Phys.C35,43(1987). P.A.Schreiner and F.von Hippel, Nucl. Phys. B58,333(1973). S.L.Adler, S.Nussinov and E.A.Paschos, Phys.Rev.D9,2125(1974). E.Paschos, L.Pasquali and J-Y.Yu, Nucl.Phys.B588,263(2000). G.Olsson et al., Phys.Rev.D17,2938(1978). L.M.Stuart et al., Phys.Rev.D58,032003(1998). S.Kumano, Nucl.Phys.B(Proc.Suppl.)ll2, 42(2002); k.J.Eskola et al., Nucl.Phys.B535,351(1998). 47. K.McFarland, Nucl.Phys.B(Proc.Suppl.)ll2,226(2002).

Session 4

Dark Matter and Double Beta Decay

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STATUS OF EVIDENCE FOR NEUTRINOLESS DOUBLE BETA DECAY, AND THE FUTURE: GENIUS AND GENIUS-TF

H. V. KLAPDOR-KLEWGROTHAUS * Max-Planck-Institut f r Kemphysik, P 0. Box 10 39 SO, 0-49029 Heidelberg, Germany

The first evidence for neutrinoless double beta decay has been observed in the HEIDELBERGMOSCOW experiment, which is the most sensitive double beta decay experiment since ten years. This is the first evidence for lepton number violation and proves that the neutrino is a Majorana particle. It further shows that neutrino masses are degenerate. In addition it puts several stringent constraints on other physics beyond the Standard Model. The result from the HEIDELBERG-MOSCOW experiment is consistent with recent results from CMB investigations, with high energy cosmic rays, with the result from the 8-2 experiment and with recent theoretical work. It is indirectly supported by the analysis of other Ge double beta experiments. The new project GENIUS will cover a wide range of the parameter space of predictions of SUSY for neutralinos as cold dark matter. Further it has the potential to be a real-time detector for lowenergy ( p p and 7Be) solar neutrinos. A GENIUS Test Facility has come into operation on May 5, 2003. This is the first time that this novel technique for extreme background reduction in search for rare decays is applied under the background conditions of an underground laboratory.

1. Introduction In this paper we will describe in section I1 the recent evidence for neutrinoless double beta decay (Ovpp),found by the HEIDELBERG-MOSCOW experiment 1 , 2 ) 3 , 4 , 5 , which is since ten years now the most sensitive double beta experiment worldwide, This result is T $ ~= (0.8 - 18.3) x 1 0 (95%c.z.) ~ ~ ~ (1) with best value of T'$2 = 1.5 x y. Double beta decay is the slowest nuclear decay process observed until now in nature. Assuming the neutrino mass mechanism to dominate the decay am litude, we can deduce (m,) = - 0.56) eV (95%c.Z.) (2)

(1.11

This value we obtain using the nuclear matrix element of 2 2 . Allowing for an uncertainty of k50% of the matrix elements (see this range widens to 5114),

*Spokesman of HEIDELBERG-MOSCOW and GENIUS Collaborations, E-mail: [email protected], Home-page: http://www.mpi-hd.mpg.de.non-acc/

263

264

(m,) = (0.05 - 0.84) €V (3) The result (2) and (3) determines the neutrino mass scenario to be degenerate The common mass eigenvalue follows then to be mcom= (0.05 - 3.2) eV (95%) (4) If we allow for other mechanisms (see ,the value given in eq. (2),(3) has to be considered as an upper limit. In that case very stringent limits arise for many other fields of beyond standard model physics. To give an example, it has been discussed recently 56 that Oupp decay by R-parity violating SUSY experimentally may not be excluded, although this would require making R-parity violating couplings generation dependent. We show, in section I11 that indirect support for the observed evidence for neutrinoless double beta decay evidence comes from analysis of other Ge double beta experiments (though they are by far less sensitive, they yield independent information on the background in the region of the expected signal). We discuss in sections IV and V some statistical features, about which still wrong ideas are around, as well as background simulations with the program GEANT4, which disprove some recent criticism. In section VI we give a short discussion, stressing that the evidence for neutrinoless double beta decay 1,2,374,5 has been supported by various recent experimental results from other fields of research (see Table 1). It is consistent with recent results from cosmic microwave background experiments The precision of WMAP even allows to rule out some old-fashioned nuclear double beta decay matrix elements (see 65). 12113,14,1

63,64166.

Table 1. Recent support of the neutrino mass deduced from OvPP decay ments, and by theoretical work.

1,2,3,5by

other experi-

Experiment >

WMAP

,

CMB Z- burst 8-2 Tritium u oscillation Theory (A4-symmetry) Theory (identical quark and u mixing at GUT scale)

0.05 - 3.2

>d>

< 0.23, or 0.33, or 0.50 < 0.7

64,66

63 54,62

0.08 - 1.3 > 0.2 <2.2 - 2.8 > 0.03 > 0.2

55 39 58,59 60

I

61

> 0.1

It has been shown to be consistent with the neutrino masses required for the Z-burst scenarios of high-energy cosmic rays It is consistent with a (g-2) deviating from the standard model expectation 5 5 . It is consistent also with the limit from the tritium decay experiments 39 but the allowed 95% confidence range 62354.

265

extends down to a range which cannot be covered by future tritium experiments. It is further strongly supported by recent theoretical work 60,61. Cosmological experimentslike WMAP are now on the level that they can seriously contribute to terrestrial research. The fact that WMAP and less strictly also the tritium experiments cut away the upper part of the allowed range for the degenerate neutrino mass eq. (4) could indicate that the neutrino mass eigenvalues have the same CP parity 16. Finally we briefly comment about the possible future of the field of double beta decay, and present first results from GENIUS-TFwhich has come into operation on May 5,2003 in Gran Sasso with first in world 10kg of naked Germaniumdetectors in liquid nitrogen 43147144. 2. Evidence for the neutrinoless decay mode The status of present double beta experiments is shown in Fig. 1 and is extensively discussed in 14. The HEIDELBERG-MOSCOW experiment using the largest source strength of 11 kg of enriched 76Ge (enrichment 86%) in form of five HP Ge-detectorsis running since August 1990 in the Gran-Sasso underground laboratory 14,5,6,2,41,37 The data taken in the period August 1990 - May 2000 (54.9813kgy, or 723.44 mol-years) are shown in Fig. 2 in the section around the Qpp value of 2039.006keV 2 5 . Fig. 2 is identical with Fig. 1 in except that we show here the original energy binning of the data of 0.36 keV. These data have been analysed 1,2,4,5 with various statistical methods, with the Maximum Likelihood Method and

',

I present

s

limits

--

Y

I potential

>

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4

54.9 13 kg

potential of future projects

Figure 1. Present sensitivity, and expectation for the future, of the most promising /3p experiments. Given are limits for (m),except for the HEIDELBERG-MOSCOWexperiment where the recently observed value is given (95% c.1. range and best value). Framed parts of the bars: present status; not framed parts: future expectation for running experiments; solid and dashed lines: experiments under construction or proposed, respectively. For references see 14,235,52350.

266

in particular also with the Bayesian method (see, e.g. 5 ) . Our peak search procedure (for details see 2 , 4 ) 5 ) reproduces (see y-lines at the positions of known weaklines 23 from the decay of '14Bi at 2010.7,2016.7, 2021.8 and 2052.9 keV. In addition, a line centered at 2039 keV shows up (see Fig. 3). This is compatible with the Q-value 25 of the double beta decay process. The Bayesian analysis yields, when analysing a 3 5 0 range around Q P (which ~ is the usual procedure when searching for resonances in high-energy physics) a confidence level (i.e. the probability K) for a line to exist at 2039.0 keV of 96.5 % c.1. (2.1 a ) (see Fig. 3). We repeated the analysis for the same data, but except detector 4,which had no muon shield and a slightly worse energy resolution (46.502kg y). The probability we find for a line at 2039.0 keV in this case is 97.4% (2.2 a ) Fitting a wide range of the spectrum yields a line at 2039 keV at 91% c.1. (see Fig.2). 1)2,495)

1,215.

Figure 2. The spectrum taken with the 76Gedetectors Nr. 1,2,3,4,5 over the period August 1990 May 2000 (54.9813kg y) in the original 0.36 keV binning, in the energy range 2000 - 2100 keV. Simultaneous fit of the 214 32 lines and the two high-energy lines yield a probability for a line at 2039.0 keV of 91%.

energy lkrV1

energy IksV]

Figure 3. Left: Frobability K that a line exists at a given energy in the range of 2000-2080 keV derived via Bayesian inference from the spectrum shown in Fig. 2. Right: Result of a Bayesian scan for lines as in the left part of this figure, but in an energy range of f5a around Q p p .

267

We also applied the Feldman-Cousins method 2 1 . This method (which does not use the information that the line is Gaussian) finds a line at 2039 keV on a confidence level of 3.1 0 (99.8% c.1.). In addition to the line at 2039 keV we find candidates for lines at energies beyond 2060 keV and around 2030 keV, which at present cannot be attributed. This is a task of nuclear spectroscopy. Important further information can be obtained from the time structures of the individual events. Double beta events should behave as single site events i.e. clearly different from a multiple scattered y-event. It is possible to differentiate between these different types of events by pulse shape analysis. We have developped three methods of pulse shape analysis 17,18,19 during the last seven years, one of which has been patented and therefore only published recently. Installation of Pulse Shape Analysis (PSA) has been performed in 1995 for the four large detectors. Detector Nr.5 runs since February 1995, detectors 2,3,4 since November 1995 with PSA. The measuring time with PSA from November 1995 until May 2000 is 36.532 kg years, for detectors 2,3,5 it is 28.053 kg y. In the SSE spectrum obtained under the restriction that the signal simultaneously fulfills the criteria of all three methods for a single site event, we find again indication of a line at 2039.0keV (see 1,2,5). With proper normalization concerning the running times (kg y) of the full and the SSE spectra, we see that almost the full signal remains after the single site cut (best value), while the 214Bilines (best values) are considerably reduced. We have used a 238Thsource to test the PSA method. We find the reduction of the 2103 keV and 2614keV 228Th lines (known to be multiple site or mainly multiple site), relative to the 1592keV 22sThline (known to be single site), shown in Fig. 4. This proves that the PSA method works efficiently. Essentially the same reduction as for the Th lines at 2103 and 2614 keV and for the weak Bi lines is found for the strong 214Bilines (e.g. at 609.6 and 1763.9 keV (Fig. 4)). The possibility, that the single site signal is the double escape line corresponding to a (much more intense!) full energy peak of a y-line, at 2039+1022=3061 keV is excluded from the high-energy part of our spectrum (see 4).

3. Support of Evidence From Other Ge-Experiments and From Recent Measurements With a 214Bi Source It has been mentioned in Section 11, that by the peak search procedure developped 2 ) 5 on basis of the Bayes and Maximum Likelihood Methods, exploiting as important input parameters the experimental knowledge on the shape and width of lines in the spectrum, weak lines of 214Bihave been identified at the energies of 2010.78, 2016.7,2021.6 and 2052.94keV 1,2,5,7. Fig. 3 shows the probability that there is a

268

- -4- .Range

5z? f-

of Bi lines + Ovpp Signal

Calihrati'm Lines

u.75

I

'I- 0.5

Figure 4. Relative suppressionratios: Remaining intensity after pulse shape analysis compared to the intensity in the full spectrum. Right: Result of a calibration measurement with a Th source - ratio of the intensities of the 1592keV line (double escape peak, known to be 100% SSE), set to 1. The intensities of the 2203 keV line (single escape peak, known to be 100%MSE) are strongly reduced (error bars are lu. The same order of reduction is found for the strong Bi lines occuring in our spectrum - shown in this figure are the lines at 609.4 and 1763.9keV. Left: The lines in the range of weak statistics around the line at 2039 keV (shown are ratios of best fit values). The Bi lines are reduced compared to the line at 2039 keV (set to l), as to the 1592keV SSE Th line.

*

line of correct width and of Gaussian shape at a given energy, assuming all the rest of the spectrum as flat background (which is a highly conservative assumption). The intensities of these 214Bilines have been shown to be consistent with other, strong Bi lines in the measured spectrum according to the branching ratios given in the Table of Isotopes 2 3 , and to Monte Car10 simulation of the experimental setup 5 . Note that the 2016keV line, as an EO transition, can be seen only by coincident summing of the two successive lines E = 1407.98keV and E = 609.316 keV. Its observation proves that the 238Uimpurity from which it is originating, is located in the Cu cap of the detectors. Recent measurements of the spectrum of a 214Bi source as function of distance source-detector confirm this interpretation 2 6 . Premature estimates of the Bi intensities given in Aalseth et.al, hep-ex/0202018 and Feruglio et al., Nucl. Phys. B 637 (2002), 345, thus are incorrect, because this long-known spectroscopic effect of true coincident summing 24 has not been taken into account, and also no simulation of the setup has been performed (for details see 5,3). These 214Bilines occur also in other investigations of double beta decay of Ge - and - even more important - also the additional structures in Fig. 2, which cannot be attributed at present, are seen in these other investigations. There are three other Ge experiments which have looked for double beta decay of 76Ge. First there is the experiment by Caldwell et al. ", using natural Germaniumdetectors (7.8% abundanceof 76Ge,compared to 86% in the HEIDELBERG-

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2 b Q 2010 2020 2030 2040 2050 2060 2070 ZOBO 2090 2104 energy [Key

2 $ $ 2010 2020 2030 2040 2050 2050 2070 2080 2090 2100

energy [KeV]

Figure 5. Result of the peak-search procedure performed for the UCBSLBL spectrum 29

(left: Maximum Likelihood method, right: Bayes method). On the y axis the probability of having a line at the corresponding energy in the spectrum is shown.

MOSCOW experiment). This was the most sensitive natural Ge experiment. With their background a factor of 9 higher than in the HEIDELBERG-MOSCOW experiment and their measuring time of 22.6 kg years, they had a statistics of the background by a factor of almost four 1 a r g e r than in the HEIDELBERG-MOSCOW experiment. This gives useful information on the composition of the background. Applying the same method of peak search as used in Fig. 3, yields indications for peaks essentially at the same energies as in Fig. 3 (see Fig. 5). This shows that these peaks are not fluctuations. In particular it sees the 2010.78,2016.7, 2021.6 and 2052.94 keV 214Bilines, but a 1s o the unattributed lines at higher energies. It finds, however, n o line at 2039 k e y This is consistent with the expectation from the rate found in the HEIDELBERG-MOSCOW experiment. About 16 observed events in the latter correspond to to 0.6 expected events in the Caldwell experiment, because of the use of non-enriched material and the shorter measuring time. Fit of the Caldwell spectrum allowing for the 214Bilines and a 2039 keV line yields 0.4events for the latter (see 5 ) . The first experiment using enriched (but not high-purity) Germanium 76 detectors was that of Kirpichnikov and coworkers 30. These authors show only the energy range between 2020 and 2064 keV of their measured spectrum. The peak search procedure finds also here indications of lines around 2028 keV and 2052 keV (see Fig. 6), but n o t any indication of a line at 2039 keV. This is consistent with the expectation, because for their low statistics of 2.95 kg y they would expect here (according to HEIDELBERG-MOSCOW) 0.9 counts. Another experiment (IGEX) used between 6 and 8.8 kg of enriched 76Ge,but collected since beginning of the experiment in the early nineties till shutdown in 1999 only 8.8 kgyears of statistics 49. The authors of 49 unfortunately show only the range 2020 to 2060 keV of their measured spectrum in detail. Fig. 6 shows the result of our peak scanning of this range. Clear indications are seen for the Bi lines

270

Figure 6. Result of the peak-search procedure performed for the ITEPrYePI spectrum 30

(upper parts), and for the IGEX spectrum 49 (lower parts). Left: Maximum Likelihood method, right: Bayes method. On the y axis the probability of having a line at the corresponding energy in the specrtum is shown.

at 2021 and 2052 keV, but also of the unidentified structure around 2030 keV. Because of the conservative assumption on the background treatment in the scanning procedure (see above) there is no chance to see a signal at 2039 keV because of the ’hole’ in the background of that spectrum (see Fig. 1 in 49). With some good will one might see, however, an indication of 3 events here, consistent with the expectation of the HEIDELBERG-MOSCOW experiment of 2.6 counts.

4. Statistical Features: Sensitivity of Peak Search, Analysis Window At this point it may be useful to demonstrate the potential of the used peak search procedure. Fig. 7 shows a spectrum with Poisson-generated background of 4 events per channel and a Gaussian line with width (standard deviation) of 4 channels centered at channel 50, with intensity of 10 (left) and 100 (right) events, respectively. Fig. 8, shows the result of the analysis of spectra of different line intensity with the Bayes method (here Bayes 1-4 correspond to different choice of the prior distribution: (1) p ( 7 ) = 1(flat), (2) p ( 7 ) = l / q , (3) p ( 7 ) = 1/&, (4) Jeffrey’s prior) and the Maximum Likelihood Method. For each prior 1000 spectra have been generated with equal background and equal line intensity using random number generators available at CERN 20. The average values of the best values agree (see Fig. 8) very well with the known intensities also for very low count rates (as in Fig. 7, left).

27 1

In Fig. 9 we show two simulations of a Gaussian line of 15events, centered at channel 50, again with width (standard deviation) of 4 channels, on a Poisson-distributed background with 0.5 eventslchannel. The figure gives an indication of the possible degree of deviation of the energy of the peak maximum from the transition energy, on the level of statistics collected in experiments like the HEIDELBERG-MOSCOW experiment (here one channel corresponds to 0.36 keV). This should be considered when comparing Figs. 3,5,6.

channel

channel

Figure 7. Example of a random-generated spectrum with a Poisson distributed background

with 4.0 events per channel and a Gaussian line centered in channel 50 (line-width corresponds to a standard-deviation of u = 4.0 channels). The left picture shows a spectrum with a line-intensity of loevents, the right spectrum a spectrum with a line-intensity of 100events. The background is shown dark, the events of the line bright (from 2 8 , 8 ) .

The influence of the choice of the energy range of the analysis around Qpp has been thoroughly discussed in Since erroneous ideas about this point are still around, let us remind of the analysis given in which showed that a reliable result is obtained for a range of analysis of not smaller than 35 channels (i.e. f 1 8 channels) - one channel corresponding to 0.36keV in the HEIDELBERGMOSCOW experiment. This is an important result, since it is of course important to keep the range of analysis as s m a 11as possible, to avoid to include lines in the vicinity of the weak signal into the background. This unavoidably occurs when e.g. proceeding as suggested in F. Feruglio et al., hep-pW0201291and Nucl. Phys. B 637 (2002) 345-377, Aalseth et. al., hep-ex/0202018 and Mod. Phys. Lett. A 17 (2002) 1475,Yu.G. Zdesenko et. al., Phys. Lett. B 546 (2002) 206. The arguments given in those papers are therefore incorrect. Also Kirpichnikov, who states 30 that his analysis finds a 2039 keV signal in the HEIDELBERG-MOSCOW spectrum on a 4 sigma confidence level (as we also see it, when using the Feldman-Cousins method 2 8 ) , makes this mistake when analyzing the pulse-shape spectrum. 215.

21518

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5. Simulationwith GEANT4 Finally the background around Qpp will be discussed from the side of simulation. A very careful new simulation of the different components of radioactive background in the HEIDELBERG-MOSCOWexperimenthas been performedrecently by a new Monte Carlo program based on GEANT4 27,8. This simulation uses a new event generator for simulation of radioactive decays basing on ENSDF-data and describes the decay of arbitrary radioactive isotopes including alpha, beta and gamma emission as well as conversion electrons and X-ray emission. Also included in the simulation is the influence of neutrons in the energy range from thermal to high energies up to 100MeV on the measured spectrum. Elastic and inelastic reactions, and capture have been taken into account, and the corresponding production of radioactive isotopes in the setup. The neutron fluxes and energy distributions were taken from published measurementsperformed in the Gran Sasso.

0

5

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20 50 real number of events

0

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20 50 real number of events

Figure 8. Results of analysis of random-number generated spectra, using Bayes and M a x mum Likelihood method (the first one with different prior distributions). For each number of events in the simulated line, shown on the x-axis, 1000 random generated spectra were evaluated with the five given methods. The analysis on the left side was performed with an Poisson distributed background of 0.5 events per channel, the background for the spectra on the right side was 4.0 events per channel. Each vertical line shows the mean value of the calculated best values (thick points) with the 10 error area. The mean values are in good agreement with the expected values (horizontal black dashed lines) (from 28,8).

Also simulated was the cosmic muon flux measured in the Gran Sasso, on the measured spectrum. To give a feeling for the quality of the simulation, Fig. 10 shows the simulated and the measured spectra for a "'Th source spectrum for as example one of our five detectors. The agreement is excellent. The simulation of the background of the experiment reproduces a 11 observed lines in the energy range between threshold (around 100keV) and 2020keV 27,8. Fig. 11 shows the simulated background in the range 2000-2100keV with all

273 2.5r

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Figure 9. Two spectra with a Poisson-distributed background and a Gaussian line with 15

events centered in channel 50 (with a width (standard-deviation) of 4.0 channels) created with different random numbers. Shown is the result of the peak-scanning of the spectra. In the left picture the maximum of the probability corresponds well with the expected value (black line) whereas in the right picture a larger deviation is found. When a channel corresponds to 0.36 keV the deviation in the right picture is 1.44keV (from a*is). N

Figure 10. Comparison of the measured data (black line, November 1995 to April 2002) and

simulated spectrum (red line) for the detectors Nrs. 1,2,3 and 5 for a 232Thsource spectrum. The agreement of simulation and measurement is excellent (from 27,8).

274

Figure 11. Simulated background of the HEIDELBERG-MOSCOW experiment in the energy range from 2000 to 2100 keV with all known background components. The black histogram line corresponds to the measured data from 20.11.1995 to 16.4.2002 (49.59kg y) (from 273).

k n o w n background components. The black histogram corresponds to the measured data in the period 20. l l . 1995 - 16.4.2002 (49.59 kg y). The background around &a0 is according to the simulations f 1 a t, the only expected lines come from 214Bi(from the 238Unatural decay chain) at 2010.89, 2016.7,2021.6,2052.94,2085.1 and 2089.7 keV. Lines from cosmogenically produced 56C0 (at 2034.76keV and 2041.16keV), half-life 77.3days, are not expected since the first 200days of measurement of each detector are not used in the data analysis. Also the potential contribution from decays of 77Ge,66Ga,or 2 2 8 A ~ , should not lead to signals visible in our measured spectrum near the signal at Qaa. For details we refer to *.

6. Proofs and Disproofs The result described in section 2.1 has been questioned in some papers (Aalseth et al, hep-ex/0202018, and in Mod. Phys. Lett. A 17 92002) 1475-1478; Feruglio et al., Nucl. Phys. B 637 (2002) 345; Zdesenko et al., Phys. Lett. B 546 (2002) 206). We think that we have shown in a convincing way that these claims against our results are incorrect in various ways. In particular the estimates of the intensities of the 214 Bi lines in the first two papers do not take into account the effect of true coincidence summing, which can lead to drastic underestimation of the intensities. A correct estimate would also require a Monte Carlo simulation of our setup, which has not been performed in the above papers. All of these papers, when discussing the choice of the width of the search window, seem to ignore the results of the statistical simulations we published in For details we refer to 2,314,5i7. 2!3p4,5.

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7. Discussion of results 7.1. Half-life and effective neutrino mass

We emphasize that we find in all analyses of our spectra a line at the value of Qpp. We have shown that the signal at Qpp does not originate from a background y-line. On this basis we translate the observed number of events into half-lives for the neutrinoless double beta decay. We give in Table 2 conservatively the values obtained with the Bayesian method and not those obtained with the Feldman-Cousins method. Also given in Table 2 are the effective neutrino masses (m)deduced using the matrix elements of 22. Table 2. Half-life for the neutrinoless decay mode and deduced effective neutrino mass from the HEIDELBERG-MOSCOW experiment.

54.98 13

Detectors 1,2,3,4,5

46.502

1,2,3,5

28.053

2,3,5 SSE

TYi2 y

(0.80 - 35.07) x loz5 (1.04 - 3.46) x 1.61 x 1025 (0.75 - 18.33) x loz5 (0.98 - 3.05) x loz5 1.50 x 1025 (0.88 - 22.38) x loz5 (1.07 - 3.69) x 1.61 x 1025

(4eV C.L. (0.08 - 0.54) 95% c.1. (0.26 - 0.47) 68% c.1. 0.38 Best Value (0.11 - 0.56) 95% c.2. (0.28 - 0.49) 68% c.1. 0.39 Best Value (0.10 - 0.51) 90% c.1. (0.25 - 0.47) 68% c.1. 0.38 Best Value

We derive from the data taken with 46.502 kg y the half-life TYi2 = (0.8 18.3) x y (95% c.1.). The analysis of the other data sets, shown in Table 2 confirm this result. Of particular importance is that we see the OvPPsignal in the single site spectrum. The result obtained is consistent with all other double beta experiments - which still reach in general by far less sensitivity. The most sensitive experiments following the HEIDELBERG-MOSCOW experiment are the geochemical l a s T eexperiment with T'$2 > 2(7.7) x y (68% c.l.), 31 the 136Xeexperiment by the DAMA group with T'$ > 1.2 x y (90% c.l.),a second enriched 76Ge experiment with T'$ > 1.2 x y 30 and a natGe experiment with TYi2 > 1 x loz4 y 29. Other experiments are already about a factor of 100 less sensitive concerning the OvPP half-life: the Gotthard TPC experiment with 1 3 6 X eyields 32 To" > 4.4 x loz3 y (90% c.1.) and the Milano Mibeta cryodetector experiment 112 TYiZ> 1.44 x y (90% c.1.). Another experiment 49 with enriched 76Ge,which has stopped operation in 1999 after reaching a significance of 8.8 kg y, yields (if one believes their method of 'visual inspection' in their data analysis), in a conservative analysis, a limit

276

of about T?Y2 > 5 x y (90% c.1.). The l z 8 T e geochemical experiment yields ( m u )< 1.1 eV (68 % c.1.) 31, the DAMA 136Xeexperiment (mu) < (1.1- 2.9) eV and the 13'Te cryogenic experiment yields (m,) < 1.8eV. Concluding we obtain, with > 95% probability, first evidence for the neutrinoless double beta decay mode. As a consequence, at this confidence level, lepton number is not conserved. Further the neutrino is a Majorana particle. If the Ovpp amplitude is dominated by exchange of a massive neutrino the effective mass ( m ) is deduced (using the matrix elements of 2 2 ) to be ( m )= (0.11 - 0.56)eV (95% c.l.), with best value of 0.39 eV. Allowing conservatively for an uncertainty of the nuclear matrix elements of f 50% (for detailed discussions of the status of nuclear matrix elements we refer to 14,5 and references therein) this range may widen to ( m )= (0.05 - 0.84) eV (95% c.1.). Assuming other mechanisms to dominate the Ovpp decay amplitude, the result allows to set stringent limits on parameters of SUSY models, leptoquarks, compositeness, masses of heavy neutrinos, the right-handed W boson and possible violation of Lorentz invariance and equivalence principle in the neutrino sector. For a discussion and for references we refer to With the limit deduced for the effective neutrino mass, the HEIDELBERGMOSCOW experiment excludes several of the neutrino mass scenarios allowed from present neutrino oscillation experiments (see Fig. 12) - allowing only for degenerate, and marginally still for inverse hierarchy mass scenarios The evidence for neutrinoless double beta decay has been supported by various recent experimental and theoretical results (see Table 1). Assuming the degenerate scenarios to be realized in nature we fix - according to the formulae derived in - the common mass eigenvalue of the degenerate neutrinos to m = (0.05 - 3.4) eV. Part of the upper range is already excluded by tritium experiments, which give a limit of m < 2.2-2.8eV (95% c.1.) 3 9 . The full range can only partly (down to 0.5 eV) be checked by future tritium decay experiments, but could be checked by some future pp experiments (see next section). The deduced best value for the mass is consistent with expectations from experimental p + ey branching limits in models assuming the generating mechanism for the neutrino mass to be also responsible for the recent indication for as anomalous magnetic moment of the muon ". It lies in a range of interest also for Z-burst models recently discussed as explanation for super-high energy cosmic ray events beyond the GKZ-cutoff and requiring neutrino masses in the range (0.08 - 1.3) eV. A recent model with underlying A4 symmetry for the neutrino mixing matrix also leads to degenerate neutrino masses > 0.2 eV, consistent with the present result from Ovpp decay The result is further consistent with the theoretical paper of 61, Starting with the hypothesis that quark and lepton mixing are identical at or near the GUT scale, Mo14333136113150111.

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BEST VALUE HEIDELBERG-

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Figure 12. The impact of the evidence obtained for neutrinoless double beta decay (best value of the effective neutrino mass ( m )= 0.39eV, 95% confidence range (0.05 - 0.84) eV - allowing already for an uncertainty of the nuclear matrix element of a factor of 50%) on possible neutrino mass schemes. The bars denote allowed ranges of (m)in different neutrino mass scenarios, still allowed by neutrino oscillation experiments (see Hierarchical models are excluded by the new Ovpp decay result. Also shown is the exclusion line from WMAP, plotted for C m, < 1.0 eV 66. WMAP does not rule out any of the neutrino mass schemes. Further shown are the expected sensitivities for the future potential double beta experiments CUORE, MOON, E X 0 and the 1 ton and 10 ton project of GENIUS 14,13,51,35 (from 15).

*

hapatra et al. " show that the large solar and atmospheric neutrino mixing angles can be understood purely as result of renormalization group evolution, if neutrino masses are quasi-degenerate (with same CP parity). The common Majorana neutrino mass then must be, in this model, larger than 0.1 eV. For WMAP a limit on the total neutrino masses of m, = x m i < 0.69 eV at 95% c.l., (5)

is given by the analysis of ref. 64. It has been shown, however, that this limit may not be very realistic. Another analysis shows that this limit on the total mass should be 66 m, = < 1.0eV at 95% c.1.

Cmi

The latter analysis also shows, that four generations of neutrinos are still allowed and in the case of four generations the limit on the total mass is increased to 1.38 eV. If there is a fourth neutrino with very small mass, then the limit on the total mass of the three neutrinos is even further weakened and there is essentially no constraint on the neutrino masses. In our Fig. 12 we show the contour line for WMAP assuming C mi < 1.0 eV.

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Comparison of the WMAP results with the effective mass from double beta decay rules out completely (see ") a 15 years old old-fashionednuclear matrix element of double beta decay, used in a recent analysis of WMAP 67. In that calculation of the nuclear matrix element there was not included a realistic nucleonnucleon interaction, which has been included by all other calculations of the nuclear matrix elements over the last 15 years. As mentioned in section 1 the results from double beta decay and WMAP together may indicate l6 that the neutrino mass eigenvalues have indeed the same CP parity, as required by the model of ". The range of ( m )fixed in this work is, already now, in the range to be explored by the satellite experiments MAP and PLANCK 9,64i66. The limitations of the information from WMAP are seen in Fig. 12, thus results of PLANCK are eagerly awaited. The neutrino mass deduced leads to 0.0022 f2,h2 5 0.1 and thus may allow neutrinos to still play an important role as hot dark matter in the Universe 42. 8. Future of pp experiments - GENIUS and other proposals With the HEIDELBERG-MOSCOW experiment, the era of the small smart experiments is over. New approaches and considerably enlarged experiments (as discussed, e.g. in will be required in future to fix the neutrino mass with higher accuracy. Since it was realized in the HEIDELBERG-MOSCOW experiment, that the remaining small background is coming from the material close to the detector (holder, copper cap, ...), elimination of any material close to the detector will be decisive. Experiments which do not take this into account, like, e.g. CUORE and MAJORANA will allow at best only rather limited steps in sensitivity. Furthermore there is the problem in cryodetectors that they cannot differentiate between a and a y signal, as this is possible in Ge experiments. Another crucial point is the energy resolution, which can be optimized only in experimentsusing Germaniumdetectors or bolometers. It will be difficult to probe evidence for this rare decay mode in experiments, which have to work - as result of their limited resolution - with energy windows around Qpp of several hundreds of keV, such as NEMO 111, EXO, CAMEO. Another important point is the efficiency of a detector for detection of a PP signal. For example, with 14% efficiency a potential future lOOkg 82SeNEMO experiment would be, because of its low efficiency, equivalent only to a 10kg experiment (not talking about the energy resolution). In the first proposal for a third generationdouble beta experiment, the GENIUS proposal the idea is to use 'naked' Germanium detectors in a huge 12133114,36,51,35,38,42)

33312,34,36,51,35,

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tank of liquid nitrogen. It seems to be at present the only proposal, which can fulfill both requirements mentioned above - to increase the detector mass and simultaneously reduce the background drastically. GENIUS would - with only 100 kg of enriched 76Ge- increase the confidence level of the present pulse shape discriminated Ovpp signal to 4a within one year, and to 7 0 within three years of measurement (a confirmation on a 40 level by the MAJORANA project would need according to our estimate at least -230 years, the CUORE project might need - ignoring for the moment the problem of identification of the signal as a pp signal 3700 years). With ten tons of enriched 76GeGENIUS should be capable to investigate also whether the neutrino mass mechanism or another mechanism (see, e.g. 14) is dominating the Ovpp decay amplitude.

9. GENIUS-TF As a first step of GENIUS, a small test facility, GENIUS-TF, is under installation in the Gran Sasso Underground Laboratory since March 2001. With up to 40 kg of natural Ge detectors operated in liquid nitrogen, GENIUS-TF could test the DAMA seasonal modulation signature for dark matter 44. No other experiment running like, CDMS, IGEX, etc., or projected at present, will have this potential 4 2 . Up to summer 2001, already six 2.5 kg Germanium detectors with an extreme low-level threshold of -500 eV have been produced. The idea of GENIUS-TF is to prove the feasibility of some key constructional features of GENIUS, such as detector holder systems, achievement of very low thresholds of specially designed Ge detectors, long term stability of the new detector concept, reduction of possible noise from bubbling nitrogen, etc. After installation of the GENIUS-TF setup between halls A and B in Gran Sasso, opposite to the buildings of the HEIDELBERG-MOSCOW double beta decay experiment and of the DAMA experiment, the first four detectors have been installed in liquid nitrogen on May 5,2003 and have started operation 43,26 (Fig. 13). This is the first time ever, that this novel technique for extreme background reduction in search for rare decays is tested under realistic background conditions in an underground laboratory. 47145

10. Conclusion The status of present double beta decay search has been discussed, and recent evidence for a non-vanishing Majorana neutrino mass obtained by the HEIDELBERG-MOSCOW experiment has been presented. Additional support for this evidence has been presented by showing consistency of the result - for the signal, a n d for the background - with other double beta decay experiments using non-enriched or enriched Germanium detectors. In particular it has been shown

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Figure 13. Left: The first four naked Ge detectors before installation into the GENIUS-TF setup. Right: Taking out the crystals from the transport dewars and fixing the electrical contacts in the clean room of the GENIUS-TF building - from left to right: Herbert Strecker, Hans Volker KlapdorKleingrothaus, Oleg Chkvorez. ~

that the lines seen in the vicinity of the signal (including those which at present cannot be attributed) are seen also in the other experiments. This is important for the correct treatment of the background. Furthermore, the sensitivity of the peak identification procedures has been demonstrated by extensive statistical simulations. It has been further shown by new extensive simulations of the expected background by GEANT4, that the background around Qpp should be flat, and that no known gamma line is expected at the energy of Qpp. The 2039 keV signal is seen o n 1 y in the HEIDELBERG-MOSCOW experiment, which has a by fur larger statistics than all other double beta experiments. The importance of this first evidence for violation of lepton number and of the Majorana nature of neutrinos is obvious. It requires beyond Standard Model Physics on one side, and may open a new era in space-time structure 5 3 . It has been discussed that the Majorana nature of the neutrino tells us that spacetime does realize a construct that is central to construction of supersymmetric theories. With the successful start of operation of GENIUS-TF with the first four naked Ge detectors in liquid nitrogen on May 5, 2003 in GRAN SASSO, which is described in 44,43 a historical step has been achieved of a novel technique and into a new domain of background reduction in underground physics in the search for rare events. Future projects to improve the present accuracy of the effective neutrino mass have been briefly discussed. The most sensitive of them and perhaps at the same time most realistic one, is the GENIUS project. GENIUS is the only of the new projects which simultaneously has a huge potential for cold dark matter search, and for real-time detection of low-energy neutrinos (see >. 12~33~38140~13~14~48152150

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References 1. H.V.Klapdor-Kleingrothaus et al. Mod. Phys. Lett. A 16 (2001) 2409 - 2420. 2. H.V.Klapdor-Kleingrothaus,A.Dietz,I.V.Krivosheina, Part. and Nucl. 110 (2002) 57. 3. H.V.Klapdor-Kleingrothaus, hep-ph/0205228, in Proc. of DARK2002, eds. by H.V. Klapdor-Kleingrothaus and R.D. Viollier, Springer (2002) 404. 4. H.V.Klapdor-Kleingrothaus, hep-pW0302248, Proc.DARK2002, Springer(2002)367. 5. H.V.Klapdor-Kleingrothaus, A.Dietz and I.V. Krivosheina, Foundations of Physics 31 (2002) 118land Corr., 2003: http://www.mpi-hd.mpg.de/non_acc/main_results.html. 6. H.V.Klapdor-Kleingrothaus et al., (HEIDELBERG-MOSCOW Col.), Eur.Phys.J. A 12(2001)147, Proc. DARK2000, ed. H.V.Klapdor-Kleingrothaus, Springer(2001)520. 7. H.V. Klapdor-Kleingrothaus,hep-ph/0303217 and in Proc. of “Neutrinos and Implications for Phys. Beyond the SM’, Stony Brook, 11-13 Oct. 2002. 8. H.V.Klapdor-Kleingrothaus et al., to be publ. in 2003. 9. H.V.Klapdor-Kleingrothaus,H.Pas,A.Yu.Smimov, Phys.Rev. D63(2001)073005. 10. H.V. Klapdor-Kleingrothaus and U. Sarkar, Mod.Phys.Lett. A 16 (2001)2469. 11. H V Klapdor-Kleingrothaus and U Sarkar, hep-pM0302237. 12. H.V.Klapdor-Kleingrothaus,Int. J. Mod. Phys. A 13 (1998) 3953. 13. H.V.Klapdor-Kleingrothaus,Springer Tracts in Modern Physics, 163 (2000)69 - 104, Springer- Verlag, Heidelberg, Germany (2000). 14. H.V.Klapdor-Kleingrothaus, ”60 Years of Double Beta Decay - From Nuclear Physicsto Beyondthe Standard Model”, WorldScient$c, Singapore (2001) 1281p. 15. H.V.Klapdor-Kleingrothaus and U. Sarkar, hep-phl0304032. 16. H.V. Klapdor-Kleingrothaus, to be publ. 2003, and Proc. BEYOND02, IOP, Bristol 2003. 17. J. Hellmig and H.V. Klapdor-Kleingrothaus,NIM A 455 (2000) 638-644. 18. J. Hellmig, F. Petry and H.V. Klapdor-Kleingrothaus,Patent DE19721323A. 19. B. Majorovits and H.V. Klapdor-Kleingrothaus. Eur. Phys. J. A 6 (1999) 463. 20. CERN number generators (see e.g. http://root.cern.ch/root/html/TRandom.html) 21. D.E Groom et al., Particle Data Group, Eur. Phys. J. C 15 (2000) 1. 22. A. Staudt, K. Muto and H.V. Klapdor-Kleingrothaus,Eul: Lett. 13 (1990) 31. 23. R.B. Firestone and V.S.Shirley, Table of Isotopes, 8th Ed., John W%S, N.Y.(1998). 24. G. Gilmore et al.“Practical Gamma-Ray Spectr.”, Wiley and Sons (1995). 25. G. Douysset et al., Phys. Rev. Lett. 86 (2001) 4259 - 4262. 26. H.V.Klapdor-Kleingrothaus,O.Chkvorets,I.V.Krivosheina,C.Tomei, in press NIM’03. 27. Ch. Don; Diplomarbeit (2002), Univ. of Heidelberg, unpubl. 28. A. Dietz, Dissertation, University of Heidelberg, 2003. 29. D. Caldwell, J. Phys. G 17, S137-S144 (1991). 30. I.V.Kirpichnikov et al. Mod. Phys. Lett. A 5 (1990) 1299 - 1306. Preprint ITEP, 1991, MOSCOW 91-91. 31. 0. Manuel et al., in Proc. Intern. Conf. Nuclear Beta Decays and the Neutrino, eds. T. Kotani et al., World Scientific (1986) 71, J. Phys. G: Nucl. Part. Phys. 17 (1991) S221-S229; T. Bematovicz et al. Phys. Rev. Lett. 69 (1992) 2341. 32. R. Liischer et al., Phys. Lett. (1998) 407. 33. H.V. Klapdor-Kleingrothaus in Proc. of BEYOND’97, IOP Bristol(l998) 485-531. 34. H.V.Klapdor-Kleingrothaus,J. Hellmig and M. Hirsch, J. Phys. G 24 (1998) 483 - 5 16.

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35. H.V. Klapdor-Kleingrothaus et al. MPI-Report MPI-H-V26-1999, hep-pW9910205, in Proc. of BEYOND’99, eds. H.V. Klapdor-Kleingrothaus and I.V. Krivosheina, IOP Bristol(2000) 915. 36. H.V. Klapdor-Kleingrothaus, in Proc. of NEUTRINO 98, Takayama, Japan, 4-9 Jun 1998, (eds) Y. Suzuki et al. Nucl. Phys. Proc. Suppl. 77 (1999) 357. 37. HEIDELBERG-MOSCOW Coll. (M. Giinther et al.), Phys.Rev.D55( 1997)54. 38. H.V. Klapdor-Kleingrothaus, Nucl. Phys. B 100 (2001) 309 - 313. 39. J. Bonn et al., Nucl. Phys. B 91 (2001) 273 - 279. 40. V.A. Bednyakov and H.V. Klapdor-Kleingrothaus, Phys. Rev. D 63 (2001) 095005. 41. H.V. Klapdor-Kleingrothaus, in Proc. eds.: D. Poenaru and S. Stoica, World Scientifrc, Singapore (2000) 123-129. 42. H.V. Klapdor-Kleingrothaus, Znt.J.Mod.Phys.A17(2002)3421,Proc. LPO1, WS 2002. 43. H.V. Klapdor-Kleingrothaus and I.V. Krivosheina, in Proc. of BEYOND02, Oulu, Finland, June 2002, IOP 2003, ed. H.V. Klapdor-Kleingrothaus. 44. H. V. Klapdor-Kleingrothaus, et al., NIM 2003, in press. 45. T. Kihm, V. F. Bobrakov and H.V. Klapdor-Kleingrothaus NIM A498 (2003) 334. 46. H.V. Klapdor-Kleingrothaus et al., Internal Report MPI-H-V32-2000. 47. H.V. Klapdor-Kleingrothaus et al., hep-pW0103082, NIM A 481 (2002) 149. 48. H.V. Klapdor-Kleingrothaus and I.V. Krivosheina, in Proc. of “Forum of Physics”, Zacatecas, Mexico, 11-13 May, 2002, eds. D.V. Ahluwalia and M. Kirchbach. 49. C.E. Aalseth et al. (IGEX Collaboration), Yad. Fiz. 63,No 7 (2000) 1299 - 1302; Phys. Rev. D 65 (2002) 092007. 50. H.V. Klapdor-Kleingrothaus, Part. and Nucl., Lett. iss. 1/2(2001), hep-pW0102319. 51. H.V. Klapdor-Kleingrothaus, hep-pWO103074 and in NOON 2000, W.S.(2001) 219. 52. H.V. Klapdor-Kleingrothaus, LowNu2, WS(2001)116,hep-pW0104028. 53. D.V. Ahluwalia in Proc. of BEYOND02, IOP 2003, ed. H.V. Klapdor-Kleingrothaus; D.V. Ahluwalia, M. Kirchbach, Phys. Lett. B 529 (2002) 124. 54. D. Fargion et al., in Proc. of DARK2000, Springer, (2001) 455,in Proc. of BEYOND02, IOP 2003, ed. H.V. Klapdor-Kleingrothaus. 55. E. Ma and M. Raidal, Phys.Rev.Lett.87(2001)011802; Erratum-ibid.87(2001)159901. 56. Y. Uehara, Phys. Lett. B 537 (2002) 256-260 and hep-pW0201277. 57. E. Ma in Proc. of BEYOND’02, Oulu, Finland, 2-7 Jun. 2002, IOP, Bristol, 2003, ed. H.V. Klapdor-Kleingrothaus. 58. KamLAND Coll., Phys. Rev. Lett. 90 (2003) 021802 and hep-ed0212021. 59. G. L. Fogli et al., Phys. Rev. D 67 (2003) 073002 and hep-pWO212127. 60. K. S. Babu, E. Ma and J.W.F. Valle (2002) hep-pW0206292. 61. R. N. Mohapatra, M. K. Parida and G. Rajasekaran, (2003) hep-pW0301234. 62. Z. Fodor, S. D. Katz and A. Ringwald, Phys. Rev. Lett. 88 (2002) 171101; Z.Fodor et al., JHEP (2002) 0206:046, or hep-pWO203198, and in Proc. of BEYOND’02, IOP, Bristol, 2003, ed. H V Klapdor-Kleingrothaus and hep-pWO210123. 63. J. E. Ruhl et al., astro-pW0212229. 64. D. N. Spergel et al., astro-pWO302209. 65. A. Pierce and H. Murayama, hep-pW0302131. 66. S. Hannestad, astro-pW0303076. 67. P. Vogel in PDG (ed. K Hagiwara et al.) Phys. Rev. (2002) D 66 010001.

CUORICINO AND CUORE: RESULTS AND PROSPECTS

A. GIULIANI, A. FASCILLA AND M. PEDRETTI Dipartamento d i Scienze CC. FF. M M . dell’universath dell’lnsubria and Sezione d i Milano dell’INFN, Como I-22100, Italy C. ARNABOLDI, C. BROFFERIO, S. CAPELLI, L. CARBONE, 0. CREMONESI, E. FIORINI, A. NUCCIOTTI, M. PAVAN, G. PESSINA, S. PIRRO, E. PREVITALI, M. SISTI AND L. TORRES Dipartimento d i Fisica dell’hiversatd d i Milano- Bicocca and Sezione d i Milano dell’INFN, Milano I-20126, Italy D.R. ARTUSA, F.T. AVIGNONE 111, I. BANDAC, R.J. CRESWICK, H.A. FARACH AND C. ROSENFELD Dept. of Physics and Astronomy, University of South Carolina, Columbia, S C 29208, U S A M. BALATA, C. BUCCI AND M. PYLE Laboratori Nazionali del Gran Sasso, Assergi ( L ’Aquila) I-6701 0, Italy M. BARUCCI, E. PASCA, E. OLIVIERI, L. RISEGARI AND G. VENTURA Dipartimento d i Fisica dell’llniversith d i Firenze and Sezione d i Firenze dell’INFN, Firenze I-50125, Italy J. BEEMAN, R.J. MCDONALD, E.E. HALLER, E.B. NORMAN AND A.R. SMITH Lawrence Berkeley National Laboratory and Dept. of Material Science and Mineral Engineering, University of California, Berkeley, C A 94’720, U S A

S. CEBRIAN, P. GORLA, I.G. IRASTORZA, A. MORALES AND C. POBES Laboratory of Nuclear and High Energy Physics, University of Zaragoza, 50009 Zaragoza, Spain

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G . FROSSATI AND A. DE WAARD Karnerling Onnes Laboratory, Leiden University, 2300 RAQ Leiden, The Netherlands V. PALMIER1 Laboratori Nazionali di Legnaro, Legnaro (Padova) I-35020, Italy After a short introduction on Double Beta Decay (DBD), general features of a bolometric experiment t o search for neutrinoless Double Beta Decay (OV-DBD) of 130Te are outlined. T h e appeal of 130Te as a DBD emitter is emphazized. After a brief description of the now closed Mi-DBD experiment, the CUORICINO experiment, an expansion of Mi-DBD, is presented and the first experimental results are given, together with a discussion on the background issues and the consequent sensitivity. CUORE experiment, a new generation OV-DBD search, is proposed on the basis of the experience and information gathered with the realization and running of Mi-DBD and CUORICINO. T h e CUORE structure is presented and the ultimate sensitivity to Majorana neutrino mass is discussed. In case of inverse neutrino mass hierarchy, the CUORE discovery potential is shown to be large.

1. Introduction

Neutrinoless Double Beta Decay (OV-DBD) is a rare nuclear process described by

( A ,2 ) -+ ( A ,2

+ 2) + 2e-,

(1)

where, unlike the standard electroweak process, no neutrino is present in the final state. In reaction (1) in fact, neutrino does not appear explicitly but it is hidden as a virtual particle joining the two electroweek vertices. This role can be played if and only if at least one neutrino eigenstate has a non-zero mass and if neutrino is a self-conjugated “Majorana” particle. Search for OV-DBDis presently the only viable experiment which can reveal the Majorana nature of neutrino. The connection between the lifetime T of process (1) and neutrino mass is quantitatively expressed by

(assuming the dominance of the so-called mass mechanism), where GoV is a phase-space factor growing steeply with the Q-value of process (l), IMouI (the “nuclear matrix element”) includes all the nuclear physics of 284

285

the decay, and (m,), sometimes defined “effective Majorana mass”, is a linear combination of the three neutrino physical masses. The coefficients of this linear combination are connected to the neutrino mass matrix, and represent therefore the bridge between flavor oscillations and OV-DBD. Present experimental limits on (m,) are of the order of 1 eV, with a large systematics originated by the difficult computation of lMoV1.

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1.1. The bolometric technique applied t o 130Te

A very sensitive approach for the experimental study of OV-DBD consists in developing a device which is at the same time source and detector of the phenomenon. In this method, the detector containing the candidate nuclides must be massive (at least of the order of 10 kg, better if of the order of 100-1000 kg for new generation experiments). Furthermore, it must exhibit high energy resolution and low radioactive background. Bolometric detection of particles is not only able to provide all these features, but it looks like the only technique capable to ensure them at the ton scale with reasonable costs. In bolometers, the energy deposited in the detector by a nuclear event is measured by recording the temperature increase of the detector as a whole. In order to make this temperature increase appreciable and to reduce all the intrinsic noise sources, the detector must be operated at very low temperatures, of the order of 10 mK for large masses. Bolometric technique can provide energy resolutions comparable to or better than those achievable with conventional devices in the MeV range.4 Since the only characteristic required to the detector material is to have a low specific heat at low temperatures, many choices are possible. In particular, when planning for a DBD experiment with bolometers one should find a compromise between the thermal properties of a compound and its content of the candidate nucleus. Several interesting bolometric candidates were proposed and tested by the Milano group.5 The choice has fallen on natural Te02 (tellurite) that has reasonable mechanical and thermal properties together with a very large (27% in mass) content of the 2P-candidate 13”Te,which makes the request of enrichment not compulsory, as it is for other interesting isotopes. Moreover, the transition energy (Qzp = 2528.8 f1.3 keV) is located in the valley between the peak and the Compton edge of the 2615 keV y-line of 208T1, at the very end of the y natural background spectrum, so that it is easier to look for the signal. In comparison to other 2P-emitters, phase-space and nuclear matrix elements look quite favorable. Equation (2) predicts for

286

130Te a lifetime of the order of y for (m,) N 0.1 eV. The typical bolometer developed by the Milano group to search for 0vDBD consists of a single tellurite crystal, with a mass of the order of a few hundreds of grams, thermally coupled to a Neutron Transmutation Doped Ge thermistor which operates as a temperature-to-voltage transducer. The crystal is weakly coupled to a heat sink kept at 5 mK by a high power dilution refrigerator. Technical details on this device and its operation parameters can be found elsewhere.6

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1.2. The M i - D B D experiments: results and implications Following the approach outlined in Sec. 1.1,an experiment using crystalline tellurite and studying 130Te (Mi-DBD experiment) has been developed by the Milano group in the last years, allowing to rea.ch one of the highest sensitivities in the world. The Mi-DBD detector was a segmented device consisting of 20 elements of 340 g each. Details on the detector array, the shieldings, the read-out, the data acquisition and the detector performances are reported e l ~ e w h e r eThe . ~ Mi-DBD array has been operated for 3.55 kgxyear of effective running time in two different configurations. The background level in the energy window relevant for DBD is (0.33 =t0.11) counts/(keV kg y) in the latter configuration. No evidence of the 2528.8 keV line due t o 130Te OV-DBD to the 0+ ground state of 130Xe has been found in the background spectrum, leading to a limit on the half-life for this process of 2 . 1 ~ 1 0y ~at~ 90% C.L. (including in the statistics also previous lower mass experiments). The corresponding limit on the lepton non-conserving channel restricts the upper bound of (m,) to values ranging from 1to 2 eV, according to most of the theoretical calculations. We would like to note that this bound is the most stringent one in the literature after that obtained in DBD experiments with 76Ge.1 2. CUORICINO: description and first results

Proposed as an intermediate step to demonstrate the feasibility of CUORE (Cryogenic Underground Observatory for Rare Events, see Sec. 3), CUORICINO is actually a true experiment, approved by the Gran Sasso Scientific Committee and by the funding authorities. The CUORICINO setup has been installed at the end of December 2002 in Hall A in the Gran Sasso National Laboratories (in the same dilution refrigerator housing previously the Mi-DBD array) and consists of an array of 44 5-cm-side cubic crystals and of 18 3 x 3 x 6 cm crystals of TeO;?,with a total active mass of about 41 kg.

287

The larger crystals are arranged in 11 four-detector independent modules, while the 18 smaller crystals are arranged in two 3 x 3 matrices. In analogy with the Mi-DBD setup, the four-detector modules and the two matrices are stacked so as t o form a tower-like structure. The main advantages of such a design are the following: each plane of the tower can be considered as an elementary four-detector module which can be optimised and tested independently (see Figure 1);the tower fills almost completely the whole experimental volume of the refrigerator; the more ambitious CUORE experiment is designed as a collection of such towers, making CUORICINO a significant small-scale test of the concept.

Figure 1. A four-detector CUORICINO module. Each crystal has a mass of 790 g.

In the last year, an intense activity of preparation for CUORICINO took place. Our efforts have been addressed both to the improvement of the detector performances (microphonic noise reduction,* conversion gain ~ t a b i l i t y energy ,~ resolution, etc.) by operating four-detector test modules in a smaller refrigerator, and to the reduction of the background. As far as the latter point is concerned, special care was taken in polishing crystal surfaces with ultra-pure powders and in etching chemically the copper elements surrounding the detectors. There is in fact a strong indication that the main source of the background in Mi-DBD experiment is due to

288

energy-degraded alpha particles originated in surface contamination. Apart from an improved cleanness of surfaces, the CUORICINO configuration is substantially identical to that of Mi-DBD. Therefore, we do not expect a dramatic improvement of the background, taking into account also that we have been forced to decrease the thickness of the internal lead shield due to the larger crystal size.

Figure 2.

The first CUORICINO pulse, acquired with a digital scope.

At the beginning of January 2003, CUORICINO was cooled down for the first time. In spite of the large mass (about 60 kg, including crystals and passive elements) the base temperature (- 6 mK) was reached in a couple of days, much more quickly than in the Mi-DBD case. This is due to an improved procedure for the cooling down and in a accurate choice of the type of copper used for the thermalization of the tower." This result proves definitely the technical feasibility of CUORE. In Figure 2, the first acquired CUORICINO signal is shown (from a 790 g element): it is possible to appreciate the very long fall time constant, of the order of 1 s, due t o the large bolometer mass. The detector performances are satisfactory: an average energy resolution of about 8 keV FWHM was reached in the 790 g crystals and of about 11keV FWHM in the 340 g crystals. This difference is probably due to the size of the Neutron Transmutation Doped thermistor,

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that was optimized in the larger crystals. Unfortunately, due to an annoying problem with the soldering of the read-out wires (low temperature soldering is never a trivial task), only 80% of the detectors are really connected to the outside world. However, the sensitive mass is large enough t o allow to start a meaningful experiment. In the next months, we will accumulate sufficient statistics to have indication on the background level and to produce new limits on OV-DBD of 13'Te. Assuming full operation of CUORICINO, 1 n sensitivity to OV-DBD of 130Te can be evaluated to be 2.17 x 1 0 2 4 f i , where T is the live time in years and b is the background level expressed in counts/(keV kg y). In three years and with a conservative background level of N 0.3 counts/(keV kg y), a limit of the order of 7 x loz4 y should be reached on OV-DBD of 13'Te, corresponding to limits on (m,) ranging from 0.14 eV to 0.91 eV, improving the present 76Ge results.12 3. CUORE: a new generation Double Beta Decay search

Like CUORICINO, CUORE will be based on an elementary module of 4 crystals. Groups of ten modules will be stacked together so as to form a 10-plane tower. The CUORE array will consist of 25 of these towers, in a 5 x 5 structure, forming a cubical configuration with 10 crystals per side, with a total active mass of 760 kg. Each tower will be very similar to the tower tested in CUORICINO and described in Sec. 2, both from the mechanical and thermal point of view, and substantially independent of the nearby towers. The close packing and the high granularity will help in background identification and rejection. The array will be housed in a specially-made high-power dilution refrigerator and operated underground at a temperature of 10-15 mK. More details on CUORE design can be found elsewhere." The time estimated for CUORE construction is of the order of five years. One of the main goals of CUORE is to reach an extremely low background level, in the range of 0.001-0.01 counts/(keV kg y) in the energy region of interest for OV-DBD of 130Te. This means an improvement by a factor 100-10 with respect to the Mi-DBD result. In order to assess if this is really achievable, we started a detailed program of Monte Carlo simulations of all the relevant background sources, introducing reasonable radiopurity levels of the most relevant materials. The sensitivity of CUORE is evaluated l 2 assuming 5 keV FWHM energy resolution at 2.5 MeV. The background rate at the same energy is assumed t o be 0.001 counts/(keV kg y), as suggested by the Monte Carlo. To be on the safe side we consider also the

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possibility that the background be higher by a factor of 10. In the optimistic case, the sensitivity to lifetime will be 3.6 x &?y (where T is the live time measured in years). This will imply that in one year of statistics CUORE will provide (m,) upper bounds smaller than 0.03 eV (with the appropriate nuclear matrix elements). These predictions could be admittedly optimistic since other sources of background, not taken into account by the Monte Carlo, could be present. Under the more conservative hypothesis of a background of 0.01 counts/(keV kg y) the upper limit on (m,) would be 0.05 eV. In conclusion the ultimate sensitivity of CUORE for Ov-DBD searches stagnates at 0.04 eV for the upper bound of (m,), with a very soft dependence on live time (T’I‘)). This sensitivity level starts to attack the neutrino mass range suggested by the oscillation results, in particular a positive result is expected in case of inverse hierarchy of neutrino masses. The CUORE set-up will enable not only an improved search for OvDBD, but also a sensitive experiment on direct interactions of WIMPS (particle candidates to the composition of Dark Matter), via the seasonal variation of their interaction rate. We also plan to investigate the possible subdiurnal modulation of the signal induced in this detector by electromagnetic interactions of axions coming from the Sun.

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References 1. 2. 3. 4. 5. 6.

7. 8. 9. 10.

11.

12.

0. Cremonesi, Nucl. Phys. B (Proc. Suppl.) 118,287 (2003). S.M. Bilenky, S. Pascoli, and S.T. Petcov, Phys. Rev. D, 64,113003 (2001). A. Giuliani, Physica B 280, 501 (2000). A. Giuliani, Proceedings of SPIE 4507 (2002). A. Alessandrello et al., Czech. J. Phys. 51 449 (2001). M. Pedretti et al., “Measurement of thermal properties for modeling and optimization of large mass bolometers”, Physica B, in the press. A. Alessandrello et al., Phys. Lett. B486 13 (2000). S.Pirro et al, Nucl. Instr. Meth. A444 331 (2000). A. Alessandrello et al., Nucl. Instr. Meth. A412 454 (1998). L. Risegari et al., “Measurement of very-low temperature thermal conductivity of copper for the optimization of the cooling down procedure of large masses”, submitted to Cryogenics (2003). C. Arnaboldi et al., “CUORE: a Cryogenic Underground Observatory for Rare Events”, Nucl. Instr. Meth. A , in the press. C. Arnaboldi et al., “Physics potential and prospects for the CUORICINO and CUORE experiments”, Astrop. Phys., in the press.

INITIAL RUNS OF THE NEMO 3 EXPERIMENT

NEMO Collaboration CENBG, IN2P3-CNRS et Universit.4de Bordeaux, 331 70 Gradignan, France LPC, LN2P3-CNRS et Universiti de Caen, 14032 Caen, France JLNR, 141980 Dubna Russia CFR, CNRS, 91190 Gifsur Yvette, France ITEP-Mosco w, Russia INEEL, Idaho Falls, ID 83415, U.S.A. JYVASKYLA University, 40351, Jyvaskyla, Finland LAL, lN2P3-CNRS et Universiti Paris-Sud, 91898 Orsay, France* MHC, South Hadley, Massachusetts 01 075, U.S.A. IReS, IN2P3-CNRS et Universit.4Louis Pasteur, 6703 Strasbourg, France CTU FNSPE, Prague, 11519 Czech Republic Charles University, Prague, Czech Republic Saga University, Saga 840-8502, Japan UCL, Gower Street London, WC 1E 6BT -UK NOON03 Conference Kanazawa, Japan Presented by

*S. Jullian The NEMO collaboration is looking to measure neutrinoless double beta decay. The search for the effective neutrino mass will approach a lower limit of 0.1 eV. The NEMO 3 detector is now operating in the Frejus Underground Laboratory. The fundamental design of the detector is reviewed and the performances detailed. Finally, a summary of the data collected in the first runs which involve energy and time calibration and study of the background are presented.

1. Introduction The recent discovery of neutrino oscillations is proof that the neutrino is a massive particle. However, the oscillation experiments are only sensitive to the difference in the square of the masses of two eigenstates of the neutrino. One method for directly measuring the absolute mass scale of neutrinos is through the

29 1

292

careful investigation of the end-point energy of single beta decay. Another method could be through neutrinoless double beta decay (PP(0v)) which is the mission of the NEMO 3 detector. The Pp(0v) process is the decay of an (A, Z) nucleus to an (A, Z+2) nucleus by the simultaneous emission of two electrons but without the emission of neutrinos. The non-conservation of lepton number is a signature of physics beyond the Standard Model. An observation of pp(0v) would be one method of seeing this new physics and the measured half-life yields information on the effective neutrino mass. In 1989, the NEMO (Neutrinoless Expcriments with Molybdenum) collaboration started a research and development program to build a detector which would be able to study the effective neutrino mass down to about 0.1 eV by looking for the pp(0v) decay process. The NEMO 3 detector [l] is now operating in the Frejus Underground Laboratory at a depth of 4800 m.w.e..

2. The NEMO 3 detector

2.1. Description The detector is cylindrical in design and divided into 20 equal sectors (Fig. 1). A thin (40-60 mg/cm2) cylindrical source foil of pp emitters has been constructed from either a metal film or powder bound by an organic glue to mylar strips. The detector houses up to 10 kg of these isotopes.

Figure 1: Schematic of the NEMO 3 detector: 1) Source foil (up to 10 kg), 2) tracking volume with 6180 drift Geiger cells 3) Calorimeter of 1940 plastic scintillators coupled to low activity photomultipliers. The double beta decay source hangs between two concentric cylindrical tracking volumes consisting of 6180 of open octagonal drift cells operating in

293

geiger mode. These cells run vertically and are staged in a 4,2, and 3 row pattern to optimize track reconstruction. The design of the drift cells calls for 50 pm anode and cathode wires to prevent rapid aging. The tracking volume is filled with a mixture of 96% helium and 4% ethanol which operates at a pressure of 7mbar above the local atmospheric conditions. The typical length of a track is 1 m with the radial and longitudinal resolution in each geiger cell being 0.2 mm (1 o) and 0.8 cm (lo), respectively. Consequently, the precision of the position of the emission vertex of the two electrons is 0.6 and 1 cm after track reconstruction in the transverse and longitudinal directions, respectively. The external walls of these tracking volumes form a calorimeter made of blocks of plastic scintillator coupled to low radioactivity 3” and 5“ Hammamatsu PMTs. The energy resolution depends on the scintillator shape and the associated PMT which range from 11% to 14.5% (FWHM) for 1 MeV electrons. The time resolution is 250 ps (lo) at 1 MeV. A laser calibration system permits daily checks on the stability of the energy and time calibration parameters. The detector contains 6 180 drift cells and 1940 scintillators. For charge recognition a solenoid surrounds the detector and produces a field of 30 Gauss to identify and reject pair production events. Finally, external shielding in the form of 20 cm of low activity iron reduces the gamma ray flux and then 30 cm of borated water suppresses the flux of neutrons. The NEMO 3 detector’s total mass is approximately 36 tons. All the materials used in the detector have been selected for their high radiopurity by y-ray spectroscopy via Germanium detectors.

2.2. NEMO 3’s Selfstudy of Backgrounds The combination of a tracking volume, calorimeter, and magnetic field allow NEMO 3 to identify electrons, positrons, y-rays and delayed-a particles. Thus, the detector can measure the internal contamination of the source by the ey, eyy or eya channels as well as reject the external background via additional cuts discussed later [4, 51. An electron (or position) track in the detector corresponds to a curved trail of activitated drift cells with at least one end of the track ending in a scintillator which has registered energy. A y-ray corresponds to a scintillator being triggered without an associated track. Finally, an alpha particle is a short track without curvature and possibly delayed by up to 1 ms. In Figures 2 , 3 , 4 and 5 one can see events characteristic of some backgrounds. Figure 2 shows pair production in the source foil. In Figure 3 one can see the decay of some “internal contamination” which yields an electron followed by a delayed alpha. Figure 4 shows an event which is known to come from an “external” source. Finally, Figure 5 shows an event with one single e- and 3 y rays. The most

sensitive channel [2]

to

see the

external background caused

294

i

Figure 2: e-e+ pair production

Figure 3 : single e- and delayed CI

Figure 4: one crossing electron

Figure 5 : single e- and 3y rays

by neutrons interacting with the detector is the one-crossing-electron channel corresponding to Compton electrons created in a scintillator and then crossing the detector. This kind of event is distinguished fiom the two electron events emitted fiom the source by time-of-flight measurements.

2.3. The Double Beta Sources in NEMO 3

2.3.1. Isotopes and Radiopurity Several sources were placed in the detector to study pp(0v) decay but also to measure other processes such as pD(2v) decay, the Majoron decay mode and the external backgrounds. Table 1 summarizes the isotopes currently housed in NEMO 3 with their total mass and decay mode of interest.

295

Table 1: List of enriched isotopes placed in the NEMO 3 detector with limits on their

activity. However, note that with the 'OOMo, 82Se and '16Cd isotopes one can not only search for pp(0v) decay, but also pp(2v) decay to the ground and excited states, and the Majoron emission decay pp(x) modes. For looMo,0.1 million pp(2v) events per year will be recorded giving high statistics for the angular distribution between the two emitted electrons and the single electron energy spectrum. The other enriched isotopes (130Te, 15'Nd, 96Zr and 48Ca) were installed to measure the pp(2v) half-life for comparison with the predictions of their respective nuclear matrix element calculations. The natural tellurium and copper are very pure, so that the events associated with these sources, in the 3 MeV region, are induced by the external y-ray flux and as such provide limits on this flux. Another interest in the varied sources is that for long range planning it is usefd to measure the contamination after enrichment and study purification and source foil production for future improvements in NEMO 3.

2.3.2. Puvijication The enrichment process failed to yield the desired levels of purity for the 100 Mo so purification techniques were developed. These techniques started with the enriched material which was a fine grey powder. In the end two techniques were developed for purification and foil production. The first technique is a physical process that was developed at ITEP. The powder is melted by an electron beam and a crystal of pure material is drawn into a long narrow cylinder. The crystal cylinders are then cut to a fiducial length and foils are obtained by rolling the crystal in a vacuum between very pure steel rollers. This process had a total yield of 2.479 kg of lo0Mo for the experiment. The second process was chemical in nature [3]. A flow chart of the chemical purification technique is shown below. The chemistry proceeds as

296

follows. The majority of the process was carried out in a class 100 clean room at INEEL. The laboratory ware is comprised of cleaned quartz, Teflon and one piece plastic disposible filter units. Quartz distilled nitric acid and ultra-purified (1 8 MQ) water were used to dissolve the Mo. Research grade He and H, gases were used during the Mo reduction cycle. The expected purification factor is more than 100 as indicated by a study made with a sample of natural molybdenum. This sample originally had an activity of 28 mBqkg before purification and less than 0.3 mBq/kg after the process. If one applies this factor to the looMoused in NEMO 3, which had a typical activity of 1.3 mBqkg you expect the final product to be at a level of 0.013 mB /kg or better. This process was applied to the 4.260 kg of chemically purified '"Mo used in NEMO 3. This level of contamination will be measured easily with the NEMO 3 detector through the eyy and eyyy channels. NEMO 3 is sensitive to 0.002mBqikg after one year of exposure.

3. Performances of the tracking detector 3.1. Generation of high-energy electrons crossing An A d B e neutron source, situated on the bottom of the detector, emits fast neutrons, thermalised in the plastic of the scintillators ; then, a radiative capture of these thermalised neutrons, in the copper present inside the detector produces a y whose energy can go up to 8 MeV. The Compton electron created by this y can cross all the detector, from one wll of scintillators the opposited one. Using crossing electron with an energy higher than 4.5 MeV, we can study properly the tracking reconstruction, since the effects of multiple scattering become negligible. From these crossing electrons, we could determine the law between the drift time and the drift distance, inside a Geiger cell, necessary for the transversal reconstruction of the tracks : the drift time is, excepted for very short ( 200 ns) or very long ( 1500 ns) drift times, roughly proportional to the racine square of the drift distance, which is logical since the electrostatique field inside a Geiger cell is inversement porportionnal to the drift distance. Looking at the distribution of the residue, defined as the difference between the drift distance and the transversal reconstructed distance, inside a Geiger cell, we could dktermine the average transversal and longitudinal resolutions for a drift cell, equal to 0.4 mm and 0.8 cm, respectivement. The charge recognition, ensured by the existence of the magnetic field, had to be checked ; therefore, we used the same sample of electron crossing events, and constrained the fi st part of the track - from the fnst wall of PM to the source foil to be reconstructed as an electron. Therefore, the study of the second part of the track - from the source foil to the opposite wall - gives us the probability to confuse an electron and a positron, equal to 3% at 1 MeV.

297

3.1.1. Spatial resolution on the vertex In each sector of the detector, there is a copper tube at the radius of the foil, which runs vertically for the height of the detector ; during energy calibration runs, each tube has inserted into it three 207Bisources of 5 nCi, for a total of sixty sources. As the position of these sources are very well-known, the study of the two conversion electrons (0.5 and 1 MeV) emitted by these sources drives us to the determination of the spatial resolution on the vertex of the tracks. In the 1-electron channel, the transversal and longitudinal resolutions are equal to 0.2 cm and 0.8 cm, respectively, at 1 MeV. In the 2-electron channel, usefd compte tenu of the signal searched by NEMO 3, they are equal to 0.6 cm and 1.O cm, respectively.

4. Radiopurity in 208Tl of the sources of 10oMo 4.1. Principle Since a 208T1nucleus emits, in 100% of its desintegration, a y-ray with the highest energy of the natural radioactivity (2.6 MeV), close to the endpoint of the pp process, situated around 3 MeV for the nuclei studied in NEMO 3, this nucleus is the most dangerous background for PPOv study. Therefore, the pollution in 208T1 of the foils has to be very well known. The principle of the study lies on the exploitation of the e-ny (1 n 3) channels, with appropriated cuts on the energy of the different particles, but also on the time of flight of them (through a x2 analysis), in order to select events emitted in the source foil. The cuts aptlied on the total energy of the photon(s), on the energy of the electron, on the x that characterizes temporally events emitted in the foil sources, the efficiencies related to the three channels, are shown in Table 2. We can consider that the possible background contribution to this analysis, which consists in external or internal *14Bi and external 208T1, is negligible with these cuts. Channel Total energy of the photons (MeV) e'y 7 2.3 e-2y 12.3 e-3y 12.6

Energy of The electron 0.5 E, 1.3 0.5 E,., 1.3 0.5 E_" 1.3

-

X

2

internal 6.7 13.8 16.3

Efficiency ("h)

*

0.294 0.005 0.369 f 0.006 0.1 14 f 0.003

298

4.2. Preliminary results Using 900 hours of data, taken in unstable conditions, we get the upper limits on the 208T1pollution of the looMo sources shown in Table 3 ; if we combine the three channels (ey, eyy and e m ) considering that the contribution of the other backgrounds (external or internal 214Bi and external 208T1) to the search for an internal 208T1signal is negligible, the upper limit on the 208Tlactivity of the 'ooMo source foils is equal to 68 pBqkh, at 90% C.L.. This limit, already better than the one measured by y-ray spectroscopy using HP Ge detectors ( 110 pBqkg) is not so far from the limit required by the NEMO 3 radiopurety criteria ( 20 pBq/kg). We expect to reach this last limit within four months of data.

1 Channel

Activities (90% C.L.)

1

86 pBq/kg

Table 3: Upper limits (90% C.L.) on the reconstructed activities in *08T1ofthe loohlosource foils, using a sample of events representing 900 hours of acquisition.

5. Double beta analysis Using the same sample of events, representing 900 hours of first test data, we could perform preliminary analysis of pp2v and ppOv signals. In this paper, this analysis is presented for looMo only. Therefore, the events selected have to be emitted on the same point of a lo0Mo foil geometrical cuts on the vertex of the electrons emitted and temporal cuts (based on a 2 analysis) devoted to the

x

selection of electrons emitted inside the source foils, are applied. Figure 6 shows a typical e-e- event.

Figure 6: an e-e-event back to back

299

Using the sample of events described below, representing 15107 events, we performed a preliminary analysis of pp2v decay. The spectrum of the sum of the kinetic energies of both electrons is shown in Fig. 7, and the angular distribution is shown in Fig. 8, there is a good agreement between data and Monte-Carlo. The half-life deduced from these data is equal to 9. f 0.08 (stat.) f 1.3 (syst.) 10l8y : it is already of the same order of magnitude than the results give by NEM02. The radio signal over background is greater then 100. c

Figure 7: e-e- energy distribution

I

Figure 8: e-e- angular distribution

Conclusion With the frst test runs taken by the NEMO 3 experiment, we have measured the main characteristics of the detector, in good agreement with what we expected: the energy and time calibration have been performed and the performances of the tracking detector have been determined. Moreover, the preliminary analysis of the 208T1pollution of the looMo source foils gave an upper limit on this pollution, equal to 68 pBqkg, at 90% C.L., the limit required by NEMO 3 should be reached within four months of data. Finally, the pp2v ananlysis show a good agreement between Monte Carlo and data, and will be applied to the data taken by the fill detector, in stable conditions.

References [l] NEMO Collaboration, NEMO 3 Proposal, LAL 94-29 (1994) [2] C. Marquet et al, Nucl. Instrum. and Methods A 457,487 (2000) [3] R. Arnold et al, Nucl. Instrum. and Methods A 474,93 (2001) [4] H. Ohsumi et al, Nucl. Instrum. and Methods A 482,832 (2002) [5] R. Arnold et al, Nucl. Instrum. and Methods A 457,487 (2000)

NEUTRINOLESS DOUBLE BETA DECAY CONSTRAINTS

HIROAKI SUGIYAMA Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan E-mail: [email protected]

A brief overview is given of theoretical analyses with neutrinoless double beta decay experiments. Theoretical bounds on the “observable”, ( m ) p p , are presented. By using experimental bounds on ( m ) p p , allowed regions are obtained on the ml-cos2012 plane, where ml stands for the lightest neutrino mass. It is shown that Majorana neutrinos can be excluded by combining possible results of future neutrinoless double beta decay and 3H beta decay experiments. A possibility to constrain one of two Majorana phases is discussed also.

1. Introduction Neutrino oscillation experiments so far supplied us with much knowledge of the lepton flavor mixing. As we know more about that, our desires of knowing better grows also about what can not be determined by oscillation experiments: How heavy are neutrinos? Are they Majorana particles? The former question can be answered directly by 3 H beta decay experiments. On the other hand, neutrinoless double beta decay (Oupp) experiments can give the direct answer to the latter one. Ovpp experiments seem to be interesting especially because some of the future Ovpp experiments are expected to probe rather small energy scale N lo-’ eV, and then will give stringent constraints on neutrino masses and mixing parameters. The constraints by Oupp experiments have been discussed by many authors.” In this talk, I will try t o give a brief overview of those in a manner as clear as possible. For generality and to emphasize future perspective, we will not use any specific results of Oupp experiments. Specific constraints can be obtained easily by replacing (m)i$”and ( m ) ? , ,which denote experimental bounds, in equations with actual results of Oupp experiments. ”For example, see references1,2~3~4~5~6~7~8~9~10~11~12~13,14~15 and the references therein

300

301

2. Theoretical constraints on ( r n ) p p

In the standard parametrization the MNS matrix for three neutrinos is

uMNS

=

[

s12c13

c12c13 -s12C23 312323

- c12s23s13ei6 c12C23 - c~2c23s13ei6 -12s23

-

sms23s13ei6

-

1

~13e-a~ S23C13

s12c23s13eib c23c13

. (1)

In most parts of this talk we assume that neutrinos are Majorana particles. Then, the mixing matrix includes two extra CP-violating phases (Majorana phases) as

U

= U M N Sx diag(1, eip, eiT).

The “observable” of Ovpp experiments

(2)

is

where Uei represent the elements in the first low of U and m i > 0 are the neutrino mass eigenvalues. The experimental constraints on mixing angles are sin2 2813 5 0.1 = sin2 28CH of the CHOOZ bound and 0.2 < cos 2812 < 0.5 (0.4 > s& > 0.25) with the best fit cos2812 = 0.37 ( s : ~= 0.315). For simplicity, Am:j F rn; - m: are fixed as Am:, = 7.3 x eV and lArnZ3I = 2.5 x eV. Hereafter, we call m l < m2 < m3 case the normal hierarchy and m3 < m l < m2 case the inverted hierarchy even if masses are almost degenerate. The lightest mass eigenvalue ml, which is m l ( m 3 ) for the normal (inverted) hierarchy, is used as the horizontal axis of all figures in this talk to avoid tedious case studies for whether the mass pattern is hierarchical or not. By choosing phase factors and 813 so as to maximize the right-hand side of ( 3 ) ,we obtain theoretical upper bounds on ( m ) O p as (m)ppI ( m l c L

+ m2sT2)cgH + m3sgH

(4)

for the normal hierarchy, and 2

( m ) p p I m1c12

+ mzs:,

(5)

for the inverted hierarchy, where S C H ( C C H ) is the largest (smallest) value of ~ 1 (3 ~ 1 3 determined ) by the CHOOZ experiment. In the similar way a bThe actual observable is the half life T;T2 = (Go” IMo”12 (n)$J)-l with the nuclear matrix elements Mo” and the calculable phase space integral Go”.

302 1

1

(a) normal 0.1 -

5F?

z

v

1 (b) inverted

0.1 -

v

O.O1

E

1

E

0.001

0.0001 0.0001

0.01 * - _ _ _ _ _ _ _ _ _ _ _ _ _ _-__ '_ _ -

A

0.001

0.0001 0.001

0.01

coS2el2= 0.2

1

,

o.wo1

0.1

mr (eV)

,

,

0.001

,

,

1

0.01

0.1

1

mdeV)

Figure 1. Shown are theoretical bounds on ( r n ) p p with ~ 0 ~ 2 6 ' 1=2 0.2 which is the bound of LMA: 0.2 < ~ 0 ~ 2 6 ' 1<2 0.5.(See the text in Sec. 2.) Figs. (a) and (b) are for the normal and inverted hierarchy, respectively. The region surrounded by those lines is allowed. Note that ( r n ) p p has the absolute lower bound, r~ 0.05 x cos 26'12 eV, for the inverted hierarchy although does not for the normal one.

theoretical lower bound is obtained as (m)pp

2 C& lmlcS2 - masfa

2 I - m3sCH.

(6)

Figs. 1 present allowed regions on the ml-(m)ppplane determined by (4), (5), and (6) for fixed 012. Fig. l(a) shows that ( m ) a p can be zero for the normal hierarchy. It occurs around ml = sf2dAmf2/cos2012 which is obtained by setting the right-hand side of (6) zero with OCH = 0. In the inverted hierarchy, almost maximal 012 is necessary for ( m ) p p to vanish because ml 21 m2, but it is outside of the LMA region. On the other hand, Fig. l ( b ) shows that ( m ) p p has the absolute lower bound for the inverted hierarchy with the value of 012. The approximate form of the absolute lower bound, ( m ) p p 2 0.05 x cos 2012 eV, is extracted by setting ml = = 0 in the right-hand side of (6) for the inverted hierarchy. Considering 0.2 5 cos2012 of LMA, ( m ) p p must be larger than about 0.01 eV. Therefore, the inverted hierarchy is rejected for Majorana neutrinos if experiments show ( m ) p p 5 0.01 eV.

d w

3. Constraints on

ml

by a

Oupp result

A neutrinoless double beta decay experiment puts experimental bounds 5 (rn)pp 5 although (m)$ vanishes for a on ( m ) p p as negative result. From now on, we try to utilize those experimental bounds. First, because the true value of ( m ) p p must be less than (m);? and larger

(m)Fp

(m)Fr

303

than the theoretical lower bound (6), we can construct an inequality

Similarly, other inequalitions with

for the normal hierarchy, and

( m ) gI m142 + m2512 2

(9)

for the inverted hierarchy. These bounds determine allowed regions on the ml-cos 2812 plane which are shown in Fig. 2. As an example (m)?; = O.leV and = 0.3eV are considered in Fig. 2(a). The bounds for the normal (solid lines) and inverted (dashed lines) hierarchies are almost same as each other because the relevant scale of energy is large enough compared with so that the degenerate mass approximation applies. The bounds by (8) and (9) are almost vertical because of small Ami,/m?. Thus, those bounds put a lower bound on ml almost independently of cos 2012, which can be written approximately 5 ml. The upper bound on ml can be extracted from ( 7 ) ,and the curve has an asymptotic line 1 cos 20121 = t&. Consequently, the upper bound on ml does not exist if Icos28121 < t&. Fortunately, it is not the case for LMA (gray band). Eventually, if and are large the bounds on ml are roughly enough compared with

(m)Fr

d

m

(m)Fp

d m ,

(m)Fp

(m)Fr

The effect of nonzero OCH is the reason why the coefficient of cos2012 is shifted from unity to 0.9. The most conservative upper bound is obtained by cos 2812 = 0.2 and then the coefficient of is approximately 6. Next, the case of (m)@ = 0.01 eV and = 0.03 eV is considered in Fig. 2(b) as another example. Future experiments are expected to be able to probe such a small energy scale. The bounds in Fig. 2(b) for two hierarchies are no longer similar to each other because Ami3/m? is not negligible in the energy scale. The smaller experiments achieve, the larger the excluded region of small 812 for the inverted hierarchy. It will be inconsistent with LMA if 5 0.01 eV, and then the inverted hierarchy is excluded as discussed in the previous section. Another interesting feature of the bounds in Fig 2(b) is that ml = 0 is allowed for the inverted hierarchy although that is excluded for the normal hierarchy. It is because that (m)$ = 0.01 eV is less than the theoretical upper bound on ( m ) p p at ml =

(m)Fr (m)Fr

(m)Fr

(m)Fr

304

<m>R = 0.01 eV ,<m>Fc = 0.03 eV

<m>@”= 0.1 eV , < m > f p = 0.3 eV \

I,,

I

,

,

I

r:

N Q)

normal

a

-

normal

0.5

0.5

0.37

0.37

0.2

0.2

-

I 0

0.5

1

1.5

2

2.5

3

mr (eV)

Figure 2. Presented are allowed regions determined by two example cases of O v p p results.(See the text in Sec. 3.) The solid (dashed) lines are the bound for the normal (inverted) hierarchy. LMA region is superimposed by the band of shadow. Note that large mixing is preferred by the inverted hierarchy. Note also that mi = 0 can be allowed even if (rn)FF # 0.

0 for the inverted hierarchy. (See Fig. l(b).) It can occur for the normal is even smaller. (See Fig l(a).) The sufficient hierarchy also if (rn)?? conditions of (rn)?; for the exclusion of rnl = 0 are obtained by using the theoretical upper bound on ( r n ) p p with rnl = 0. Those are

for the normal hierarchy, and

for the inverted hierarchy. 4. A possibility of excluding Majorana neutrinos

Without information of the mass hierarchy, the hypothesis of Majorana neutrinos can not be rejected by Oupp experiments even if ( r n ) p p = 0. (See Fig. l(a).) For the rejection, some help of other experiments is necessary. In this section we consider a possibility of the rejection with a help of 3 H beta decay experiments which give direct measurement of the neutrino mass. The sensitivity limit is expected to be 0.3 eV, which is still in the degenerate mass regime, in the future KATRIN experiment. Here, we consider the situation that a positive result with rnl > 0.3eV is discovered. On the other hand, a negative result of O v p p experiments put an upper bound on ( r n ) p p , and the bound is translated to an upper bound on rnl

(rn)?r

305 <m>rg = 0.1 eV , <m>rf

< m > y = 0.1 eV , <m>;;p”’= 0.3 eV

= 0.3 eV

1

0.5 COS2012

0.37

0

0.5

2 0

normal

= 0.2 -

U

-

-

-

inverted - - -

-0.5

1

0.2

0.4

0.6

0.8

1

0

0.02

0.04

mr (eV)

0.06

0.08

0.1

ml (eV)

Figure 3. Shown are allowed regions by using two example cases of 0vpp results.(See the text in Sec. 5.) Bold, normal, and thin lines correspond to cos2812 = 0.5, 0.37, and 0.2 which are upper, best fit, and lower values of LMA, respectively. Solid (dashed) lines are for the normal (inverted) hierarchy. Insides of same line species are allowed. Presented bounds in Fig. 3(a) are only for the normal hierarchy because those bounds are almost independent of hierarchy in the energy scale. For instance, if 3 H beta decay experiments show ml > 0.5eV, we can put an upper bound on a Majorana phase as cos 2 p -0.25 in Fig. 3(a). Lower bounds on cos 2p seem to be difficult to obtain.

5

as discussed in Sec. 3. Those two bounds on ml will be inconsistent with each other if (m);? becomes small enough. It means the rejection of the Majorana neutrino hypothesis. The critical value of for the rejection is obtained by setting the right-hand side of (10) equal to 0.3eV which is the expected sensitivity of the future 3 H beta decay experiment. Consequently, the necessary condition for the rejection with cos 2812 = 0.2 is

(m)Fr

( m ) ; , < 0.05eV.

(13)

The critical value 0.05 eV seems to be very important goal of OuPP experiments because it is accidentally the same as at the SK best fit value where the difference between two hierarchies starts to arise.

d

m

5. Placing a constraint on the Majorana phase When Majorana neutrinos are considered, it is quite natural to hope that one day we will will be able to access the Majorana phases. In general, it is impossible even if we have precise values of ( m ) p p , mi,6, and mixing angles because two unknown Majorana phases are involved in (3). Nature, however, gives us a possibility to obtain information of a Majorana phase at the price of the possibility for another phase y. It can be seen in (3) by noting that 813 is tiny and 812 is not.

306

By choosing 813 and y - 6 appropriately in (3), we obtain an inequality which includes /3 as

(4;r2 ( m ) m Similarly, we obtain

+

I c& .\/m: cf2 mz sf2+ 2 ml m2 c f 2sf2cos 2p

+ m3 sgH (15)

for the normal hierarchy, and (rn);;

5 ( m ) p p I dmy cf2 + mg sf2+ 2m1 m2 cf2 sf2cos2p

(16)

for the inverted hierarchy. Note that ( 7 ) , ( 8 ) , and (9) are reconstructed by (14), (15), and (16) with cos2,B = 1 or -1. Those inequalities determine allowed regions on the ml-cos 2/3 plane for given 8 1 2 . We present the bounds on ,B in Figs. 3; The allowed regions are insides of the two lines with respective width. Presented in Fig. 3(a) are only for the normal hierarchy, but bounds for the inverted hierarchy are almost the same as those of the normal hierarchy because the relevant energy scale is large enough for the degenerate mass approximation to apply. Note that projecting the allowed region upon ml axis results in the allowed region of ml which is nothing but the one obtained in Sec. 2. In Fig. 3(a), the bounds determined by exclude large values of cos2p for large ml, and those bounds cross the line of cos 2p = 1 at around ml = almost independently of cos2812. Thus, an upper bound on cos2/3 is extracted if 3 H beta decay experiments show that ml is larger than On the other hand, the bounds determined by (m)FE exclude small values of cos 2,B for small ml in Fig. 3(a). In principle, it is possible t o put a lower bound on cos 2p if other experiments give a stringent upper bound on ml. In practice, however, it seems to be too difficult because the values of ml that give a lower bound on cos 2p tend to lie within too narrow region of too small energy scale; For example, the region is 0.1-0.2 eV in Fig. 3(a) for the most conservative case of cos 2812 = 0.5. The difference between bounds for two hierarchies can be seen in Fig. 3(b). For the inverted hierarchy, the region of large cos2p is excluded becomes less than 0.01 e V , whole region of cos 2p for all ml. When is excluded for the inverted hierarchy. It means the exclusion of the inverted hierarchy as discussed in Sec. 3.

(m)rr

(m);r

(m)rr (m)Fr.

307

6. Summary In this talk, I presented an overview of constraints on neutrino masses and mixing imposed by neutrinoless double beta decay (OuPP). First, it was shown that ( m ) p p for the inverted hierarchy has an absolute lower bound N 0.05 x cos2812eV, and stringent experimental upper bounds on ( m ) p p can exclude the hierarchy. Second, constraints on the lightest neutrino mass ml was extracted by using a OuPP result. If the energy scales of a result is large enough compared to the constraints are (m)?; ml (m)?F/(O.S~ 0 ~ 2 8 1 2 )Furthermore, . considering the expected sensitivity limit on ml of the future 3H beta decay experiment and assuming a positive result, we uncovered a possibility of rejecting the Majorana neutrino hypothesis. It is necessary for the rejection that OuPP experiments show ( m ) p p < 0.05eV. Next, it was shown that a bound on a Majorana phase P can be placed if a positive result of 3H beta decay experiments is obtained as ml > (m)??. Finally, I would like to emphasize the importance of precise determination of the nuclear matrix elements M’”. They are crucial to obtain stringent constraints on neutrino properties in a manner fully utilizing the accuracy of OuPP experiments.

5

5

Jm,

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

13.

14. 15.

S. T. Petcov and A. Y. Smirnov, Phys. Lett. B 322, 109 (1994) H. Minakata and 0. Yasuda, Phys. Rev. D 56, 1692 (1997) R. Adhikari and G. Rajasekaran, Phys. Rev. D 61, 031301 (2000) S. M. Bilenky, C. Giunti, W. Grimus, B. Kayser and S. T. Petcov, Phys. Lett. B 465, 193 (1999) M. Czakon, J. Gluza and M. Zralek, Phys. Lett. B 465, 211 (1999) F. Vissani, JHEP 9906, 022 (1999) H. V. Klapdor-Kleingrothaus, H. Pas and A. Y. Smirnov, Phys. Rev. D 63, 073005 (2001) Y. Farzan, 0. L. Peres and A. Y . Smirnov, Nucl. Phys. B 612, 59 (2001) S. Pascoli, S. T. Petcov and L. Wolfenstein, Phys. Lett. B 524, 319 (2002) W. Rodejohann, arXiv:hep-ph/0203214. K. Matsuda, T. Kikuchi, T. Fukuyama and H. Nishiura, Mod. Phys. Lett. A 17, 2597 (2002) V. Barger, S. L. Glashow, P. Langacker and D. Marfatia, Phys. Lett. B 540, 247 (2002) H. Nunokawa, W. J. Teves and R. Zukanovich Funchal, Phys. Rev. D 66, 093010 (2002) S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. Lett. B 549, 177 (2002) H. Minakata and H. Sugiyama, Phys. Lett. B 567, 305 (2003)

NEUTRINO MIXING AND (PP)o,--DECAY

S.T. PETCOV * Scuola Internazionale Superiore di Studi Avanzati, and INFN - Sezione d i fiieste, I-5’4014 fiieste, Italy The physics potential of the experiments, searching for ( p p ) ~ -decay ,, and having sensitivity to I<m>l X 0.01 eV, for providing information on the type of the neutrino mass spectrum, on the absolute scale of neutrino masses and on the Majorana CP-violation phases in the PMNS neutrino mixing matrix is reviewed.

1. Introduction

There has been a remarkable progress in the studies of neutrino mixing and oscillations in the last two years. The evidences for solar v, oscillations obtained in the solar neutrino experiments Homestake, Kamiokande, SAGE, GALLEX/GNO, Super-Kamiokande (SK) 1,2 were spectacularly reinforced by the data of the SNO experiment on the charged current (CC) and neutral current (NC) reactions induced by solar neutrinos, v, + D + e - + p + p and v + D -+ v + n + p , and by the first results from the KamLAND experiment s . Under the plausible assumption of CPT-invariance, the KamLAND data practically establishes the large mixing angle (LMA) MSW solution as unique solution of the solar neutrino problem. This result brings us, after more than 30 years of research, initiated by the pioneer works of B. Pontecorvo and the experiment of R. Davis et al. 7, very close to a complete understanding of the true cause of the solar neutrino problem. The combined 2-neutrino oscillation analyses of the solar neutrino and KamLAND data identify two distinct solution sub-regions within the LMA solution region - LMA-1,II (see, e g . , 8,9,10). At 90% C.L. one finds 8 : 314

Am;

E

(5.6 - 17) x lo-’ eV2,

tan2 Bo

(0.32 - 0.72) .

(1)

where 0 0 and Am& are the solar neutrino oscillation parameters. for v, + v, (D, + z7,) There exists also very strong evidences oscillations of the atmospheric v p (0,) with (almost) maximal mixing *Also at: INRNE, Bulgarian Academy of Sciences, 1789 Sofia, Bulgaria.

308

309 sin2 20atrn E (0.89 - 1.0) (90% C.L.), and neutrino mass squared difference of l2

2.1 x lOP3eV2 S [Am;

I

S 3.3 x 10-3eV2 ,

90% C.L.

(2)

The SK atmospheric neutrino (and the K2K) data do not allow one to determine the sign of Am: . The two possible signs of Am; in the case of 3-neutrino mixing correspond to two different types of neutrino mass spectrum: with normal and with inverted hierarchy (see, e.g., l3ll4). The interpretation of the solar and atmospheric neutrino, and of the KamLAND data in terms of neutrino oscillations requires the existence of 3-neutrino mixing in the weak charged lepton current: 3

j=1

Here U ~ L 1, = e , p, r , are the three left-handed flavor neutrino fields, u j is the left-handed field of the neutrino uj having a mass m j and U is the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) neutrino mixing matrix 15. In the convention in which always l 3 > l 4ml < m2 < m3 we are going to use in what follows, one has Am; Am:, > 0, and the spectra with normal and inverted hierarchy correspond to the following two choices of Am& > 0: Am& = Am?jl and Am& = Am:,. The two types of spectra will be called normal hierarchical (NH) and inverted hierarchical (IH) if ml << m2 << m3 and ml << m2 2 m3, respectively. The spectrum can also be of quasi-degenerate (QD) type: ml 2 m2 2 m3, m4,2,3>> \Am: I. As is well-known, information about the absolute scale of neutrino masses can be derived, e.g., in the 3H /?-decay experiments l 6 > l 7 ,and from cosmological and astrophysical data (see, e.g., ref. 18). The PMNS mixing matrix U can be parametrized by three angles, Oatrn, 8 0 , and 8, and, depending on whether the massive neutrinos uj are Dirac or Majorana particles - by one Dirac - 6, or by one Dirac - 6, and two Majorana - cu21/2 and a31/2, CP-violation phases The angle 8 is limited by the data from the CHOOZ and Palo Verde experiments 21. A combined 3-u oscillation analysis showed that

~

=

19120.

sin2 8

< 0.05,

99.73% C.L.

(4)

The oscillations between flavour neutrinos are insensitive to the Majorana CP-violating phases a 2 1 , a31 19. Information about ( ~ 2 1 , 3 1can be obtained, in principle, in the (/?P)oy-decay experiments 13J4,22,23324. In this article we review the potential contribution the investigations of

310

+ + +

(,O,D)oY-decay,( A ,2)-+ (A,2 2) ee-, can make to the studies of neutrino mixing. If (,O,&,-decay is generated only by the (V-A) charged current weak interaction via the exchange of the 3 Majorana neutrinos u j , to be assumed in what follows, we get for the (/3P)oy-decay amplitude: A(PP)Ov

<m>

,

(5)

where M is the corresponding nuclear matrix element (NME) and

I<m>l = ImllUel12

+ m2lUe2I2 eicval+ m31Ue3I2 eiaslI

,

(6)

is the effective Majorana mass (see, e.g., 021 and 031 being the two Majorana CP-violating phases of the PMNS matrix 19,20. If CP-invariance holds, one has 27 021 = kn-,031 = k'n-, where k , k' = 0 , 1 , 2 ,.... In this case 25726),

7/21

E eiazl = =t1,

qsl

eia31

(7)

=

represent the relative CP-parities of u1 and u2, and u1 and u3, respectively. Stringent upper bounds on I<m>l have been obtained in the 76Ge exI < m > I < 0.35 eV periments by the Heidelberg-Moscow collaboration (90% C.L.) ', and by the IGEX collaboration 3 2 , I<m>l < (0.33-1.35) eV (90% C.L.). The NEMO3 experiment 33 with looM and 82Se,and the cryogenics detector CUORICINO 3 4 , which uses 130Te,are expected t o reach a sensitivity to values of J < m > l N 0.2 eV. Up t o an order of magnitude better sensitivity, i.e., to I < m > I ? 2.7 x lop2 eV, 1.5 x lo-' eV, 5.0 x eV, 2.5 x lo-' eV and 3.6 x eV is planned to be achieved in the CUORE 3 4 , GENIUS 3 1 , EXO, MAJORANA and MOON experiments 35 with 130Te, 76Ge, 136Xe,76Ge and '"Mo, respectively. High sensitivity experiments with 136Xe- XMASS, and with 48Ca - CANDLES 3 7 , are also being considered. As we will discuss in what follows, the studies of (,DP)oY-decay and a measurement of a nonzero value of I < m >I X few I O V 2 eV: Can establish the Majorana nature of massive neutrinos. Can give information on the type of neutrino mass spectrum Can give unique information on the absolute neutrino mass scale 2 3 . With additional information from other sources (3H ,&decay experiments or cosmological and astrophysical data and considerations) on the absolute neutrino mass scale, the (PP)ov-decay experiments can provide unique information on the Majorana CP-violation phases 021 and a 3 1 -

-

38,39114140.

-

-

13114,22,23,24.

"Evidences for (P/3)ov-decay taking place with a rate corresponding to 0.11 eV 5 Il 5 0.56 eV (95% C.L.) are claimed to have been obtained in 29. The results announced in 29 have been criticized in 30 and further discussed in 31. bThe quoted sensitivities correspond to values of the relevant NME from ref. 36.

31 1

2. The Effective Majorana Mass

The value of 1 < m > I depends in the case of 3 - u mixing on 41 Am;, 80, Am&,ml and on 8. Given Am&,Am;, do and sin28, (<m>( depends strongly on the type of the neutrino mass spectrum and on the values of the phases 13,39,14 a21,31. For my,2,3>> Am;,Am& (QD spectrum), I<m>( is essentially independent on Am; and Am& . The NH (IH) spectrum corresponds to ml 5 (2 x lop2) eV, while one has a QD spectrum if m1,2,3 2 mve X 0.20 eV. For ml --” (lop3 (2 x lop2) - 0.20) eV, the spectrum is with partial normal (inverted) hierarchy (see, e.g., 1 4 ) . In the case of NH neutrino muss spectrum (ml << m2 << m3)one has m2

d-,

m3

d x ,

~ ~ ~ 3 sin26, 1 2

and correspondingly

d w

with c& cos2 80, etc. Since the largest u-mass m3 E S 6.0 x lop2 eV enters in I<m>l with the factor sin2 8 < 0.05, we have (<m>l < l o p 2 eV: for sin2 0 = 0.05 (0.01) one finds, e.g., I < m > I 5.9 (3.9) x lop3 eV (Table 1). For the allowed values of Am; , Am:,, , 60, 0, ml and ( ~ 2 1 , 3 1 ,there can be a complete cancellation between the contributions of the three terms in eq. (8) and one can have 2 3 I<m>( = 0. If the neutrino muss spectrum is of the IH type, we have ml << m2 % m3 (see, e.g. 1 4 ) , m2 S m3 lUel E sin2 8. Neglecting ml sin2 8 in eq. (6), we find l 3 (see also

<

d q , 39114):

I<m>l s J

X

c

o

s

2

8

d

m

.

(9)

Even though v1 “decouples”, the value of 1 < m > 1 depends on the Majorana CP-violating phase a 3 2 (a31 - ( ~ 2 1 ) .Obviously 1 3 ,

=

JG&os2el

c o s 2 0 ~5~ (<m>l

5 JZcos20.

(10)

The upper and the lower limits correspond to the CP-conserving cases = 0 and a 3 2 = h r.Most remarkably, since according to the existing data cos280 N (0.35 - 0.40), we get a significant lower limit on (<m>l , typically exceeding lop2 eV, in this case 38,23 (Tables 1 and 2). Using, e.g., the best fit values of Am; and tan2 Ba one finds: J<m>JX 0.018 eV. The maximal value of I < m > 1 is determined by Am; and can reach I<m>( 6 x lop2 eV. The indicated values of I<m>l are within the range of sensitivity of the next generation of (PP)oy-decay experiments. a32

-

312

The expression for I<m>l , eq. (9), permits to relate the value of sin2(a31 - a 2 1 ) / 2 to experimentally measured quantities 1 3 J 4 :

In the case of three QD neutrinos, ml “- m2 ”= m3 = mo, mi >> Am; , mo X 0.20 eV. The masses m1,2,3 s mo effectively coincide with mve measured in the 3H P-decay experiments: mo = mDe.Thus, mo < 2.2 eV , or if we use mo < (0.3 - 0.7) eV. For J<m>J we get:

’*,

<

(0.35-0.40) favored One has mo (c0s26’~( (<m>(2 mo. For cos2ea by the solar neutrino and the KamLAND data one finds a non-trivial lower limit on I<m>l , I<m>l X (0.06 - 0.07) eV. The specific features of the predictions for 1 < m >I for the three types of spectra discussed above are illustrated in Fig. 1. N

3. Constraining the Lightest Neutrino Mass An experimental upper limit on I<m>l , I<m>J < I<m>( e z p , will determine a maximal value of ml, ml < (ml)maz in the case of normal mass Am& (Fig. 1). For the QD spectrum, for instance, hierarchy, Am: we have ml >> Am: ,Am; , and up to corrections Am: sin2 eo/(2m5) and Ami sin2 0/(2m4)one finds 23:

-

N

N

(m1)maz-

I<m>l ~ C O S28,

ezp

e - sin2 el

COS~

We get similar results in the case of inverted mass hierarchy, Am& E Am;, , provided the experimental upper limit J<m>(e x p is larger than

gin

(Fig. l), predicted by taking the minimal value of (<m>(, I<m>l into account all uncertainties in the values of the relevant input parameters (Am1 , Am: , 0 0 , etc.). If Il e x p < I<m>( then either i) the neutrino mass spectrum is not of the inverted hierarchy type, or ii) there exist contributions to the (P,C)ov-decay rate other than due to the light Majorana neutrino exchange (see, e.g., 4 2 ) that partially cancel the contribution from the Majorana neutrino exchange. The indicated result might also suggest that the massive neutrinos are Dirac particles. ( X 0.02 eV if Am: A measurement of J<m>J = ( J < m >)ezp Am& , and of (<m>( = (I<m>l )ezp X d q c o s 2 0 in the case of

gin,

313

=

Am:, , would imply that ml X 0.02 eV and ml X 0.04 eV, Am& respectively, and thus a neutrino mass spectrum with partial hierarchy or of the QD type l 4 (Fig. 1). The vl mass ml will be constrained t o lie in a narrow interval, (ml)min5 ml 5 (ml)max c . If the measured value of 1 <m > I lies between the minimal and maximal values of 1 < m >1 , predicted in the case of inverted hierarchical spectrum (Fig. l),ml again would be limited from above, but we would have (ml)min= 0. 4. The Neutrino Mass Spectrum and (PP)oU-Decay

The possibility to distinguish between the NH, IH and QD neutrino mass spectra is determined by the maximal values of (<m > 1 in the cases of NH NHJH and IH spectra, I < m >I max , and by the minimal values of I < m >I for the IH and QD spectra, I< m>l In Table 1 (taken from 4 0 ) we show the NH values of I < m >I max and I < m > 1 calculated for the best-fit values of tan2 80 and Am: in the LMA-I solution region. In Table 2 (from 40) we give the same quantities, calculated using the best-fit values of the neutrino oscillation parameters, including 1 s.d. (3 s.d.) “prospective” uncertainties of 5% (15%) on tan28B and Am& , and of 10% (30%) on Am;. The possibility of determining the type of the neutrino mass spectrum if I < m >I is found to be nonzero in the (/3/3)oy-decayexperiments, depends crucially on the precision with which Am;, $0,Am; , sin2 8 and I<m >I will be measured. It depends also crucially on the values of 80 and of I< m >( . High precision measurements of Am;, tan2 OD, Am& and 8 are expected to take place within the next 7 years. Thus, the largest prospective uncertainty in the comparison of the predicted and measured values of I< m >I could be associated with the corresponding (P&-decay NME. Following we will parametrize the uncertainty in (<m>l due t o the imprecise knowledge of the relevant NME through a parameter C,5 2 1:

zf”.

2hQD,

-

24740,

is the value of I < m > 1 obtained from the measured where (I < m > 1 (/3P)oy-decay half life-time of a given nucleus using the largest nuclear matrix element, and A is the experimental error. The currently estimated range of C2 for experimentally interesting nuclei varies from 3.5 for 48Cat o 38.7 for 130Te, see, e.g., Table 2 in 2 6 . In order to be possible t o distinguish between NH and IH, NH and QD, and IH and QD spectra, the following inequalities must hold, respectively: CAnalyticexpressions for ( T T L ~ and ) ~ ( ~m ~ l)maz are given in 23. dFor further details concerning the calculation of the uncertainty in I<m>l see

24,40.

314 NH

QD

NH

IH

< l < m > b B a x < I < ~ >Z nI , < I < ~ > max I < I < ~ >min, I cI<m>I max < ( 2 1. These conditions imply 40 upper limits on tan2 80 which I < m >I are functions of the neutrino oscillation parameters and of <. The detailed study performed in 40 showed, in particular, that it would be possible t o distinguish between the NH and QD spectra for the values of tan2 80 favored by the data for values of ( z 3, or even somewhat bigger than 3. In contrast, the possibility to distinguish between the NH and IH spectra for 2 3 depends critically on the value of sin2& this would be possible for the current best fit value of tan28a and, e.g., Am; = (5.0 - 15) x lop5 eV2, provided sin2 0 6 0.01. For C X 2, distinguishing between the IH and QD spectra in the case of mo 2 0.20 eV requires too small, from the point of view of the existing data, values of tan2Ba. For mo X 0.40 eV, the values of tan2 O0 of interest fall in the ranges favored by the solar neutrino and KamLAND data even for = 3. ~~~~~

<

<

5. Constraining the Majorana CP-Violation Phases The problem of detection of CP-violation in the lepton sector is one of the most formidable and challenging problems in the studies of neutrino mixing. The possibility to get information on the CP-violation due to the Majorana phases c ~ 2 1 , 3 1by measuring \<m>)was studied recently in 43124. After making a certain number of assumptions about the experimental and theoretical developments in the field of interest that may occur by the year 2020 e , the authors of 43 claim to have shown “once and for all that it is impossible to detect CP-violation from (PP)oy-decay in the foreseeable future.” In 24 the conditions under which CP-violation might be detected from a measurement of I < m > 1 and mDeor C = ml m2 + m3, or of I < rn > I and a sufficiently stringent upper limit on C, were determined. The results in the case of QD neutrinos mass spectrum can be summarized as follows. The possibility of establishing that the Majorana phases ~ 2 1 , 3 1have CPnonconserving values requires quite accurate measurements of I< m >I and, say, of mDeor C, and holds only for a limited range of values of the relevant parameters. More specifically, proving that CP-violation associated with Majorana neutrinos takes place requires, in particular, a relative experimental error on the measured value of )<m >)not bigger than (15 20)%, an uncertainty in the value of ) < m >I due to an imprecise knowledge of the corresponding NME smaller than a factor of 2, a value of tan2 Ba X 0.55,

+

~

eIt is supposed in 43, in particular, that ll will be measured with a 25% (1 s.d.) error and that the uncertainty in the (PP)ov-decay nuclear matrix elements will be reduced to a factor of 2.

315

-

and values of the relevant Majorana CP-violating phases c\121,31 typically within the ranges of (7r/2 - 37r/4) and (57r/4 - 37r/2).

-

6. Conclusions

Future (,!?p)ov-decay experiments have a remarkable physics potential. The knowledge of the values of the relevant (p,!?)oV-decay nuclear matrix elements with a sufficiently small uncertainty is crucial for obtaining quantitative information on the neutrino mixing parameters from a measurement of (/3,!?)ov-decay life-time.

7. Acknowledgments This work was supported by the Italian MIUR under the program “Fenomenologia delle Interazioni Fondamentali” .

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zax

Reference

(tan200)BF

8

0.46 0.42 0.43

9 10

(Am;),, 7.3 7.2 7.0

I<m>l m&x NH 5.9 (3.9) 5.7 (3.7) 5.7 (3.7)

I<m>l 18.4 20.3 19.8

2"

I<m>l 59.9 67.2

2:

65.3

12;

Table 2. The values of I < m > I <m > " : 1 and I < m > (in units of l o W 3eV), calculated using the best-fit values of solar and atmospheric neutrino oscillation parameters from Table 1 and including 1 s.d. (3 s.d) uncertainties of 5% (15%) on tan200 and Am&, and of 10% (30%) on Am:. In this case one has: I < m > = 54.5(59.2) x eV. (From4'.) Reference

I<m>l

:zx

(6'

= 0.05)

8

6.1 (6.7)

9

6.0 (6.5) 6.0 (6.5)

in

I<m>lx: :

(s2 = 0.01) 4.1 (4.4) 3.9 (4.2) 3.9 (4.2)

I<m>l

zn

16.5 (12.9) 18.3 (14.6) 17.9 (14.1)

I<m>l

2;

55.9 (48.2) 63.3 (55.9) 61.4 (54.0)

317 ,

~

5

-4

-3

,

-2

.

,

. . , .

~1

.

,

,

0

.

,

5

4

~3

-2

-1

0

Figure 1. The dependence of I<m>l on m l for the solution LMA-I, Am& = Am;, (normal hierarchy) and Am& = Am:, (inverted hierarchy), and for the best fit values (upper left panel) and the 90% C.L. allowed values (upper right and lower panels) of the neutrino oscillation parameters found in refs. 8,12. The values of sin2 B used are 0.0 (upper panels), 0.02 (lower left panel) and 0.04 (lower right panel). In the case of CP-conservation, I < m > ] takes values: i) for the upper left panel and Am& = Am;, (Am& = Am&) on a) the lower (upper) solid line if 7 2 1 ( 3 2 ) = 1 and 731(21) = +I, h) the long-dashed (dotted) line if 721(32) = -1 and 731(21) = +1; ii) for the upper right panel and Am& = Am;, ( A m 6 = Am:,) - in the medium grey (light grey) regions a) between the two lower solid lines (the upper solid line and the short-dashed line) if ~ ~ ~ ( = 3 21 )and 731(21) = f l , h) between the two long-dashed lines (the dotted and the dash-dotted lines) if 7 2 1 ( 3 2 ) = -1 and 731(21) = +l; for the two lower panels and Am& = Am;, - in the medium grey regions a) between the two lower solid lines if 721 = 731 = 1, b) between the long-dashed lines if 721 = -731 = 1, c ) between the two lower dash-dotted lines if 721 = -731 = -1, d) between the two lower short-dashed lines if 7 2 1 = 731 = -1; and iii) for the two lower panels and Am& = Am:, - in the light grey regions delimited a) by the upper solid and the upper short-dashed lines if 732 = &721 = 1, h) by the dotted and the upper dash-dotted lines if 7 3 2 = + 7 2 1 = -1. Values of I<m >I in the dark grey regions signal CP-violation. (From 4 4 . )

THE MAJORANA EXPERIMENT: A STRAIGHTFORWARDNEUTRINO MASS EXPERIMENT USING THE DOUBLE-BETA DECAY OF 76GE H. S. MILEY FOR THE MNORANACOLLABORATION^ Pacific Northwest National Laboratory*, Richland, WA, USA 99352 E-mail: [email protected] The Majorana Experiment proposes to measure the effective mass of the electron neutrino to as low as 0.02 eV using well-tested technology. A half-life of about 4E27 y, corresponding to a mass range of [0.02 - 0.071 eV can be reached by operating 500 kg of germanium enriched to 86% in 76Ge deep underground. Radiological backgrounds of cosmogenic or primordial origin will be greatly reduced by ultra-low-background screening of detector, structural, and shielding materials, by chemical processing of materials, and by electronic rejection of multi-site events in the detector. Electronic background reduction is achieved with pulse-shape analysis, detector segmentation, and detector-to-detector coincidence rejection. Sensitivity calculations assuming worst-case germanium cosmogenic activation predict rapid growth in mass sensitivity (T% at 90%CL) after the beginning of detector production: [0.080.281 eV at -1 year, [0.04-0.141 eV at -2.5 years, [0.03-0.101 eV at -5 years, and [0.02 - 0.071 eV at -10 years. The impact of primordial backgrounds in structural and electronic components is being studied at the 1 yBqkg level, and appears to be controllable to below levels needed to attain these results.

1. Measurement of 76GeDouble-Beta Decay The goal of the Majorana experiment is to determine the effective Majorana mass of the electron neutrino. Detection of the neutrino mass implied by oscillation results is now technically within reach. This exciting physics goal is best pursued using the well-established technique of searching for the neutrinoless double-beta (OV pp) decay of 76Ge,augmented with recent advances in signal processing and detector design. The Majorana experiment will consist of a large mass of 76Ge in the form of high-resolution detectors located deep underground within a low-background environment. Observation of a sharp peak at the pp endpoint, 2038.6 keV, will quantify the Ov PP-decay half-life and thus the effective Majorana mass of the electron neutrino. The Majorana The membership of the Majorana Collaboration is available at http://majorana.pnl.gov. * Pacific Northwest National Laboratory is managed for the U.S. Department of Energy

by Battelle Memorial Institute under contract DE-ACO6-76RLO-1830.

318

319

Collaboration is actively refining estimates of the ultimate sensitivity of the experiment. The original and conservative estimation method, based on experimentally achieved results, predicts an achievable OV Po-decay half-life limit of -4827 y. Depending on the nuclear matrix elements chosen, the effective neutrino mass sensitivity becomes <m,> = r0.02 - 0.071 eV which is within the range implied by recent neutrino oscillation experiments. Improving the attainable T% for Ov Po-decay is done in two general ways: adding 76Ge atoms and reducing background. Since some backgrounds are related to the germanium mass and surface area, isotopic enrichment of the germanium from a natural abundance of 7.6% to 86% in 76Gegives a large boost in sensitivity without an increase in background. Previous germanium PP-decay experiments have used multiple large germanium detectors enriched in 76Ge,and these can be scaled up (from the order of lOkg to 500 kg). While this scaling up is not inexpensive, background reduction is much more challenging. Fortunately, a number of research groups have spent decades identifying screening technology, radiopure materials, and construction methods that minimize background.

2. Background Reduction in Germanium: Cosmogenic Isotopes 2.1 Experimental Starting Point for Background Estimation The history of background reduction by members of the Majorana Collaboration has been documented elsewhere'. One lesson from this experience was that after the identification and elimination of each source of background, another was discovered. This has led in a recent experiment to a background rate of 0.2 countskeVkgIy at the energy of interest'. While this rate is quite low, such a rate for 5000 kg-y of detector operation (500 kg for 10 years) would result in 5000 counts in a 5 keV analysis window, where Po-decay in this enriched material at T% = 4e27 y would yield only 7 decays. A factor of about 500 in background reduction is required to obtain a signal to noise ratio of 1. Fortunately, this is possible today using care in detector design and construction and new technology adapted to background rejection. The measurement achieving 0.2 cts/keV/kg/y was with germanium detectors that had been recently introduced to an underground location, such that cosmogenic activation of 68Gefrom high energy cosmic ray secondary neutrons was likely the majority of the contributing background. Eventually, the decay of 68Ge(TM = 271 d) would allow cosrnogenic 6oCo(T% = 5.2 y) to be the major

320 background contributor in the germanium. Given that waiting for @ k odecay is not a practical solution, the contribution of these isotopes can be mitigated in two reasonable ways: reduced cosmogenic exposure before introduction underground and application of electronic techniques to suppress their signals. Reduced exposure can be achieved readily by clever logistics including transit shielding, just-in-time delivery, and some amount of underground germanium detector manufacturing. The ingrowth of 68Ge begins near the final enrichment steps, and the ingrowth of 6oCo effectively begins much later, with the final stages of intrinsic germanium refinement (zone refinement and crystal pulling). The time above ground after crystal production can be minimized or eliminated by moving some manufacturing steps underground, thereby strongly suppressing non-germanium contaminants in the crystals.

2.2 Multiplicity-based background reduction The remaining cosmogenic contaminants in the crystals can be suppressed by virtue of the dissimilarity in the multiplicity of energy deposition sites between PP-decay and internal contaminants. Because of the limited range of the electrons in PP-decay, this energy deposition is essentially single-site. The most troublesome internal contaminants (68Ge-68Gaand 6oCo)each have a beta and multiple gamma rays, which must scatter multiply to produce an event near the region of interest. This multiplicity can be effectively detected by using the pulse-shape information in each pulse and by contact segmentation of the germanium crystal. The pulse-shape analysis recently demonstrated by members of the collaboration3 allows three pulse parameters to be calculated for each pulse, resulting in a three-dimensional space populated by pulses of different origin. Sources such as the 1592.47 keV double escape of the "*Tl transition at 2614.47 keV produce a characteristic single site spatial population in the three dimensional parameter space. Events encountered outside the spatial extent of this distribution can be discarded as backgrounds, with an appropriate efficiency correction. An example of the use of this cut is shown in figure 1. The original data is the upper curve. Applying the single-site parameterization cut reduces the efficiency for photopeaks by 74%, and the efficiency for single site events by 20%. The lower curve has been adjusted up by 20% to match the original double-escape peak intensity. Since the multiplicity of internal 68Ge and 6oCo events is expected to be even larger than full-energy external single gamma ray events such as those in the 1620.6 keV 212Bipeak, the efficacy of the cut for rejecting ordinary gamma ray peak events is conservative. Segmentation plays a similar role, but the segmentation data is quite different. While pulse shapes are formed by the image charges formed on the germanium contacts while the electrons and holes are drifting apart along (essentially radial) field lines, segmentation can distinguish between multiple-

321 energy depositions along the z and phi .axes of the cylindrical germanium crystal. Going further, several researchers have demonstrated the capability to resolve multiple energy depositions at modest energies within a single segment using the signals on adjacent segments. In the sensitivity estimates computed so far for the Majorana Experiment, only a simplistic segmentation cut has been simulated: If any two or more segments have over 30 keV energy deposition, the event is discarded as background. This approach obviously varies in efficacy depending on the size of the individual segments. Many segmentation schemes are possible, but a scheme selected for low cost rather than high performance has been selected for the purpose of conservatively estimating suppression. v)

c

5 3000 8

gamma efficiency = 0.2645

1500

1000

500

n "

1560

1580

1600

1620

1640

1660

1680

1700

keV Figure 1. Original and pulse-shape-discriminated spectra. This is experimental confirmation that high-multiplicity signals (e.g. 228Ac 1587.9 keV peak) like our anticipated 6OCo and 68Ge contaminants are strongly suppressed while single site events (e.g. double escape peaks) like double-beta decay are only slightly decreased. The lower, filled spectrum has been slightly (+20%) renormalized.

2.3 Sensitivity calculation The two electronic background rejection methods, pulse shape analysis and segmentation, reduce background by a factor of 4 and 7, respectively, while

322

decreasing the signal by 20% and lo%, respectively. If we compute a figure of merit (FOM) based on the remaining signal fraction divided by the square root of the remaining background, we can compute a factor that shows the effective multiplication of the T% obtainable if a certain background were the limiting contribution. The impact on the neutrino mass range will then be inverse of the square root of this FOM. The FOMpulse=1.6 and the FOM,,, = 2.4, with the total background reduction factor for cosmogenics of 4. Coupled with decay factor of about 20, weighted by isotope and based on previous experience with cosmogenics in germanium, the total reduction in cosmogenic background would equal about 480, or a rate of about 0.21480 = 0.00042 cts/keVlkg/y. This produces about 10 counts in the analysis region in 5000 kg-y of operation. A more sophisticated estimate is represented in Figure 2. Assuming quarterly shipments of enriched germanium with similar initial cosmogenic activation to the previous estimate, the growth of sensitivity vs. time can be calculated. This calculation assumes essentially worst case cosmogenics in germanium and the effects of decay and multiplicity-based cuts as discussed above. .---I__-^-__I_-

".

..____"

"_^

"

1.E+28

-I

Fast Production

.-

~

-f $

0

2

4

6

8

10

12

Time (Years after detector production begins)

Figure 2. One computation of sensitivity vs. time for the Majorana Experiment. The trend lines overestimate sensitivity at short times. Slow and fast detector production schedules are shown. The slow schedule is a ramp from 50 kgly to 100 kgly vs. the fast schedule of 200 kgly.

323 This estimate of background reduction of the germanium cosmogenic isotopes is considered quite conservative, as it assumes a worst case exposure that we plan to minimize in the Majorana Experiment and it assumes a very simplistic segmentation background cut.

3.

Other Backgrounds

The sensitivity calculation above based on cosmogenics may lead one to expect that primordial isotopes (U, Th and progeny) are being ignored. While cosmogenics were shown from empirically-based computations to account for the complete signal seen in the experiment cited above, there is still some possibility of a primordial or other contribution up to the size of the error bar on that measurement. Possibilities include cosmogenics or primordials in copper, primordials in small parts inside the detector, or other small mass materials, such as surface treatments on the germanium. A specialized measurement of the copper itselp using a detector formerly used for PP-decay measurements estimated that the electroformed copper contained <25 pBq/kg 226Raand -9 pBq/kg **'Th. This copper was produced using improved methods in 1995. Since then, the interpretation of these results has changed to allow the possibility that the activity was neither in the copper or the lead shielding.. In addition, copper production improvements in practice and new methods have been developed since 1995. For instance, cleaner reagents are available, multiple bath re-crystallizations and sequential electroforming can all reduce the radioactive contaminants of the copper. If the copper is truly starting at 9 pBq/kg of either primordial decay chain, our estimates of suppression lead us to believe that we need no lower than about 1 pBqkg, so the copper is not far from acceptability. These methods will be tested using very sensitive methods of screening. The cosmogenic production of 6oCoin copper can also be greatly reduced by sequential electroforming underground, where starting copper stock is electroformed into a secondary, purified copper stock, which is then electroformed into a final part, with no possibility of surface-level neutron exposure. Finally, materials low in mass used to construct detectors will be screened. These materials include obvious items like electronic components, cabling, FET interconnect wires and bonding materials. Less obvious potential contributors include surface treatment chemicals for germanium detectors; while evidence exists that bulk germanium in a germanium crystal is free of primordials, surface

324

preparations may be partly responsible for the activity originally attributed to the copper. All of these materials can be effectively screened to minimize their background contribution, and options exist to replace them with Collaborationmanufactured clean parts and materials. These parts will require screening on low-background, underground systems formerly used for PP-decay measurements. Two such systems are being commissioned in the Soudan mine at the time of this writing. A third system, currently under construction, will consist of 18 70% germanium detectors surrounding a central sample volume. This system should be able to screen each of the aforementioned items or materials to below the potential to contribute one background count in the region of interest during the Majorana Experiment.

4.

Configuration and Design

The Majorana Experiment has a number of possible configurations. These variations include the exact manner of copper cryostat and support, or may include the possibility of alternative cooling such as direct nitrogen immersion or the use of active liquid scintillation veto around the copper cryostats. This sort of consideration is based largely on the expected impact of residual radioactive contamination in copper and other structural materials. This point may be made irrelevant by the potential reduction in copper contamination, as mentioned above. In any case, a reference plan consisting of a minimized copper structure with highly screened parts and materials minimizes the risk of project delays. Germanium detectors may be readily repackaged into an alternative structural or cooling scheme should the straightforward reference plan prove unsuitable in early testing or should an alternative prove irresistibly effective. Another design consideration is the segmentation plan. Segmentation technology exists for both p-type and n-type materials, but n-type crystals allow complex lithographic contacts to be applied in any configuration, etched off and reapplied. Several parameters need to be considered in the optimization of segmentation schemes for the Majorana Experiment. First, the FOM for a scheme also must consider the detector mass, the detector packaging plan, and the expected major isotopic contamination and location. Second, the production rate of the detectors affects the overall rate at which physics results will be derived. Third, the number, type, and instrumentation cost of each contact must be considered from the viewpoint of finance and heat load in the cryostat. These segmentation design issues are being explored by simulation, but future plans include experimental demonstration of segmentation benefits using an enriched detector developed for this purpose and highly segmented detectors

325 currently being operated by collaboration members. Simulation to date has focused on 6oCo,68Ge-68Ga,and 'T1 in various locations from the crystal to the copper support. (Simulation of 214Biwill be completed soon.) These simulations have shown the viability of a simple, commercially successful segmentation plan based on -450 1.1 kg n-type crystals segmented into two 500 g segments and packaged in 57-crystal cryostats. Other, higher performance plans are being considered as potentially more optimal on the basis of risk, performance, and time to the design goal of <m,,> = [0.2-0.71 eV.

5. Conclusions The Majorana Experiment offers a straightforward method of determining the mass of the electron neutrino. The Collaboration is ready to begin this experiment, and is performing the needed engineering, material screening, and optimization studies to accelerate the beginning of physics results after approval. No proof-of-principal R&D is required, as a reference plan exists that seems to satisfy each experimental need in the measurement. In addition, several opportunities for performance or cost improvements over the reference plan exist.

Acknowledgments Pre-approval work on the Majorana Project is supported at Collaboration institutions by: the U.S. Department of Energy Office of Science, the National Nuclear Security Administration Office of Research and Engineering, several US National Laboratory Laboratory-Directed Research and Development offices, the National Science Foundation, several university research offices, and international research support institutions.

References 1. R. L. Brodzinski et al, NIMA292 337-342 (1990). 2. F. T. Avignone et al, Nucl. Phys. B (Proc. Suppl.) 28A 280-285 (1992). 3. C. E. Aalseth, Ph. D. dissertation (unpublished), University of South Carolina, 2000 and to be submitted, IEEE Nuclear Science Symposium, October 21-24,2003, Portland, OR. 4. R. L. Brodzinski, et al, Journal of Radioanalytical and Nuclear Chemistry, Articles, Vol. 193, No. 1,61-70 (1995).

MOON(M0 OBSERVATORY OF NEUTRINOS) FOR NEUTRINO STUDIES BY DOUBLE BETA DECAYS AND LOW ENERGY SOLAR NEUTRINOS *

H. EJIRI, T. ITAHASHI AND T. SHIMA R C N P , Osaka University, Ibaraki, Osaka, 567-004 7, Japan E-mail: [email protected] R. H A Z A M A ~Y. IKEGAMI, K. MATSUOKA, H. NAKAMURA, M. NOMACHI, Y. SHIMADA, Y. SUGAYA AND S. YOSHIDA

Physics and OULNS, Osaka University, Toyonaka, Osaka, 560-0043, Japan E-mail: [email protected]

K. FUSHIMI, K. ICHIHARA AND Y . SHICHIJO Integrated Arts and Sciences, Tokushima University, Minami- Josanjima, Tokushima 770, Japan M. GREENFIELD Natural Sciences, International Christian University, Mitaka, Tokyo 181-8585, Japan P.J. DOE, R.G.H. ROBERTSON, O.E. VILCHES, J.F. WILKERSON AND D.I. WILL CENPA, University of Washington. Seattle, Washington, 98195, USA S.R. ELLIOTT Los Alamos National Laboratory, New Mexico, 87545, USA J. ENGEL Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina, 27599, USA

326

A. PARA Fermilab, P.O. Box 500 Batavia IL 60510, USA

M. FINGER Physics, Charles University, Prague, Czech Republic K. KURODA C E R N , Geneva, Switzerland A. GORIN, L. MANOUILOV AND A. RJAZANTSEV

IHEP, Protvino, Russia V. KUTSALO AND V. VATULIN VNIIEF, Sarov, N. Novgorod Region, 6071 90, Russia

V. KEKELIDZE, G. SHIRKOV, A. SISAKIAN, A. TITOV, V. VORONON JINR, Dubna, Moscow Region, 141980, Russia

The MOON (Molybdenum Observatory Of Neutrinos) project is a hybrid double beta ( p p ) decays and solar Y experiment with looMo. It aims a t high sensitive studies of pp with a sensitivity of < m, >-0.03 eV and real-time studies of p p and 7Be solar v’s. The double p rays from looMo are measured in prompt coincidence for the Ovpp studies, and the inverse p rays from solar-u captures of looMo are measured in delayed coincidence with the subsequent fl decay of looTc. The Ovpp decay t o the first excited O+ state of looRu can utilize a y-y coincidence technique and is a complement to the ground state transition of the Ovpp decay. Measurements with good position resolution enable one to select true signals by spatial and time corrclations.

-

The recent experimental data and theoretical analyses for v oscillation experiments suggest effective Majorana v masses of the order of 0.1 0.01 eV if the neutrino is a Majorana particle and the mass spectrum is of the almost degenerate type or with inverted mass hierarchy. Besides, the new ‘Work supported by a grant-in-aid of Scientific Research and Ministry of Education, Science and Culture, Japan. t Speaker on behalf of the MOON collaboration.

327

328

data from the astrophysical (WMAP) observations place important consequences for neutrino experiments, which disfavor a u oscillation interpretation of the LSND experiment, exclude the determination of the absolute u mass in the planned KATRIN experiment, a,nd can rule out a large portion of the parameter space that claimed by the Heidelberg-Moscow experiment Thus it is of great interest t o measure p,8 decays with the sensitivity of the effective mass < m, >- 0.03 eV. Realtime studies of solar u’s have been made of the high energy component of *B u’s, which constitute only a fraction of less than lop4 of the total solar u flux. Then the importance of realtime studies of individual low energy solar u’s, which are major components and its fluxes are calculated much precisely, is emphasized ‘. looMo is shown to have large responses for both the PP decays and the low energy solar u’s ‘. The MOON (Molybdenum Observatory Of Neutrinos) project is a ”hybrid” Pp and solar u experiment with 1 ton of looMo. It aims at high sensitive studies of the PP decays with sensitivity to Majorana u mass of the order of < m, >-0.03 eV and the charged-current neutrino spectroscopy of the major components of the p p and 7Be solar u’s 5 . The oscillation survival probability exhibits a strong change with energy below 1 MeV. The unique features of MOON are as follows. 1. The PI and ,& with the large energy sum of El Ea are measured in coincidence for the OuPP studies, while the inverse P-decay induced by the solar u and the successive /? decay are measured sequentially in an adequate time window for the low energy solar-u studies. The isotope looMo is just the one that satisfies the conditions for the PP-u and the solar-u studies. 2. The large Q value of Qpp=3.034 MeV gives a large phase-space factor Go” t o enhance the OuPP rate and a large energy sum of El Ea = Qpp t o place the Oupp energy signal well above most BG. The transition rate for the possible u-mass of < m, > = 0.02-0.03 eV is of the same order of magnitude as the solar-u capture rate. 3. The energy and angular correlations for the two &rays identify the v-mass term for the Oupp decay. Besides the precise study of 2vpP-decay differential characteristics offers a new possibility to decide whether one low-lying state dominates or not, which is crucial problem of the theoretical 2upP decay studies ‘. 4. Measurements of the Oupp decays t o both the ground and the 1.132 MeV excited O+ states in looRu may complementary to each other since their experimental conditions are quite different (Fig. 1). The OupP phase space for the excited state is smaller by one order of magnitude than that for

-

+

+

329

the ground state, but the 2vpp transition rate is two orders of magnitude smaller, as shown in Table 1. Thus the 2 v p p tail in the 0vpp window is much less for the excited state. Nuclear matrix elements for the two Ovpp decays may be different. a 5. The low threshold energy of 0.168 MeV and the large responses for the solar-v absorption allow observation of low energy sources such as p p and 7Be. The p p and 7Be v's are captured only into the ground state of looTc and the rate ratio of p p and 7Be v's is independent of the B(GT) value. This is quite important in terms of the measurement of their ratio which can exclude exotic solutions to the solar v problem experimentally The capture rate of which can be obtained from the EC capture rate '. 6. The tightly localized p-p event in space and time windows are quite effective for selecting 0vpp and solar-v signals and for reducing all kinds of BG. 7. MOON is based on the recent pp studies of looMoby ELEGANT V l o and the solar v studies by SNO l l .

'.

Table 1. Expected signal rates per year per ton of looMo. Source OvBB(ground state) 2vpp (ground st ate) O U P ~ ( Ostate) ~

~V,BB(O; state)

Raw rate 31(< m,

> /50meV)'

3.6~10'

4(< m,,

> /50me~)'

6.9~10~

PP(LMA)

121(70)

Be( LMA)

39(20)

The pp transition rate for < m, > = 0.05 eV is evaluated to be 31 per year(y) per one ton(t) of looMo isotopes for the ground state transition. Here the nuclear matrix element calculated by RQRPA is used 1 2 . This is one order of magnitude larger than the rate for 76Ge. The rate for the excited state is expected t o be around 4 per y per t by using the same matrix element as for the ground state. The charged current v capture rates for individual solar v sources are derived from the B(GT) values measured by the (3He,t) reaction 4 , as shown in Table 2 Here capture rates for other nuclei are also shown.

'.

"If the O+ states are considered to be two-phonon-like states, the smallness of the involved transition matrix element is discussed recently 7.

330 Table 2.

Solar-v capture rates in units of SNU.

Nucleus

-Q value(MeV)

pp

7Be

13N

pep

150

8B

Total

37c1

0.814

0

1.1

0.1

0.2

0.3

6.1

7.9

71Ga

0.236

70.8

35

3.7

2.9

5.8

12.9

132

1151~

0.120

468

116

13.6

8.1

18.5

14.4

639

looMo

0.168

639

206

22

13

32

27

965

The raw count rates for the p p and 7Be v’s are expected t o be 121 and 39, respectively, without v oscillations, and around 70 and 20 with the LMA oscillation. In order to achieve adequate sensitivities for both the Ovpp decays and the low energy solar v’s, the MOON detector is required to have 1. looMo isotopes of the order of 0.5 N 1 ton. 2 . Energy resolution of D = 0.03 0.04 /*. 3.Position resolution of lo-’ ton of looMot o reduce 2vPP and RI accidental coincident B G ’s. 4.RI impurities of the order or less than Bq /ton (0.1 ppt of U and Th). to reduce correlated and accidental BG’s. Enriched looMoisotopes with 85-90 % enrichment are obtained by large centrifugal separation and/or laser separation systems in reasonable time and cost. Purification of the source to the ppt level is realistic 1 3 . Research and development for solid and liquid scintillators are under progress. A possible option for the solid scintillator is a supermodule of hybrid plate and fiber scintillators. One module consists of a plate scintillator and two sets of x-y WLS/fiber scintillator planes, between which a thin looMo film is interleaved. The WLS/fiber scintillators coupled with multi-anode PM’s enable one to get the good position resolution of N 10W9 and the scintillator plate (x-y plane) with multi PM’s at both x and y sides give the adequate energy resolution as required. Most of natural and cosmogenic RI BG’s are accompanied by y rays and/or pre-(post-)P/cu. decays. They are removed by SSSC (signal selection by spatial correlation) and SSTC(signa1 selection by time correlation). MOON may be used to study other /I@ isotopes such as 150Nd and ‘16Cd as well by replacing Mo isotopes with other isotopes. looMo has been shown t o have large CC responses for supernova v’s, and thus MOON can be used to study the low energy v, spectrum and the v, t v, oscillation by using thick “Mo plates of the order of 100 tons 14. N

33 1

Figure 1. Level and transition schemes of looMo for double beta decays (81Pz) and two beta decays (88') induced by solar-v absorption. GR is the Gamow-Teller giant resonance. Qpp, Q e C ,and y are given in units of MeV.

Acknowledgments The authors thank the Center for Experimental Nuclear Physics and Astrophysics, University of Washington for suport and discussions. Multi-agency involvement is anticipated for MOON collaboration and the authors would like t o thank the present all collaborators

References 1. K. Cheung, Phys. Lett. B 562 97 (2003) and references therein. 2. J.N. Bahcall, hep-ex/0106086. 3. H. Ejiri, Phys. Rep. C 338 265 (2000). 4. H. Akimune, et al., Phys. Lett. B394 23 (1997). 5. H. Ejiri, J. Engel, R. Hazama, P. Krastev, N. Kudomi, and R.G.H. Robertson, Phys. Rev. Lett. 85 2917 (2000). 6. F. Simkovic, P. Domin, and S.V. Semenov, J . Phys. G 27 2233 (2001). 7. J. Suhonen and M. Aunola, Nucl. Phys. A 723 271 (2003). 8. H. Nunokawa, hep-ph/0105027. 9. A. Garcia et al., Phys. Rev. C 47 2910 (1993). 10. H.Ejiri, et al., Phys. Rev. C 63 65501 (2001). 11. Q. R. Ahmad et al., Phys. Rev. Lett. 87 71301 (2001). 12. A. Faessler and F. Simcovic, J . Phys. G 24 2139 (1998). 13. R.G.H. Robertson, Prog. Part. NucZ. Phys. 40 113 (1998). 14. H. Ejiri, J. Engel, and N. Kudomi, Phys. Lett. B530 27 (2002).

EXO: A NEXT GENERATION DOUBLE BETA DECAY EXPERIMENT

C. HALL* Stanford Linear Accelerator Center, 2575 Sand Hall Road, Menlo Park, CA 94025, USA E-mail: [email protected]

The Enriched Xenon Observatory (EXO) is an experiment designed to search for the neutrinoless double beta decay 136Xet136Ba++e-e- . To dramatically reduce radioactive backgrounds, the E X 0 collaboration proposes to tag the final state barium ion event-by-event through its unique atomic spectroscopy. We describe here the current status of the E X 0 R&D effort.

1. The E X 0 proposal The recent discovery of neutrino mass in atmospheric, solar, and reactor neutrinos has led to renewed interest in the physics potential of neutrinoless double beta decay. Ovpp is the most promising process to distinguish between Majorana and Dirac neutrinos, and may also provide valuable information on the overall scale of the neutrino mass spectrum. The E X 0 (Enriched Xenon Observatory) collaboration has proposed to search for the Ovpp decay 13sXe+136Ba++e-e- '. Xenon has several properties which make it an attractive candidate for a Ovpp experiment. It is a good ionization and scintillation medium, so it can serve as its own calorimeter for the final state electrons. As a noble gas it can be highly purified of radioactive contaminants, and may be repurified in situ if necessary. Xenon has no long lived radioactive isotopes, and as a gas at room temperature its isotopic enrichment is relatively easy through ultra-centrifugation. Most importantly, the final state nuclear species of xenon double beta decay is barium, and single barium ions are routinely observed using mod*for the E X 0 collaboration, http://hepl6.stanford.edu/exo/

332

333

ern atomic spectroscopic techniques. This raises the possibility of tagging the barium ion on an event-by-event basis, eliminating all radioactive backgrounds and leaving only the 2vpp and O v p B decays a . These two processes can then be separated by their energy distributions. We are considering both a high pressure gaseous xenon T P C and a cryogenic liquid xenon detector. While both options have strengths and weaknesses, this article will focus on our liquid xenon work, which is at a more advanced stage. The E X 0 roadmap is as follows. We are currently performing R&D work to demonstrate the feasibility of the barium tag technique. In parallel we are developing a 200 kg prototype which will not have the barium tag feature. The goals of the prototype are to measure the half life of the 2uPp process in 136Xe,to understand the radioactive backgrounds, and to set a limit on the Ovpp half life which is competitive with other current experiments. The prototype would be followed by a one ton experiment with barium tagging, t o be operated for five years, and expanding to a ten ton experiment operated for ten years. 2. Barium spectroscopy results The Ba+ ion has three energy levels which define its spectroscopyb. The 2S1/2ground state and 2Pl/2excited state are separated by a 493 nm (blue) transition. Once in the excited state, there is a 30% probability t o decay to the metastable (47 second lifetime) 4D3/2state by a 650 nm transition (red), and a 70% probability to return to the ground state. If both transitions are saturated by lasers at the appropriate frequencies, then the ion will rapidly cycle between all three states and scatter the laser light into 47r at a rate of lo7 photons per second. This is enough light to “see” a single ion with the naked eye. Several techniques can distinguish laser scattering due to the barium ion from ambient backgrounds. For example, one can scan the frequency of the blue laser across the expected transition frequency and observe the resonance. This is shown in Figure 1, where the signal from a single barium ion observed in the E X 0 spectroscopy lab is plotted. This data was taken with the ion held in an RF quadrupole trap in vacuum. As expIained in N

”The barium tag was suggested by M.K. Mae 2 , and in a different format by M. Miyajima, S. Sasaki, and H. Tawara bthe Ba++ ion created by the Ovpp decay is expected to collect one (but not two) electrons from the liquid xenon, leaving it in the charge $1 state.

334

t'8 I 0.2

a

I

'

I

0.4

I

I

I

0.6

'

I

' I

0.8

SJW 07/17/02

8

8

,

"

'

1

I

a

a

I

I n

I

' I

I

I

a

I I

1 1.2 1.4 1.6 1.8 Blue Frequency [f-303710 GHz]

Figure 1. P M T count rate as a function of the frequency of the blue laser. The resonance is due to the light scattered by a single barium ion. Note the suppressed zero on the y-axis.

Section 3, we expect that the E X 0 spectroscopy will be done in a xenon buffer gas, perhaps up to a pressure of several atmospheres. In the near future we intend to check that the spectroscopy is possible under these conditions. However, similar work in argon and helium buffer gases was successful, so we do not anticipate any fundamental problems '. 3. Ion grabbing experiments

In the case of a liquid xenon EXO, it will be difficult, if not impossible, to do the barium spectroscopy at the event location. This is because the liquid will scatter the laser light, causing large backgrounds, and because the energy levels of the barium ion change significantly in a liquid xenon bath. Therefore we are developing a system to transfer the barium ion from the liquid to a trap above the surface where it can be identified in a xenon buffer gas. Our basic model for this system is an electrostatic probe which can be inserted into the liquid to the event location and "grab" the barium ion with an applied voltage. The probe would then be removed to the trap

335

location, and the ion released. To test the ion grabbing concept we have built a prototype electrostatic probe. To simplify the experiment we use 226Thand "'Ra ions to simulate the barium ions, since these isotopes can be easily identified by their alpha decays, and because they have similar chemistry to barium. To get the radium and thorium into the liquid xenon we use a 230U source, which is deposited on a foil immersed in the liquid xenon. When the uranium alpha decays, the recoil of the decay can kick the produced thorium ion off the foil and into the liquid xenon. The thorium then alpha decays to radium. The first version of the electrostatic probe is simply a tungsten rod with a spherical tip, about one millimeter in diameter. To grab the ions, the probe is placed in the liquid xenon near the ion source and a voltage is applied. To detect the ions the probe is retracted to an upper station above the liquid surface where an alpha counter is located. We find that when the voltage of the probe is set to collect positive ions, the alpha counter subsequently observes the radium and thorium daughter alphas. If no voltage is applied, or if the wrong sign voltage is applied, no alphas are observed. This demonstrates that ion grabbing in liquid xenon is possible. Releasing the ions from the probe is more difficult that collecting them. We are currently pursuing a cold-probe technique, where the ion would be embedded in a layer of xenon ice on the probe. To release the ion the ice would be allowed t o melt. We expect t o have initial results from this technique very soon.

4. Liquid xenon energy resolution results Barium tagging would eliminate all radioactive backgrounds except for the 2vpP decay of xenon. Like the 0vPp decay, the final state nucleus of the 2vpP decay is barium, so theses two processes can only be distinguished by their energy spectra. Therefore E X 0 requires the best energy resolution possible in liquid xenon. To study the energy resolution of liquid xenon we have built a small gridded ionization chamber with a 207Bi source. This isotope produces gammas at 570 keV and 1064 keV, as well as associated escape electrons and xrays. The ionization produced when the gammas and electrons interact in the liquid xenon is collected on an anode and amplified with a charge amp. In addition, a photomultiplier tube observes the 175 nm scintillation light produced by the interaction in the liquid xenon. We find that the energy resolution of the ionization signal is a ( E ) / E=

336

u

0

-

200

400 600 PMT signal [photoelectrons]

800

1000

Figure 2. Scatterplot of the ionization and scintillation signals of a '07Bi source in the liquid xenon gridded ionization chamber at a field of 4 kV/cm. The two islands correspond to the 570 keV and 1064 keV gammas and their satellite internal conversion peaks. The rotation of the islands demonstrates that the energy resolution can be improved by using a linear combination of the ionization and scintillation signals. The one-dimensional projections are shown on each axis.

3.7% for the 570 keV gamma at a field of 4 kV/cm, in agreement with the results of other authors5c. The energy resolution of the scintillation signal observed with the P M T is much worse. However, we also find that the P M T signal is anti-correlated with the ionization signal on an event-byevent basis, as shown in Figure 2. This means that the scintillation signal can be used to make a correction to the ionization signal and improve upon the previous state-of-the-art energy resolution in liquid xenon. At 4 kV/cm we are able to achieve an energy resolution of a ( E ) / E= 3.0% at 570 keV after making the scintillation correction6.

'These resolutions are after a small correction to remove electronic noise.

337 5.

Plans for a 200 kg prototype

We are proceeding with plans to build a 200 kg liquid xenon E X 0 prototype. The prototype will be located underground at the DOE Waste Isolation Pilot Plant (WIPP) in Carlsbad, New Mexico. The 200 kg of xenon, enriched to 80% in 136Xe by ultra-centrifugation in Russia, has already been obtained. The prototype will not have barium tagging, but will measure the 2 v p p half-life of 136Xe,as well as study the other radioactive backgrounds. We also intend to set a limit on the half-life of the Ovpp decay which is competitive with the most sensitive double beta decay experiments. 6. Sensitivity

We have calculated the expected sensitivity of E X 0 to neutrinoless double beta decay under the assumption that barium tagging has eliminated all radioactive backgrounds. For a one ton detector] enriched to 80% in 136Xe, with an efficiency of 70%, five years of live-time, and an energy resolution of a ( E ) / E= 2.8% at 2.5 MeV, we anticipate a half-life sensitivity of 8.3 x years, which corresponds to a neutrino mass sensitivity between 51 meV and 140 meV (depending on the nuclear matrix element calculation). A ten ton detector, operated for ten years, with an improved energy resolution of a ( E ) / E = 2.0% at 2.5 MeV, could push the half-life sensitivity up to 1.3 x lo2* years (neutrino mass between 13 and 37 meV). Acknowledgments

The author would like to thank the workshop organizers for arranging a delightful and stimulating meeting. This work was supported by US-DOE grant DE-FG03-90ER40569-AO19,by a Terman Fellowship of Stanford University, and DOE contract DE-AC03-76SF00515. References 1. M. Danilov, et. al. ( E X 0 collaboration), Phys. Lett. B 480, 12 (2000). 2. M.K. Moe, Phys. Rev. C44, R931 (1991). 3. M. Miyajima, S. Sasaki, and H. Tawara, Proceedings of the Sixth Workshop on Radiation Detectors and Their Uses, KEK Proceedings 91-5 (1991).

4. E. Erlacher and J. Hunnekens, Phys. Rev. A 46, 2642 (1992). 5. E. Aprile, R. Mukherjee, and M. Suzuki, Nucl. Instr. Meth. A 302, 177 (1991), and references therein. 6. E. Conti, et. al. ( E X 0 collaboration), hep-ex/0303008, to appear in Phys. Rev. B.

C A N D L E S FOR THE STUDY OF @@ DECAY OF 48CA

T. KISHIMOTO, I. OGAWA, R. HAZAMA, S. YOSHIDA, S. UMEHARA, S. AJIMURA, K. MATSUOKA, H. SAKAI, D. YOKOYAMA, T . MIYAWAKI, K. MUKAIDA, K. ICHIHARA, Y. TATEWAKI Department of Physics, Osaka University, Toyonaka, Osaka, 560, Japan E-mail: [email protected] K. FUSHIMI Faculty of Integrated A r t s and Science, T h e University of Tokushima, Tokushima 770-8502, Japan

H. OHSUMI Faculty of Culture and Education, Saga University, Honjo, Saga 840-8502, Japan CANDLES is the project to search for double beta decay of 48Ca by using CaF2 crystals. Study of double beta decay becomes of particular importance after confirmation of neutrino oscillation which shows that neutrinos have mass. We have been studying double beta decays of 48Ca by using ELEGANTS VI detector system which features CaFz(Eu) crystals. We gave the best limit on the lifetime of neutrino-less double beta decay of 48Ca though further development is highly desirable to reach the mass region of current interest. CANDLES is our detector system to sense the mass region. Here we describe the concept and design of detector and current status of development.

1. Double beta decay of 48Ca

Recently many indications on the neutrino oscillation have been acquired. They are deficits of atmospheric v p , solar v,, accelerator v p and rea,ctor v,. Those data clearly show that neutrinos have mass. Mass differences have been constrained by these data though mass itself need be measured independently. If they have mass, it could be either Dirac type or Majorana type. It is only neutrinos that could have Majorna mass. If neutrinos have Majorana mass they violate lepton number conservation and neutrino-less double beta (Ov-pp) decay can then take place. Therefore the study of the

338

339

Ov-pp decay is one of the most fundamental research to be carried out in a coming decade. We have been studying the pp decays of 48Ca. The Q value of the 48Ca +48 Ti pp decay is the highest (4.27 MeV) among potential pp decay nuclei. Table 1 lists Q values and phase space factors (Goy)of typical pp nuclei. Sum energy of two electrons from the Ov-pp decay is equal to the Q value. The Q value of the 48Ca/3/3 decay is far above energies of y rays from natural radioactivities (maximum 2.615 MeV from 208T1decay), therefore we can expect small backgrounds in the Q-value region. The large Q value also means large phase space factor which enlarges the Ov-pp decay rate for a given Majorana mass and nuclear matrix element. Another advantage is the least contribution from the 2v-PP decay. In the standard model 2upp decay is possible. Since two neutrinos carry certain fraction of energy, sum energy of two electrons can never be the same as that of the Q-value. However, finite energy resolution of detectors makes leak of the 2v-pp decay into the Ov-pp region unavoidable. The large Q value of the 48Capp decay makes the leak of minor concern for a given energy resolution.

Table 1. Qvalues and phase factors (c) if nuclal. 48ca

Q value

7

1

0

0

~

116cd ~

1 3 6 ~ l ~5 0 ~ d

6

~82se ~

4.27

2.04

3.00

3.03

2.80

2.48

3.37

2.44

0.244

1.08

1.75

1.89

1.81

8.00

(MeV) Gov x

(year-1eV-2)

However, these nice features of the 48Capp decay are counterbalanced by the low natural abundance of 48Ca (0.187 %) because of which a few experiments have been carried out so far. 112,3,4,5,637

2. CaF2 scintillator

2.1. EL EGANT S VI We developed a detector system (ELEGANT VI) where 25 CaFa(Eu) crystals with a dimension of 45 mm cube are placed at the center of the detector. They are surrounded by active and passive shields. The detector was meant to explore the dark matters and pp decay of 48Ca. The lgF nucleus has the

340

best figure of merit (cross section times abundance) for the search of the spin coupled dark matters although we now concentrate our discussion on the study of pp decay of 48Ca. We need to measure low energy and rare signals for which background reduction is essential. The central CaFz (Eu) crystal has light guides of CaFz(pure) crystals which are also scintillators. Background signals, which give dominant energy deposit t o the light guides, are effectively rejected by this design. It achieved good performance. The schematic drawing of the detector is shown in figure 1.

CSI (Tl)

\

CaF2 (E,”)

C a F 2 (Pure)

t i g h t Box f f ine LiF

3. sheet

Pb Figure 1. Schematic view of ELEGANTS VI

The CaFz scintillators and CsI scintillators veto y rays from outside. They are in the air-tight box which purges radon by a flow of pure N2 gas. Oxygen-free high-conductivity (OFHC) copper shield of 5 cm thick and lead shield of 10 cm thick are used t o passively shield y-rays. For the detection of low energy signals particularly for dark matter search neutrons are of primarily concern. We have layers of LiH-loaded paraffin of 15 mm thick, Cd sheet of 0.6 mm thick and whole system is surrounded by H3B03loaded water tank. Details of the ELEGANTS VI system have been given elsewhere’

341 2.2.

4

T

active shield

The characteristic of the ELEGANTS VI system is its capability of 4n active shield. CsI(T1) scintillators (65 x 65 x 250 mm3) actively shield y rays from outside. Usually scintillators have weak shield in the PMT direction for which long light guide have been used t o passively shield y rays from outside. The central CaF2(Eu) is sandwiched by two CaF2(pure) crystals which act not only as a light guide and passive shield but also as an active shield since the CaFz(pure) is also a scintillator. Its scintillation light is dominantly in the ultra-violet (UV) region although CaF2(Eu) emits visible light. Using PMT’s sensitive to UV light, a number of photoelectrons per energy from the pure CaF2 crystal is about 1/3 of that from the CaFz(Eu). The UV-light cannot pass the central CaF2(Eu) thus background signals that has a hit in the CaF2(pure) gives large pulse height only either side of PMT’s. Thus the background events can be rejected by setting a proper window on the asymmetry parameter (roll-off-ratio) between the signals from 2 PMT’s. The roll-off-ratio ( R ) is defined to be,

where VL,VRare the pulse heights of left and right PMT’s, respectively Using the 4n active shielding system, we can suppress the background. This method is particularly effective for low energy signals.

2.3. Oto Cosmo Observatory ELEGANT VI has been in operation at Oto Cosmo Observatory (OCO) located in Nara, Japan. The location is quite convenient. It is about 70 km south of Osaka University and roughly 2 hours drive takes us there. It is a 5 km tunnel originally constructed for railroad. Figure 2 shows schematic drawing of OCO. The depth is around 500 meters which corresponds to 1.3 km water equivalent shield. The muon flux has been given as a function of the depth for various underground laboratories lo and that of OCO was found to follow the relation. It is an almost straight tunnel and wind is always blowing. This makes OCO ideal for the reduction of background from radon. Reduction of radon is particularly important for detection of low energy signals. Usually underground laboratories have concentration of radon a couple of orders-ofmagnitude higher than that in the laboratory at surface of the Earth. We observed no particular radon concentration in OCO.

342

5036 Schematic view of Oto Cosmo Observatory.

Figure 2.

3. Limits on the lifetime of

Ov-pp decay of 48Ca

Here we show a result from the duration of middle of 1998 t o end of 1999 (total live time of 5567 hours). Figure 3 shows energy spectrum of CaF2(Eu) obtained in the duration after the event selection described in ref l 1 > l 2 . Total weight of 23 CaF2(Eu) crystals is 6.66 kg which corresponds t o 9.61 x lo2' 4xCa atoms. The statistical significance of the energy spectrum is 4.23 kg yr. No events are observed in the Ou-pp decay energy window which is a 3 c peak interval centered at 4.27 MeV as shown in figure 3 by a double-headed arrow. Since we observed no event in the &-value region, we set lower limit on the lifetime of the Ou-pp decay. In order t o derive the limit we estimated background events in this energy window. Because of the highest Q value it is particular t o 48Ca that only three radioactivities are conceivable for the backgrounds in addition t o the 2u-pp decay. They are 2 1 4 ~ iQO

-

3.27 MeV} 2 1 4 p 0 ( ~ 1 / 2

= 164.3 psec) Q a = 7.83 MeV)

210

Pb, (1)

in the uranium chain, and 208Tl

QB

= 5.00 MeV

2 1 2 ~ iQO

= 2.25 MeV

}

'08Pb,

(2) 'OXPb,(3)

in the thorium chain. The radioactivities have t o be in the crystals t o be backgrounds in the Q value region. The radioactivities in the crystals were derived by observing the successive decays listed above and were used t o estimate backgrounds by a simulation. Since decay time of CaF2 signal is quite long (- lpsec), we have 4 p sec for the ADC gate. Therefore two successive decays are frequently in a same gate if lifetime of an intermediate nucleus is short. The a decay has quenching factor of 114 thus the decay N

343

Energy (keV)

Energy (keV)

(4

(b)

Figure 3. (a)A comparison of Monte Carlo simulations from the internal radioactivities (dashed line) and the 2vBB of 48Ca (dotted line) with experimental data (solid line) of a statistical significance of 4.23 kg yr. The double-headed arrow indicates the Ov-pp energy window. (b)Simulated background spectra for each decay - dotted line : decay (l), dashed line : decay (2) and solid line : decay (3).

(3) can be the largest background in the Q value region. Total simulated energy spectrum from the decays ( I ) , (2) and (3) is plotted in Fig. 3 (a) with experimental data. Also shown in Fig. 3(b) are simulated background spectra for each decay. The simulation well reproduced shape and absolute yield of the experimental spectrum in an energy range of 2.8 4.0 MeV. The shoulder at around 2.6 MeV in the experimental spectrum can be from '08T1 decay in the CsI(T1) scintillators which is irrelevant for present analysis. The known half-life of the 2u-pp decay 4,5 was used t o simulate an expected spectrum in Fig. 3 (a). For the current limit contribution from the 2u-PP of 48Ca in the Ou-Pp energy window was found to be negligible. The expected number of background events in the Ou - pp energy window is 2.63 k 0.13, where 2.35 0.12 is from decay (l),0.124 k 0.007 from (2) and 0.158 2~ 0.006 from (3). The detection efficiency was derived t o be about 51 % from the Monte Carlo simulation and other experimental conditions. We extracted a half-life limit for the Ov-pp of 48Ca following the procedure given elsewhere 1 3 . The number of excluded events in the 30 energy region is 1.18 (0.25) with 90 % C.L. (68 % C.L.). The resulting ~

*

344

lower limit of half-life (for the O+

+ O+

transition) is

T;T2 2 8.6 x loz2 year (68 % C.L.) - 1.8 x >

year (90 % C.L.).

This result can be converted t o the upper limit for the effective Majorana neutrino mass (m,) neglecting right-handed currents. Depending on the theoretical nuclear matrix elements (see Table 8 & 9 in Ref.14), the upper bound at the 90 % C.L. is (m,)

< (6.3 - 39.4) eV

Our value is better than the current limit of 9.5 x yr (76 % C.L.) given by Beijing group using 37 kg of CaF2 scintillation crystals. It has to be noted that we have no background in the signal region although Beijing group had 365 events. Therefore our measurement is not limited by backgrounds. In order t o explore the mass region of Am2 10-(2-3)eV, one needs t o design detector sensitive to lifetime of year for Ov-pp decay of the 48Ca. One then need to prepare atoms of 48Ca which corresponds to several tons of calcium since the natural abundance of the 48Cais very tiny (0.187 %). N

4. CANDLES

4.1. Conceptual Design

In the future detector for the study of 48Ca pp decay, we need to have much larger amount of CaF2 crystal t o measure the region of interest for the neutrino mass. So far we have -5 kg.y of CaF2 in ELEGANTS VI. We wish to increase amount of CaF2 crystals more than 4 orders-of-magnitude to sense the region around 50 meV region. In order to achieve this we proposed CANDLES which stands for M l c i u m florid for the study of Neutrinos and Dark matters by Low Energy Spectrometer. Conceptual design of the detector is schematically shown in figure 4. Pure CaF2 crystals with a dimension of -10cm cube are immersed in a liquid scintillator. Scintillation light is viewed by large PMT’s. Use of the CaFa(pure) crystal is essential to build large detector as described in the following. Liquid scintillator acts as an active shield to veto backgrounds as well as a passive shield. The active shield can be achieved by observing pulse shape as described in the following.

345

CaF, crystal

liquid scintillator

20 inch PMT

Figure 4. Schematic cross sectional view of the proposed CANDLES detector.

4 . 2 . CaF2 (Eu) and CaF2(pure) crystals

Usually we use a CaFz(Eu) crystal as a scintillator. Europium is doped in the CaF2 crystal to increase light output of scintillation. The ELEGANTS VI system used CaF,(Eu) crystals as the central detector and CaFz(pure) crystals were used as active light guides. The light output of the CaFz(Eu) in ELEGANTS VI gives energy resolution of 3 % (FWHM) at the Q-value region. High light output of the CaF2(Eu) crystal was obtained, however, by sacrificing attenuation length which is as short as around 10 cm. This is why the CaF,(Eu) crystals were expanded in two dimensions (5 in width and 5 in height) keeping a length in the P M T side short in the ELEGANT VI system. Therefore if one wants to stick t o the CaF,(Eu) crystal to keep high light output, scale up is possible only in two dimensions which is quite inefficient. On the other hand, the CaFa(pure) crystal is a scintillator and has long attenuation length of a meter or longer. Therefore there is essentially no limit in scale up and we can construct huge detector. Problem is the low light output of the CaFz(pure) crystal which is about 1/3-1/4 of that of CaF,(Eu) with a PMT's sensitive to UV light. The light emission

346

of scintillation is centered in the UV region. We tried t o increase the light output of CaFz(pure) crystals by using wave-length shifter since the scintillation light is in the UV region. Light output was studied for various wave-length shifter with CANDLES I detector. CANDLES I is a prototype detector and has simple configuration that a 45 mm cube CaFz(pure) crystal is immersed in liquid scintillator in 5” cube lucid container. Scintillation lights are viewed by four 5” PMT’s. We found that light output can be increased up t o about 60% of the CaF2(Eu) crystal. This light output gives 3% (FWHM) energy resolution in the Q value region if we have PMT’s which cover whole solid angle. Contribution of 2u-pp decay is unavoidable and depends on the energy resolution. The contribution in the window of the Q value is small enough for the lifetime of years which enable us to search for the neutrino mass of 0.05 eV region. CANDLES thus has no problem t o build big detector sensitive to the mass region. N

4.3. Pulse shape and background rejection Backgrounds have t o be further reduced from the measurement of the ELEGANT VI to sense the mass region of interest. The liquid scintillator has very short decay time (- l0nsec) although that of CaFz crystal is quite long (lpsec). We employed this difference to reject background signals that fire liquid scintillator.

4

Figure 5.

4 usec

c

Pulse shape of the liquid scintillator and CaFz signal is schematically shown.

Figure 5 shows schematically how the signal t o noise separation is achieved by using two time gate as shown in figure 5. One sees how the signal to noise separation is achieved in figure 6. Background signals have

347

large prompt component though signals from CaFz crystal has little prompt component. This clearly demonstrate that CANDLES is capable t o reject y ray backgrounds outside of the detector.

08 07

m c

06 05

I

Q

04 Q

03 02

Of

0 0

1000

2000

3000

4000

5000

6000

7000

Total

Figure 6.

The background rejection is clearly demonstrated.

We now know that the backgrounds in the &-value region are solely from the successive ,L?- and a decays from radioactivities contained in a crystal. Sum energy of the two decays can be as large as that of the Q value. Actually the biggest background is from the decay ( 3 )since the intermediate '12Po has lifetime of 0.299psec. This dominant background can be reduced by observing pulse shape of the signal. We measured pulse shape of signals of ELEGANTS VI using 100 MHz Flash ADC and demonstrated that we can detect a rise of second signal if the separation is more than 2 channels (N 25 nsec). We can thus reduce the background down t o 5%. Since this separation largely dependent on the time resolution of the detection system, we hope to reduce it down to 1%by introducing 500 MHz Flash ADC. We are developing the DAQ system for that. We also noticed that there is a difference in decay times between a decay and ,L? (or y) decays. The difference can also be used to reduce backgrounds. Quantitative value for the reduction will be given after our analysis although currently we can already reduce the background more than an order-of-magnitude.

348

4.4. Position resolution background rejection The decay of 208T1has large Q value though it emits 2.6 MeV y rays. The probability that the high energy y rays are contained in a single crystal of -1Ocm cube is small. However, if we are interested in a very rare signal it could be a background seriously considered. The "'T1 decay has a preceding CY decay with a lifetime of 3 minutes. If a counting rate is small enough we can reduce the background by identifying the preceding CY decay. The counting rate can be reduced if we have good position resolution. The position resolution was tested by CANDLES I detector where two crystals were immersed in a scintillator and four PMT's gave position information. We obtained a few centimeter for the position resolution. The resolution is very good. This, however, may be due to small size of CANDLES I. We will study the position resolution for a larger detector in CANDLES 11. 4.5. Future progress

Currently we are assembling CANDLES I1 detector which has 9 CaFz crystals with a dimension of 45 x45 x 70 mm3. This will demonstrate the design of the CANDLES where we have more than 2 crystals in the liquid scintillator. We are designing the CANDLES 111detector which will have around 200 kg CaFz crystals. This will be constructed in our laboratory which is at the sea level. For the construction of the detector, low radioactive contamination in a crystal is essential. We are having collaboration with crystal makers to develop crystals with low radioactive contamination.

5. Conclusion We are developing CANDLES for the study of pp decay of 48Ca. So far CANDLES has no problem to construct detector which is huge enough to be sensitive t o mass region of interest. CANDLES has ways to reduce backgrounds and we will demonstrate by constructing series of CANDLES detectors. 6. Acknowledgments

This experiment is financially supported in part by the Grant-in-Aid for Scientific Research 14204026. References 1. E.der Mateosian and M. Goldhaber, Phys. Rev. 146 (1966) 810.

349 2. 3. 4. 5. 6. 7. 8.

R.K. Bardin et al., Nucl. Phys. A 158 (1970) 337. K. You et al., Phys. Lett. B 265 (1991) 53. A. Balysh et al., Phys. Rev. Lett. 77 (1996) 5186. V.B. Brudanin et al., Phys. Lett. B 495 (2000) 63. A. Bakalyarov et al., Nucl. Phys. A 700 (2002) 17. R. Bernabei et al., Nucl. Phys. A 705 (2002) 29. R. Hazama et al., Proc. of the 4th Int. Conf. on Weak and Electromagnetic Interactions in Nuclei (WEIN 95), Osaka, Japan, June 1995, World Scientific, Singapore P. 635; R. Hazama et al., Proc. of the XIV Int. Conf. on Particles and Nuclei (PANIC 96), CEBAF, USA, May 1996, World Scientific, Singapore p. 477; R. Hazama et al., Proc. of the Int. Workshop on the Identification of Dark Matter (IDM 96), September 1996, Sheffield, UK, World Scientific, Singapore p.397; T. Kishimoto et al., Proc. of the 2nd RESCEU Int. Symp. on Dark Matter in the Universe and its Direct Detection, November 1996, Tokyo, Universal Academy Press Inc., Tokyo, p. 71; I. Ogawa et al., Nucl. Phys. A663-664 (2000) 869c; T. Kishimoto et al., Proc. of the Identification of the Dark Matters (IDM2000), September 2000, York, UK. 9. R. Hazama, Doctoral thesis Osaka University (1998). 10. P. F. Smith and J. D. Lowing, Phys. Rep. 187 (1990) 203 11. I. Ogawa et al., Proc. Int conf. Particles and Nuclei Nucl. Phys. (2002) 12. I. Ogawa et al., Nucl. Phys. A. submitted 13. G.J. Feldman and R.D. Cousins, Phys. Rev. D 57 (1998) 3873. 14. J. Suhonen and 0. Civitarese, Phys. Rep. 300 (1998) 123.

CAMEO/GEM PROJECTS AND DISCOVERY POTENTIALITY OF THE FUTURE 2p DECAY EXPERIMENTS

YU.G. ZDESENKO: F.A. DANEVICH, V.I. TRETYAK Institute f o r Nuclear Research, MSP 03680 Kiew, Ukraine

The demands to the future super-sensitivity 2p decay experiments (aiming to discover the neutrinoless 2p decay or to advance restrictions on the neutrino mass t o mu 5 0.01 eV) are considered and requirements to their discovery potentiality are formulated. The most realistic next generation 20 projects are reviewed and conclusion is obtained that only several of them would completely satisfy these severe demands and requirements. Nevertheless, the most of the recent projects (CAMEO, CUORE, DCBA, EXO, GEM, GENIUS, MAJORANA, MOON) could certainly reach the level of sensitivity to the neutrino mass of m, 5 0.05 eV.

Recent observations of neutrino oscillations 1 , 2 , 3 , 4 , demonstrating that neutrinos have nonzero masses (m,), provide important motivation for the double beta ( 2 p ) decay experiments 5 ~ 6 , 7.a Because oscillation experiments are sensitive to the neutrino mass difference, the only measured Ou2P decay rate can give the absolute scale of the effective Majorana neutrino mass and, consequently, could allow one to test different neutrino mixing models. Despite the numerous efforts, the Ov2p decay still remains unobserved (see latest reviews 5 , 6 , 7 , 9 ) . Recently the impressive half-life limits for Ov mode were set in direct measurements with several nuclides: T;Y2 2 yr for '16Cd l o , 128Te,I3OTe 1 1 , 136Xe1 2 ; and To" 1/2 > - loz5 yr for 76Ge 1 3 J 4 . These results have already brought the most stringent restrictions on the values of the Majorana neutrino mass (m, 5 0.3-3 eV), the right-handed *Corresponding author. e-mail: [email protected] "The neutrinoless (Ov) double p decay forbidden in the standard model (SM) of electroweak theory since it violates lepton number ( L ) conservation requires neutrinos t o be massive Majorana particles s. At the same time, many extensions of the SM incorporate L violating interactions and, thus, could lead to this process, which, if observed, will be a clear evidence for a new physics beyond the SM and an unique confirmation of the Majorana nature of the neutrino 5 , 6 , 7 . ~

~

350

351

admixture in the weak interaction (Q M X M lop6), the neutrinoMajoron coupling constant ( g M M lop4), and the R-parity violating parameter of minimal supersymmetric standard model ( E M 10V4). But nowadays the 2,B decay research is entering new era, when the desired discovery of the neutrinoless 2p decay has become realistic. However, to do this, it is necessary to enhance the present level of the experimental sensitivity by a large step (at least up to mu 5 0.05 eV) It is thc great challenge and a lot of projects were proposed during a few past years aiming to reach this goal. As regards these projects, two circumstances should be noted. First, it is widely recognized now that 2,B decay searches must be performed with several candidates. It is because that reliable values (or restrictions) of the neutrino mass can be derived from experiments on the basis of the theoretical calculation of the nuclear matrix elements (NME) for the 0u2P decay, whose uncertainties are often unknown 7,15,16.b Another reason is the difficulties in developing of the experimental techniques. If the Ou2,B decay will be finally observed in one experiment, such a discovery certainly has t o be confirmed with other nuclides and by using other experimental techniques, which should be well developed by then. However, because of the super-low background nature of the 2,B studies, the corresponding development is a multi-stage process and consequently a rather long one. For instance, the first valuable result for the Ou2P decay of 76Ge was obtained in 1970 as T$Y2 2 1021yr 18. After 30 years of strong efforts, this limit was advanced up t o T$’.. 2 yr (that is neutrino mass bound was improved by two orders of magnitude) l 3 > l 4 . Secondly, practically all proposed experiments require a large mass production of enriched isotopes, thus their costs have become comparable with those of the accelerator experiments. Because most of these projects need strong efforts and perhaps long time to prove their feasibility, it is very important to choose those of them, which will be really able to observe the Ou2P decay rate corresponding to neutrino mass mu M 0.01 eV, and could be developed and constructed during reasonable time. With this aim in the present paper we consider demands to the future high sensitivity 2,B decay experiments, and formulate requirements to their discovery potentiality. 516,7.

bSee, e.g., ref. 1 7 : “The nuclear structure uncertainty can he reduced by further deuelopment of the corresponding nuclear models. A t the same time, b y reaching comparable experimental limits i n several nuclei, the chances of a severe error i n the N M E will he substantially reduced .”

352

Then, several recent projects are reviewed and discussed. There are two classes of 2/3 decay experiments: (i) with “passive” source, and (ii) with “active” source, where detector containing 2/3 candidate nuclei serves as source and detector simultaneously. If neutrinoless 2/3 decay occurs in the source, the sharp peak at the &pa value - its width is determined by the detector energy resolution - would be observed in the electron sum energy spectrum of the detector(s). The best Tf,& limits on Ov2P decay obtained in the most sensitive direct experiments and the corresponding restrictions on the Majorana neutrino mass are given in Table l.c Table 1. The best reported T:Yz and m, limits from direct 2/3 decay experiments.

I

Nuclide

76Ge

I Experimental limit TPI”Z,(yr) I 68% C.L. 3.1~10’~ -

lI6Cd 130Te ls6bXe *)

4 . 2 ~ 1 0 ’*) ~ 2.6~10’~ -

90% C.L. 1 . 9 ~ 1 0 ~ ~ 1.6~ 2 . 5 ~ 1 0*) ~ ~ 1.7~10’~ 2.1 x 4.4~1023

Reference

13 14 2o 10 11 12

I Limit on m, (eV) on the basis of l 9 68% C.L. 90% C.L. 0.27 0.35 0.38 0.24 0.31 1.4 1.7 1.5 2.2 ~

Results were established 2o by analyzing the cumulative data sets of the Heidelberg-Moscow l3 and IGEX l4 experiments

It is obvious from Table 1 that 76Gestudies performed by the IGEX l4 and Heidelberg-Moscow l3 collaborations (by using enriched HP Ge semiconductor detectors with the total mass of ~ 1 kg) 0 have brought the most stringent restrictions on the neutrino mass, at the level of ~ 0 . 2 - 0 . 3eV. It is interesting to note that other experiments offer m, bounds in the range of ~2 eV, which is not so drastically weaker, especially if taking into account that, e.g., “‘Cd result was obtained with small ‘l‘CdW04 crystal scintillators (total mass of 330 g) l o +This fact demonstrates the importance of the choice of 2/3 decay candidate nuclei for study, which we consider next with the help of the formula for the Ov2P decay probability (right-handed contri-1

butions are neglected) ’lJ6: (Tfy2)

= G0,“,.(NME12.(m,)2,where NME

and GZm are the corresponding nuclear matrix elements and phase space integral of the Ov2P decay. If we skip the problem of the NME calculation, ‘The mv constraints are determined on the basis of the NME calculations of ref. 19, which were chosen because of the most extensive list of 2/3 nuclei calculated in this work, allowing one to compare the sensitivity of different experiments within the same scale.

353

it is evident from this equation that the available energy release (&OD) is the most important parameter for the sensitivity of a 2p decay study with particular candidate. First, it is because the phase space integral GO,”, strongly depends on the &pa value (roughly as 2 1 , 1 6 . Second, the larger the 2p decay energy, the simpler it is - from an experimental point of view - t o overcome background problemsd. Among 35 candidates, there are only 13 nuclei with Qpp larger than ~ 1 . MeV 7 2 2 . They are listed in Table 2, where &pa, the natural abundance S 2 3 , and the calculated values of the phase space integral G”,”m 21,16,24 and T$. x (m,)2 l9 are given. Note, that due to the low Qpp value of 76Ge (2039 keV), its phase space integral GO,”, is about 7-10 times smaller as compared, with e. g., those of 48Ca, “Zr, looMo, ‘16Cd, 130Te and 136Xe.

&go)

Table 2.

I

130Te ‘”Xe 14’Nd I5’Nd “‘Gd

2529 2468

p

decay candidates with Q p p

34.08

3367

8.87 5.7 5.6

1730

I 21.86

1929

I

Double

4.1 4.4 -

19

I -

I

2

1.7 MeV.

4 . 9 ~loz3 2 . 2 ~ 1 0 ~ ~ 1 . 4 loz4 ~ 3.4x 1022 8.6~10”

Now let us consider the experimental sensitivity, which can be expressed in terms of a lower half-life limit as follows T1f2N & . S J ( r n . t ) / ( R .B ) . Here E is the detection efficiency; 6 is the abundance or enrichment of candidate nuclei contained in the detector; t is the measurement time; m and R are the total mass and the energy resolution (FWHM) of the detector, respectively; and B is the background rate in the energy region of the Ov2P decay peak (expressed, e.g., in counts/yr.keV.kg). First of all, it is clear from the last equation that efficiency and enrichment are the most important characteristics of the set ups for 2p decay 699:

-~

~

dNote that the background from natural radioactivity drops sharply above 2615 keV, which is the energy of the y’s from ’08T1 decay (232Thfamily).

354

studies, because any other parameters are under the square root. Obviously, the 100% enrichment is very desirable.e In order to reach the sensitivity to neutrino mass of about 0.01 eV one has to exploit enriched sources, whose masses should exceed at least some hundred kg. The latter immediately restricts the list of candidate nuclei given in Table 2 because a large mass production of enriched materials is possible only for several of them. These are 76Ge, 82Se, loOMo,‘16Cd, 130Te and 136Xe,which could be produced by means of centrifugal separation’ Note that two nuclides from Table 2 (130Te and 160Gd) can be used without enrichment owing to their relatively high natural abundances ( ~ 3 4 % and ~ 2 2 % respectively). , Secondly, one would require the 100% detection efficiency, which is possible, in fact, only for the “active” source technique. Indeed, the mass of “passive” source can be enlarged by increasing its thickness, which in turn lowers detection efficiency due to absorption of electrons in the source, broadening and shifting of the Ov2P decay peak to the lower energies, etc. Thirdly, the energy resolution of the detector is an extremely important for the O v 2 P decay quest. Foremost, with the high energy resolution it is possible to minimize the irremovable background produced by the 2 v 2 p decay events. It is because for the case of a poor resolution, the events from the high energy tail of the 2v distribution could run into the energy window of the Ov peak and, thus, generate the background which cannot be discriminated from the Ov2P decay signa1.g However, the better is the energy resolution, the smaller part of the 2v tail can fall within the Ov interval, and the irremovable background would be decreased too. Likewise, the role of the energy resolution of the detector is even more crucial for the discovery of the Ov2P decay. Indeed, because this process manifests itself by the peak at &PO energy, the great advantage of the Ov2P decay experiments is the possibility to search for the sharp peak on the continuous background.h Since the width of the Ov2P decay peak is determined eLet us consider two detectors with different masses ( m l , mz) and enrichments (61, 6 2 ) . Supposing that their other characteristics ( E , t , R, B ) are the same and requiring equal sensitivities = T;,,), we can obtain the relation between the masses and enrichment ratios of the detectors: m1/m2 = (S~/61)~, which speaks for itself. fCentrifugal isotope separation requires the substances to be in gaseous form. Thus, Xe gas can be used directly. There also exist volatile Ge, Se, Mo and Te hexafluorides, as well as the metal to organic cadmium-dimethyl compound 2 5 . gAll their features are similar: the same two particles are emitted simultaneously from one point of the source, with near the same energies and identical angular distribution. hVice versa, if discovery of the Ov2p decay is claimed, the corresponding Ou peak must be demonstrated.

355

by the energy resolution of the detector, the latter should be sufficient to discriminate this peak from background and, hence, to recognize the effect. Practically, it would be very useful t o determine the minimal level of the energy resolution which is needful to detect the Ou2P decay with the certain T;Y2 value and at given 2u2p decay rate. Aiming to make such an estimation quantitatively, let us consider Fig. 1 with three examples, in which the 2u distribution of “‘Cd (with TfY2 = 3 x lo1’ yr) overlaps the three Ou peaks with half-life corresponding to: (a) 6 . 7 ~ 1 yr; 0 ~ (b) ~ 1 . 6 ~ 1 yr; 0 ~and ~ (c) 3 . 8 ~ 1 yr.’ 0~~ In Fig. l a the Ou peak with the amplitude M and 2u2p decay spectrum are meeting at the relative height h / M = 0.1, and due to this the separation of the effect is excellent. However, it seems that such a demand ( h / M = 0.1) is too severe. At the same time Fig. l c demonstrates other extreme case (meeting at the relative height h / M = l ) , which does not allow one to discriminate the effect at a l l j In our opinion, the example shown in Fig. l b , where the 2u distribution and the Ou peak are meeting at h / M = 0.5, represents the minimal requirement for the effect recognition, which can be still reasonable in the experimental practice. Therefore, if we accept the last criteria, the discovery potentiality of the set up with the fixed energy resolution can be defined as the halflife of the Ou2p decay, which could be registered by satisfying this demand ( h / M = 0.5) at given T$. value. The dependences of this quantity (let us call it “the discovery potentiality”) versus the energy resolution were determined for several 2P decay candidate nuclei, and they are depicted in ‘The spectrum of the sum of electron energies for 2v2p decay (O+ - O+ transition, 2n-mechanism) was obtained (as described in z6) by integrating the theoretical 2dimensional energy distribution p l z ( t 1 , t 2 ) : p l + z ( t ) = p l z ( t - t 2 , t z ) d t z , where t, is the kinetic energy of the i-th electron, t is the sum of electron energies (ti and t are in units of the electron mass rnoc’). The basic 2-dimensional distribution is taken from 2 7 : p 1 2 ( t l l t 2 ) = e l p l F ( t l , Z ) e z p z F ( t z , Z ) ( t o- tl - t ~ )where ~ , to is the energy available in the 2p process (Qpp for decay t o the ground state), ei = ti 1, and p i is the momentum of the i-th electron, p i = d m (in units of rnoc). The Fermi function is defined 17 = a Z e / p , as 2 8 : F ( t , 2)= const . p 2 s - 2 e T q I r ( s ill) 12, where s = 01 = 1/137.036, 2 is the atomic number of the daughter nucleus, and r is the gamma function. Then the obtained 2v distribution for the sum of electron energies was properly convoluted with the response function of the detector, whose relative energy resolution given at Q p p (in our case F W H M = 4%) depends on energy as E - 1 / 2 . jThe discrimination of the effect and background in case h / M = 1 could be, in principle, possible if: (i) the theoretical shape of the 2v2p decay spectrum near the Qpp energy is known exactly; (ii) the statistics accumulated in the experiment is very high, which, however, is a great technical challenge (see Fig. 3); (iii) the contributions from the different background origins to the measured spectrum near the Qpp value are precisely known too, which looks quite unrealistic task (see discussion in ref. 2 0 ) .

[i

+

+

d v ,

356

Fig. 2. Similarly, the exposures (product of detector mass by measuring time), which are needed t o collect ten counts in the Ov peak at given TfT2 value, were calculated for each nucleus (under assumption that detection efficiency and enrichment both equal loo%), and results are shown in Fig. 3. We will use these dependences below when discussing different projects. 1

0.5

0

I 2500

3500

3000

Ov, Tl12=1 . 6 ~ 1250 yr

2

0.5

3 $

0

2500

3000

2500

3000

3500

1

0.5

0

3500

Energy (keV) Figure 1. Definition of the discovery potentiality. The 2v distribution of ‘lGCd (with ~ yr; yr) overlaps the Ov peaks with half-life corresponding to: (a) 6 . 7 loz3 T$,, = 3 x (b) 1 . 6 ~ 1 yr; 0 ~and ~ (c) 3 . 8 ~ 1 0 ’yr. ~ Correspondingly, the Ov peak with the amplitude M (the energy resolution at 2.8 MeV is E W H M = 4%) and 2v spectrum are meeting at the relative height: (a) h / M = 0.1; (b) h / M = 0.5; (c) h / M = 1.

In summary, we can formulate the following requirements to the future ultimate sensitivity 2p decay experiments: (i) The use of highly enriched (S -+ 100%) detectors and “active” source

357

<m,,>,eV

TI29 Yr

10 -l

1

10

10

1

10

10

1

10

10 - l

1

10

10 - l

1

10

10 -l

1

10

Energy resolution at Qpp (FWHM), % Figure 2. The dependences of the discovery potentiality versus the energy resolution calculated (bold line for h / M = 0.5; thin line for h / M = 0.1) for 28 decay candidate nuclei (76Ge, looMo, '16Cd, 130Te, 136Xe, and lsoNd).

technique because only in this case the total detection efficiency could be close to 100%. (ii) The energy resolution is a crucial characteristic, and its value at Qop energy must correspond to the required discovery potentiality for given nucleus (Fig. 2). (iii) The exposure (m x t ) needed to reach certain value should be in accordance with Fig. 3 (20-30 t x y r for T:Y2 M lo2* yr). (iv) Because of the square root dependence of the sensitivity versus source mass and measuring time, it is not enough, however, to increase the exposure alone. The background must be reduced down practically to zero.

Tfb

358

Exposure

10 1 10

Figure 3 . The exposure (product of detector mass by measuring time) needed to collect ten counts in the Ov peak at given T;Y2 value calculated for different nucleus under assumption that detection efficiency and enrichment both equal to 100%.

(v) Measuring time of the future experiments will be of the order of e l 0 yr, hence, detectors and set ups should be as simple as possible to provide stable and reliable operation during such a long period. Evidently, it could be very difficult t o find the project and t o build up the experiment, which would completely satisfy these severe requirements. However, perhaps some of recent proposals could do it to a great extent, thus let us consider them briefly. The DCBA project is under development in KEK (Japan) 2 9 . The drift chamber placed in the uniform magnetic field (0.6 kG) can measure the momentum of each p particle emitted in 2p decay and the position of the decay vertex by means of a three-dimensional reconstruction of the tracks. With 18 kg of an enriched 150Nd passive source (50 mg/cm2), the 5 29. projected sensitivity to the Majorana neutrino mass is ~ 0 . 0 eV The project MOON to study the Ou2P decay of looMo (&PO = 3034 keV) 30 calls for the use of 34 tons of natural Mo (i.e. 3.3 tons of looMo)

359

per detector module in the form of passive foil (x50 mg/cm2). The module will be composed of x60,OOO plastic scintillators (6 mx0.2 mx0.25 cm), the light outputs from which are collected by 866,000 wave length shifter fibers (01.2 mm x 6 m), viewed through clear fibers by 6800 16-anode photomultiplier tubes. The sensitivity to the neutrino mass could be of the order of x 0.05 eV 30. The 160Gd (Qpp = 1730 keV) is an attractive candidate due to large natural abundance (21.9%), allowing to construct sensitive apparatus with natural Gd2SiOS:Ce crystal scintillators (GSO). The large scale experiment with lsoGd by using the GSO multi-crystal array with the total mass of one-two tons (x200-400 kg of '"Gd) is suggested with the sensitivity to the Majorana neutrino mass x 0.05 eV 3 6 . EXO. A new interesting approach to study 2p decay of 136Xe (Qpp = 2468 keV) makes use of the coincident detection of 13'Ba2+ ions (the final state of the 136Xedecay on the atomic level) and the O v 2 P signal with the energy of 2.5 MeV in a time projection chamber (TPC) filled with liquid or gaseous Xe 32,33,34. Recently, the E X 0 project has been considered 35, where the resonance ionization spectroscopy for the 136Ba2+ions identification would be applied in a 40 m3 T P C (the energy resolution at 2.5 MeV is F W H M M 7%.) operated at 5-10 atm pressure of enriched xenon (xl tons of 136Xe). Estimated sensitivity to neutrino mass is x0.05 eV 3 5 . CAMEO. This project 38 intends to operate ~ 1 0 kg 0 of enriched l1'CdW04 crystal scintillators (the energy resolution at 2.8 MeV is F W H M M 4%) allocated in the liquid scintillator of the BOREXINO 39 Counting Test Facility (CTF). The pilot experiment performed by the KievFlorence collaboration with '16Cd and results of Monte Carlo simulations evidently show that CAMEO sensitivity (in terms of the T:T2 limit) is yr, which translates to the neutrino mass bound m, <_ 0.06 eV 3 8 . Moreover, these results can be advanced further by exploiting one ton of 'l'CdW04 detectors placed in one of the existing or future large underground neutrino detectors such as BOREXINO 3 9 , SNO 40 or KamLand 3 . The sensitivity is estimated as T:,& >loz7 yr, which corresponds to a restriction on the neutrino mass of w 0.02 eV 3 8 . The proposed CAMEO technique with 'l'CdWO4 crystals is extremely simple and reliable, thus, such an experiment can run stably for decades. CUORE. The running CUORICINO set up for the 2/3 decay quest of 130Te is designed as a pilot step for a future CUORE project, which would consist of one thousand TeOa bolometers (with total mass of 750 kg) oper-

''

360

ating a t ~ 1 mK. 0 The excellent energy resolution of TeOz bolometers ( ~ 1 0 keV at 2.5 MeV) is a powerful tool for discriminating the Ov signal from the background. The projected CUORE sensitivity is quoted by the authors for the different background rates at 2.5 MeV (0.1-0.01 counts/yr.kg.keV) and would be as high as TfT2 2 (O.3-1)x1Oz6 yr or m, 5 0.1-0.05 eV 31,37. Besides, three large scale projects for the 2p decay quest of 76Ge (MAJORANA 41, GENIUS 42 and GEM 45) were proposed, which we are going to discuss in more details. MAJORANA. The idea of this proposal is to use 210 HP Ge (enriched in 76Get o x 86%) semiconductor detectors ( ~ 2 . 4kg mass of a single crystal), which are contained in a “conventional” super-low background cryostats 41. The detectors are shielded by HP lead or copper. Each crystal will be supplied with six azimuthal and two axial contacts, and hence spatial information will be available for the detected events. It is anticipated that a segmentation of the crystals and a pulse-shape analysis of the data would reduce the background rate of the detectors to the level of ~ 0 . 0 1 counts/yr.kg.keV at the energy 2 MeV. On this basis the projected halflife limit can be determined as T:Tz yr, and depending on the NME calculations, one expects the neutrino mass limits: m, 5 0.05-0.15 eV. GENIUS. This project intends to operate one ton of “naked” HP Ge (enriched in 76Ge to M 86%) detectors placed in extremely high-purity liquid nitrogen (LNz), which simultaneously serves as a cooling medium and as a shielding for the detectors 42. In accordance with the Monte Carlo simulations the necessary dimensions of the liquid nitrogen shield, which could fully suppress the radioactivity from the surroundings, are about 1 2 m in diameter and 12 m in height, and the required radioactive purity of the liquid nitrogen should be at the level of g/g for 40K and 238U,~ 5 x l O W ’g ~/ g for 232Th,and 0.05 mBq/m3 for 222Rn42,43. Due to this the total GENIUS background rate in the energy region of the 2p decay of 76Ge may be reduced down to M 0.2 c0untslyr.keV.t 42,43. The projected T1l2limit can be estimated for 10 yr measuring time as T;T2 >.loz8 yr, which translates to a neutrino mass constraint of m,~0.015-0.05 eV. However, to reach such a sensitivity the GENIUS apparatus must satisfy very stringent, and, in some cases, contradictory demands. These problems can be examined and perhaps solved with the help of the test facility (GENIUS-TF), which is under development now 44. Anyhow, it is clear that production, purification, operation, and maintenance (together with safety requirements) of more than one kiloton of ultra-high purity liquid nitrogen in an underground laboratory requires additional efforts and will 42143

36 1

be both costly and time consuming. GEM. Aiming t o make realization of the high sensitivity 76Ge experiment simpler, the GEM design is based on the following main ideas 45: (a) About 400 “naked” HP Ge detectors (enriched in 76Geto 86%, mass of ~ 2 . kg 5 each) will operate in ultra-high purity liquid nitrogen, which will serve simultaneously as both a cooling medium and a first layer of shielding. (b) Liquid nitrogen is contained in the vacuum cryostat, which is made of HP copper. The dimensions of the cryostat (diameter of 5 m), and consequently the volume of liquid nitrogen, are as small as possible consistent with necessity of eliminating contributions of the radioactive contaminants in the Cu cryostat t o the background of the HP Ge detectors. (c) The shield is composed of two parts: (i) an inner shielding - ultrahigh purity liquid nitrogen, whose contaminations are less than g/g for 40K and 238U, ~ z 5 x l O Wg/g ~ ~ for 232Th, and 0.05 mBq/m3 for ”’Rn; (ii) an outer part - high purity water, whose volume is large enough (811x l l m) to suppress any external background to a negligible level. Such a design of the GEM set up reduces the LN2 volume substantially (only x40 t instead of ~ 1 0 0 0t in GENIUS) and allows one to solve the problems of thermoinsulation, ultra-high purity conditions, LN2 consumption, safety requirements, etc. The GEM realization seems to be reasonably simple due to the fact that the design of the set up has practically no technical risk. In addition, there is the possibility to use the already existing BOREXINO CTF as an outer shield, because it fits all the GEM requirements concerning radiopurity and dimensions of the water shield. It was proved by the Monte Carlo simulations 45 that projected sensitivity of the GEM experiment is similar to that of GENIUS: T;Y2 yr and, consequently, the neutrino mass bound of about ~ 0 . 0 eV. 1 Now let us analyze the discovery potentiality of reviewed projects by using calculated dependences of that quantity versus the energy resolution of the detector (Fig. a),and by taking into account the resolutions claimed in each particular proposal. Unfortunately, the results of such an analysis are not so optimistic, and conclusion is clear: only projects with the high energy resolution (GEM, GENIUS, MAJORANA with the HP 76Gedetectors, and CUORE with I3OTeO2 bolometers) have a chance to detect the Ou2P decay with the rate corresponding t o neutrino mass m, E 0.01 eV. As regards the CUORE, it should be noted, however, that complexity of cryogenic technique requires the use of a lot of different construction materials in the set up, which makes it quite difficult t o reduce background to the same super-low level as those obtained in the best experiments with semi-

362

conductor and scintillation detectors Because of this, the CUORE sensitivity would be limited, and in fact, the expected results are quoted by the authors for the different background rate at 2.5 MeV 31,37. The discovery potentiality of other proposals is much more modest. For example, for the E X 0 (with the FWHM = 5% at the Qpp energy) it equals T:;. M yr (that is to m, M 0.15 eV), while for the CAMEO (FWHM = 4%) the corresponding value is Tf,& M 2 ~ 1 yr 0 (m, ~ ~M 0.15 eV), and so on. Let us remind, however, that 'l6CdW04 crystals, to be used in the CAMEO experiment, can also work as cryogenic detectors with the energy resolution of about 10 keV 46. Therefore, if the '16CdW04 crystals produced for CAMEO project would be installed and measured (on the next step of research) in the CUORE apparatus, the discovery potentiality of the CAMEO will be enhanced substantially (see Fig. 2). At the same time, such a measure would allow one to overcome the drawback of the CUORE set up associated with the background limitation. First, it is because that Qpp energy of '16Cd (2.8 MeV) is higher than that for 130Te (2.5 MeV) - see footnote d. Secondly, as it was successfully demonstrated with C a w 0 4 crystals 47, the simultaneous phonon and scintillation light detection which is also possible with 116CdW04 crystals - is a very powerful tool for additional background discrimination. Hence, we can conclude that a challenging scientific goal to observe the Ov2P decay with the rate corresponding t o neutrino mass mu M 0.01 eV could be feasible for the several future 2/3 experiments (namely, GEM, GENIUS, MAJORANA with HP 76Ge detectors, and CUORE with 116CdW04 crystals), while other projects (CAMEO, CUORE with 130Te02 crystals, DCBA, EXO, 16'Gd, MOON, etc.) would be able to set the restrictions on the neutrino mass at the level of mu <_ 0.05 eV. 10113,14.

~

References 1. Y. Fukuda et al. (Super-Kamiokande Collaboration), Phys. Rev. Lett. 81 (1998) 1562; 82 (1999) 1810; 82 (1999) 2430; 86 (2001) 5651. 2. Q.R. Ahmad et al. (SNO Collaboration), Phys. Rev. Lett. 87 (2001) 071301; 89 (2002) 011301; 89 (2002) 011302. 3. K. Eguchi et al., Phys. Rev. Lett. 90 (2003) 021802. 4. M.H. Ahn et al., Phys. Rev. Lett. 90 (2003) 041801. 5. J.D. Vergados, Phys. Rep. 361 (2002) 1. 6. Yu.G. Zdesenko, Rev. Mod. Phys. 74 (2002) 663. 7. S.R. Elliot and P. Vogel, Ann. Rev. Nucl. Part. Sci. 52 (2002) 115. 8. J. Schechter and J.W.F. Valle, Phys. Rev. D 25 (1982) 2951. 9. V.I. Tretyak and Yu.G. Zdesenko, At. Data Nucl. Data Tables 80 (2002) 83.

363 10. F.A. Danevich et al., Phys. Rev. C 62 (2000) 045501; P.G. Bizzeti et al., Nucl. Phys. B (Proc. Suppl.) 110 (2002) 389. 11. C. Arnaboldi et al., Phys. Lett. B 557 (2003) 167. 12. R. Luescher et al., Phys. Lett. B 434 (1998) 407. 13. H.V. Klapdor-Kleingrothaus et al., Eur. Phys. J. A 12 (2001) 147. 14. C.E. Aalseth et al., Phys. Rev. D 65 (2002) 092007. 15. A. Faessler and F. Simkovic, J. Phys. G: Nucl. Part. Phys. 24 (1998) 2139. 16. J. Suhonen and 0. Civitarese, Phys. Rep. 300 (1998) 123. 17. P. Vogel, nucl-th/0005020 (2000); in Current Aspects of Neutrino Physics, ed. by D. Caldwell (Springer-Verlag). 18. E. Fiorini et al., Lett. Nuovo Cimento vol. 111, n. 5 (1970) 149. 19. A. Staudt et al., Europhys. Lett. 13 (1990) 31. 20. Yu.G. Zdesenko et al., Phys. Lett. B 546 (2002) 206. 21. M. Doi, T. Kotani, E. Takasugi, , Prog. Theor. Phys. Suppl. 83 (1985) 1. 22. G. Audi and A.H. Wapstra, Nucl. Phys. A 595 (1995) 409. 23. K.J.R. Rosman and P.D.P. Taylor, Pure and Appl. Chem. 70 (1998) 217. 24. T. Tomoda, , Rep. Prog. Phys. 54 (1991) 53. 25. A.A. Artyukhov et al., Phys. Atom. Nucl. 61 (1998) 1236; A. Pokidychev, M. Pokidycheva, Nucl. Instrum. Meth. A 438 (1999) 7. 26. V.I. Tretyak and Yu.G. Zdesenko, At. Data Nucl. Data Tables 61 (1995) 43. 27. M. Doi et al., Prog. Theor. Phys. 66 (1981) 1739. 28. J.M. Blatt and V.F. Weisskopf, "Theoretical Nuclear Physics", 7-th ed., John Wiley, New York, 1963. 29. N. Ishihara et al., Nucl. Instrum. Meth. A 373 (1996) 325; A 443 (2000) 101. 30. H. Ejiri et al., Phys. Rev. Lett. 85 (2000) 2917. 31. E. Fiorini, Phys. Rep. 307 (1998) 309. 32. M.K. Moe, Phys. Rev. C 44 (1991) 931. 33. M. Miyajima et al., KEK Proc. 91-5 (1991) 19. 34. M. Miyajima et al., AIP Conf. Proc. 338 (1997) 253. 35. M. Danilov et al., Phys. Lett. B 480 (2000) 12. 36. F.A. Danevich et al., Nucl. Phys. A 694 (2001) 375. 37. G. Gervasio (for the CUORE coll.), Nucl. Phys. A 6638~664(2000) 873. 38. G. Bellini et al., Phys. Lett. B 493 (2000) 216. 39. G. Bellini (for the Borexino coll.), Nucl. Phys. B (Proc. Suppl.) 48 (1996) 363. 40. J. Boger et al., Nucl. Instrum. Meth. A 449 (2000) 172. 41. C.E. Aalseth et al., hep-ex/0201021 (2002). 42. H.V. Klapdor-Kleingrothaus et al., J. Phys. G 24 (1998) 483. 43. O.A. Ponkratenko, V.I.Tretyak, Yu.G.Zdesenko, Proc. Int. Conf. on Dark Matter in Astro and Particle Phys., Heidelberg, Germany, 20-25 July 1998, eds. H.V. Klapdor-Kleingrothaus and L. Baudis, IOP 1999, Bristol, Philadelphia, p. 738. 44. H.V. Klapdor-Kleingrothaus et al., Nucl. Instrum. Meth. A 481 (2002) 149. 45. Yu.G. Zdesenko et al., J. Phys. G: Nucl. Part. Phys. 27 (2001) 2129. 46. A. Alessandrello et al., Nucl. Phys. B (Proc. Suppl.) 35 (1994) 394. 47. M. Bravin et al., hep-ex/9904005 (1999).

XMASS EXPERIMENT

S. MORIYAMA (ON BEHALF O F THE XMASS COLLABORATION) Kamioka Observatory, Institute f o r Cosmic Ray Research, University of Tokyo, Higashi-Momma, Kamioka, Gifu 506-1205, J a p a n

The XMASS project utilizes ultrapure liquid xenon and aims to detect pp and 7Be solar neutrinos by means of v e scatterings. Our goal is a 10 t scale detector in which an ultralow background can be realized in a fiducial volume. Since it requires extremely low background, it will give great opportunities for us to search for dark matter and double beta decay signals with high sensitivity. Here we will discuss a detector design common for solar neutrino and dark matter detection and a new design devoted for the double beta decay experiment. The status of the current 100 kg xenon detector will also be shown.

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1. Introduction

The recent observations by Super-Kamiokandel and SNO’ experiments provided evidence that the solar neutrino problem is caused by neutrino oscillations. However, both experiments only observed sB neutrinos which contain a very small fraction (0.17%) of solar neutrinos. Most of the solar neutrinos are low energy, so called pp and 7Be neutrinos. The next generation solar neutrino experiments should reveal solar neutrino spectrum and provide a better understanding about solar neutrino oscillations. The XMASS p r o j e ~ t ~utilizes > ~ i ~ liquid xenon as a scintillator and aims to detect pp and 7Be neutrinos. Although there are many advantages for using liquid xenon as a solar neutrino detector, no directional information nor coincidence information for solar neutrinos are available. Therefore, it is clear that we must realize an ultralow background in the fiducial volume of the detector. The key idea for it is to utilize the self-shielding power of xenon. We only need 30 cm to shield low energy external gamma rays since xenon has a large atomic number. The self shielding is quite useful for solar neutrino detection as well as dark matter detection. Since the solar neutrino detector requires large mass, we are now designing an 800kg detector which aims to detect dark matter but is also important as a prototype of the solar neutrino detector. It can give very

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important results for dark matter detection and provide a good milestone for solar neutrino detection. It will be discussed in Sec. 4. In Sec. 3, the current status of the 100 kg detector is shown. We are ready t o demonstrate actual vertex and energy reconstruction, self shielding, and purification method. However, the self shielding for higher energy is not effective. A few MeV gamma rays can penetrate xenon without any interaction. Since PMTs have large radioactivity in general, we cannot reduce background effectively at the Q value of the double beta decay of 136Xe, 2.48MeV. This prohibits the use of PMTs near the sensitive volume. To overcome this situation, we need another detector design. It is discussed in Sec. 5. 2. General Properties of Xenon and Self Shielding The most important property of liquid xenon is its light yield as a scintillator. It gives 42,000 photons for 1MeV energy deposition by an electron, which is comparable with that for NaI(T1). Although the scintillation lights are vacuum ultra1 violet (VUV), they can be directly read out by PMTs. As for the background due to the radioactive sources inside the detector, we have prospects to realize the required background as discussed in Ref.3. The prospects are mainly because xenon is a rare gas, and can be purified by using gas phase, liquid phase, and solid phase. One more important advantage is that we can purify xenon even after the experiment starts. If we use crystal scintillators or doped liquid scintillators, this is quite difficult to perform. The effect of self shielding is shown in Fig. 1. Since the 2 of xenon is 54, the photoelectric effect works well to absorb external gamma rays. The figure shows that 30cm is enough to absorb low energy gamma ray background. If the volume is divided into many sub-detectors, we cannot utilize this advantage. It is noteworthy that the recent, mostly successful experiments of Super-Kamiokande, SNO, and KamLAND employed this kind of design and reduced their background as expected. 3. 100 kg detector

The motivation of the lOOkg detector is to confirm our key ideas. It is important to demonstrate the self-shielding of liquid xenon, vertex and energy reconstruction, low background environment, electron/gamma ray separation, attenuation length, and a newly developed purification system. The details of background estimation and the reconstruction method are

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......... 0-3000 keV ......

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Figure 1. Self shielding effect. External gamma rays from U and T h chain are assumed. The horizontal axis corresponds to the depth of interacted vertex measured from the detector surface. If we define a fiducial volume 30cm inside the detector, six orders of magnitude in reduction can be expected for low energy events.

described in Ref. '. On Feb. 2003, we performed a cooling test and took test data with this detector. Since we used only 6 PMTs to avoid possible damage for all PMTs we have, data itself is difficult to discuss. However, the most important things from the test are that the operation was quite smooth and stable and that the handling of the large amount of xenon was safely done. This is mainly because we prepaired many monitors: five level sensors which monitor the level of liquid xenon, 22 temperature sensors, two vacuum gauges, two pressure gauges, and a gas flow meter. We successfully operated the detector with complete understanding of the low temperature behavior of the detector. Fig. 2 shows a raw distribution of ADC counts for background data. Although its resolution is very poor, we can see small bumps around 3300 counts and 1900 counts, which are suggested as a "*Tl peak and a 40K peak. A Monte Carlo study including scintillation photon propagation gives similar ADC distribution. For detailed discussion, we need to wait for a full operation scheduled in this summer where all 54 PMTs will be installed and event reconstruction will be applied. An unexpected but most encouraging thing is that the PMTs seemed to be working well though they were cooled down to -90C. Since we did

367 106 1o5

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500 1000 1500 2000 2500 3000 3500 4000 4500 5000 6 PMT sum [ADC channel]

Figure 2. Background test data with 6 PMTs without any gamma ray shield. Each P M T is located at the center of each face. Horizontal axis corresponds to the summation of ADC channel for 6 P M T s after subtracting their pedestals. Top histogram shows the raw data in which ADC cutoff can be seen around 3600 channel. To constrain for the vertices, we applied a balance cut by using u / p , in which u is the variance of 6 P M T counts and p is the average of 6 PMTs.

not expect they would work at this low temperature, we put thermal insulators between PMTs and the chamber. Although it is our failure that we cooled them down to -9OC, we accidentally showed they can work a t this temperature without damage. One thing we added to the P M T design is aluminum strips on their photocathode which avoid increasing resistance of the photocathode a t low temperatures. It turned out that they worked very well. 4. 800 kg detector

Since the signal of dark matter increases exponentially as we lower the energy threshold, photoelectron yield is most important for dark matter searches. However, the lOOkg detector has only 0.6p.e./keV4 due to its low photocathode coverage by PMTs. Hence it cannot give a low energy threshold expected for dark matter detection. In addition to that, the 100 kg detector has difficulty in event reconstruction since PMTs have some dead angles inside the detector. This is because the detector has a cubic shape geometry and total reflection at the windows. If we can make a detector with a spherical geometry and immerse PMTs into the liquid xenon,

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this problem can be solved easily.

Figure 3. is 80 cm.

Schematic view of 800 kg detector. It has spherical geometry and its diameter

Based on these experiences, we are now designing a next 800 kg detector. Fig. 3 shows the schematic view of the detector. It has 642 2” PMTs and large photocathode coverage greater than 70%. Since it can give 5 p.e./keV, which gives 20% resolution even for 5 keV events, we can extend its energy threshold down to 5 keV. As for the background, we expect background sources in our PMTs can be reduced 1/10 compared with current PMTs since we have already identified the main source of background of our PMTs. Fig. 4 shows the expected background spectrum with dark matter signals. The signals of dark matter whose cross section is 10V’pb for protons can be clearly seen. To estimate the sensitivity for dark matter, we listed up possible candidates of the origin of background and estimated the requirements for them. They are not discussed here but it seems they are achievable. If we impose the requirement for the total background as 2x /keV/kg/day, we can obtain Fig. 5 . As shown in the figures, we can improve sensitivity more than two orders of magnitude compared with existing experiments.

5. Dedicated detector for double beta decay experiment

A great advantage to utilize xenon is that it can be purified even after the experiment starts. If we use crystals or foils as a target, it is quite difficult to improve its purity afterward. However, one can see a problem in Fig. 1 that we cannot expect the self shieding effect for high energy region in which signals from the Ovpp decay are expected. That means PMTs should not be placed near the detector.

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energy (keV)

Figure 4. Expected background spectrum for the 800 kg detector. Gamma rays originating outside the Xe volume are considered. The thick dotted histogram corresponds t o a 60 cm diameter fiducial volume and the thick solid histogram corresponds to a 40 cm diameter fiducial volume (100 kg mass). Horizontal axis corresponds t o reconstructed energy. It is expected t o reach 8 x 10P5/keV/kg/day in the low energy region. Typical dark matter signals are overlapped (spin independent, l o P s pb for protons, and At, = 50 GeV and 100 GeV) Also, the expected spectrum from low energy solar neutrinos, pp and 7Be chain are shown.

To overcome this situation, we are now developing a dedicated detector for the Ovpp decay search. The idea is t o use room temperature liquid xenon contained in an acrylic, transparent pressure vessel. If we can put this vessel into a water tank equipped with large numbers of PMTs, we can detect scintillation lights far from the vessel. The water works t o reduce background from PMTs and rocks significantly. The key technology for the method is a wavelength shifter. Since the xenon emits vacuum ultra violet light (175nm), we need to covert the light to visible light. Fortunately, we can utilize wavelength shifters already developed by some authors6. We estimated the sensitivity for the effective mass of the neutrinos. We assumed (1) The background only comes from the acrylic container which usually contains U and T h around 10-l2g/g. (2) The container has cylindrical geometry whose inner diameter is 4cm and outer diameter is 10 cm. (3) Xenon is 10 kg enriched 136Xewhich we already have. (4) The energy resolution is 57 keV rms for &as = 2.48 MeV which was calculated based on assumptions: 50% scintillation yield at room temperature (needs to be confirmed), 90% conversion efficiency by the wavelength shifter, 80%

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water transparency, 20% P M T photocoverage, and 25% QE for PMTs. Fig. 6 shows the simulated background. Based on the result, we estimated the sensitivity as T l p , o v p p = 1 . 5 lOZ5yr, ~ which corresponds to < m, >= 0.2 0.3eV. If we can use plastic scintillators as a vessel and time correlation analysis, we can further reduce background which originates from the vessel. We also need the water shield and PMTs. Although the most suitable detector seems t o be the Super-Kamiokande detector, we cannot put this kind of pressure vessel inside easily. Another idea is shown in Fig. 6. The cross section of the water tank is an ellipse with mirrors inside. On one focus, the xenon targets are located, and on another focus, several P M T s are equipped. The scintillation lights go to the P M T s as shown in the figure with only one reflection on the mirror. Since the paths for all light are common, the effect of water attenuation is uniform. It can be constructed quite cheaply. Once we make this kind of facility, it is useful for use with N

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Figure 6. Left: expected background for double beta decay experiment. The peak around 2600 keV originates from 208T1gamma rays. Right: Double-focus detector. Its cross section is ellipse and mirrors inside.

any scintillators. 6. Summary

The XMASS project utilizes ultrapure liquid xenon and aims to detect pp and 7Be solar neutrinos, dark matter and Oupp decay. Our key ideas will be confirmed by using a lOOkg detector which is ready to be operated. After this confirmation, we will develop an 800kg detector whose target is dark matter detection. It is expected to improve sensitivity for dark matter searches by at least two orders of magnitude by lowering its energy threshold and background level down to 2 x lop4f keV f kg f day. For double beta decay search we are also developing a dedicated detector which has a sensitivity for the effective mass of neutrinos down to 0.2 to 0.3 eV. References 1. The Super-Kamiokande Collaboration, Phys. Rev. Lett. 86, 5651 (2001), Phys. Rev. Lett. 86, 5656 (2001) 2. The SNO Collaboration, Phys. Rev. Lett. 87,071301 (2001)

3. Y. Suzuki, hep-ph/008296. 4. S. Moriyama, et al., in the proceedings of the international workshop on Technique and Application of Xenon Detectors World Scientific, 2003 Jan. 5. S. Moriyama, et al., in the proceedings of the 4th international workshop on the Identification of Dark Matter (IDM2002). 6. M. A. Iqbal, et al., NIMA 243 (1986) 459; L. Periale et al., NIMA 478 (2002) 377; C. H. Lally et al., NIMB 117 (1996) 421.

COSMOLOGICAL CONSTRAINTS ON NEUTRINO MASSES AND MIXINGS.

A. D. DOLGOV INFN, sezione di Ferrara, Via Paradiso, 12 - 44100 Ferrara, Italy; ITEP, Bol. Cheremushkinskaya 25, Moscow 113259, Russia E-mail: [email protected] The bounds on neutrino masses and mixing that follows from the data on light element abundances, large scale structure formation, and angular fluctuations of cosmic microwave background radiation are analyzed. The role of neutrino oscillations in BBN and the bounds on cosmological lepton asymmetry are discussed.

Neutrinos have the weakest interactions among all known elementary particles. They have also the smallest mass among all known massive particles. These two properties, on one hand, make it difficult to study neutrino properties directly, in particular, to measure their mass in laboratories. On the other hand, the same properties make neutrinos very important cosmologically and, at the present time, measuring neutrino masses looking at the sky seems more promising than terrestrial experiments. Significant cosmological role played by neutrinos arises from their large number density. Neutrinos are the second most abundant particles in the universe, after photons in Cosmic Microwave Background Radiation (CMBR) with the number density n-, M 410/cm3. According to the standard cosmology, the universe is filled, in addition to CMBR, by the Cosmic Neutrino Background Radiation (CvBR) with the present-day number density:

for any neutrino flavor a = e , p , - r . It is usually (but not always) assumed that neutrinos are not degenerate (i.e. their chemical potentials are zero or negligibly small) and the number densities of neutrinos and antineutrinos are equal. However, contrary to well observed CMBR, the existence of CvBR is only a theoretical prediction, and though practically nobody has any doubts of that, direct observation of CvBR is still missing and it seems that there

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is no chance for direct registration of cosmic neutrinos today and maybe even in the foreseeable future. Thus, one has to rely on indirect methods studying features imprinted by cosmic neutrinos on: 1) formation and evolution of astronomical Large Scale Structure (LSS); 2) angular fluctuations of CMBR; 3) light element abundances created at Big Bang Nucleosynthesis (BBN); 4) propagation of Ultra High Energy Cosmic Rays (UHECR). In what follows we will consider the first three subjects only. One can find a more detailed discussion of the issues presented below, as well as of the problem of interaction of UHECR with CVBR,and hopefully a complete list of references in the review When the temperature of the cosmic plasma was above a few MeV, neutrinos were in thermal equilibrium with the electromagnetic component of the plasma, i.e. with photons and e+e--pairs. Electronic neutrinos decoupled from e+e--pairs when the temperature dropped below Tie) x 1.9 MeV, while vP and I/, decoupled a little earlier at TJ') x 3.1 MeV. At the moment of decoupling and later down to T M m e = 0.511 MeV temperatures of neutrino and electromagnetic components were equal, T, = T7. Below T = m ethe annihilation of e+e--pairs heats up photons and themselves, while leaves neutrino temperature intact. As a result the initial equilibrium ratio of neutrino-to-photon number densities becomes diluted by the factor 4/11. From this result the present-day neutrino number density (1) is obtained. Any additional energy release after TJ") which might (0). increase the photon number density would correspondingly diminish n,,

'.

Neutrino spectrum is close t o the equilibrium form: fJeq) = [exp(p/T, - I ) 1]-l, where p is the neutrino momentum, T, is the temperature, and = p/T is dimensionless chemical potential; for adiabatic expansion 6 remains constant. Usually chemical potentials of different neutrino species are assumed to be negligible, at the level of baryonic asymthough much larger values, even close to 1, are not excluded. metry, Moreover, there exist theoretical models which predict a small baryon asymmetry and simultaneously large lepton ones. Equilibrium with respect to pv-annihilation enforces 6, ID = 0 but if neutrino charge asymmetry is generated at low temperatures this condition may be violated. One more comment is in order: if neutrino mass is non-negligible in comparison with the temperature, their spectrum is non-equilibrium because the latter contains exp(E/T) but not exp(p/T). At the present time T, M 1.7. eV. If the neutrino mass is larger than this value the deviations from the equilibrium distribution may be significant. This must be true at least for two out of three neutrinos because from the atmospheric

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neutrino anomaly bm2 = (2 - 5) . eV2 and from the solar neutrino deficit and KAMLAND data 6m2 = (6 - 7) . l o p 5 eV2. Still, even at high temperatures (T >> m,) a deviation from equilibrium was non-negligible. Indeed, the decoupling of neutrinos from e+e--pairs is not instantaneous and the annihilation e+e- + v V at T 5 me would heat the neutrino component of the plasma and distort its spectrum. According to analytical estimates of ref. the spectral distortion for v, has the form: b f u e /f,, M 3 . lop4 (E/T) ( l l E / 4 T - 3 ) . Most accurate numerical solution of the kinetic equation that governs non-equilibrium corrections to the neutrino spectrum was performed in ref. According to the calculations the excess of energy density of v, and v ~ are, respectively ~ bp,, / p , = 0.9% and bp,,,,,, / p , = 0.4%. Together with the plasma corrections which diminish the energy density of the electromagnetic component, the total relative rise of neutrino energy density reaches approximately 4%. This phenomenon has very little impact on production of primordial 4He but can be observable in the shape of the angular fluctuations of CMBR in the forthcoming Planck mission. If observed, then together with BBN, it would present evidence of physical processes which took place in the universe when she was about 1 sec old. The corresponding red-shift is about 1O1O. Knowing the present-day number density of relic neutrinos one can easily calculate their energy density and obtain an upper limit, on their mass. Such bound was derived in 1966 by Gerstein and Zeldovich The result was re-derived 6 years later by Cowsic and Mc Lelland but in their work the effect was overestimated by the factor 2 2 / 3 . In contemporary form the limits reads: C , rnva 5 94eV Oh2, where the sum is taken over all neutrino species, a = e, p, 7 ; R = p / p c is the cosmological mass fraction of matter, pc = 10.5 h2 keV/cm3, and h x 0.7 is the dimensionless Hubble parameter. According to the different and independent pieces of astronomical data R < 0.3 and correspondingly C , m,<,< 14 eV. Since the data on neutrino oscillations show that the neutrino mass difference is much smaller than eV, the mass of any neutrino flavor should be below 4.7 eV. This limit can be further improved if one takes into account a possible role that massive neutrinos might play in the process of formation of the large scale structure of the universe. The point is that in neutrino dominated universe all the structures on the scales smaller than the neutrino free streaming length, I,, should be erased. The mass inside the free-streaming volume can be estimated as Mu M 5 . 1017Ma(leV/m,)2. If density perturbations are adiabatic, then neutrino out-stream would leave behind less power at small scales inhibiting structure formation at these scales. The

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larger is 0, the larger is the effect. Moreover, the larger is the fraction of relativistic (hot) dark matter the later structure formation begins. Hence observation of structures at large red-shifts allows to conclude that 0, < 0.1 and m, < 1.5 eV a . The analysis of the recent data from 2dF Galaxy Redshift Survey permitted to put the limit Camva < 2.2 eV or individual masses should be below 0.73 eV. As argued in ref. detailed analysis of structure formation by the Sloan Digital Sky Survey would be sensitive to neutrino mass at the level of (a few)x0.1 eV. This limits are based on certain assumptions about the form of the spectrum of perturbations, their character (adiabatic or isocurvature), and about neutrino interactions. A question may arise whether neutrinos can supply all the dark matter in the universe if we relax any or all these assumptions, introducing an arbitrary shape of the perturbation spectrum and/or new neutrino interactions (of course inside the established limits). The answer would still be negative because of the Tremain-Gunn limit ll. This limit manifests quantum mechanical Fermi exclusion principle at the kiloparsec scales and demands that neutrinos must be heavier than roughly speaking 100 eV if they form all dark matter in galaxies. So it seems that the only way out is to make a crazy assumption that neutrinos are bosons and not fermions which in light of the discussed today search of C P T violation maybe looks not so crazy because CPT-theorem is heavily based on the standard relation between spin and statistics. The impact of neutrinos on the shape of angular spectrum of CMBR temperature is based on the following two effects (for details see e.g. the recent review 12). First, a change of the energy density of relativistic matter (neutrinos) would change the cosmological expansion regime and this in turn would change the physical size of the horizon at recombination. It would shift the positions of the acoustic peaks in the temperature fluctuations. More important is another effect which changes the heights of the peaks because relativistic matter creates gravitational force which varies with time creating resonance amplification of the acoustic oscillations. These phenomena permit to measure neutrino mass and the number of neutrino families at the recombination epoch. The recent measurements of the angular fluctuations of CMBR by WMAP 1 3 , together with the analysis of LSS by 2dF, permitted to impose surprisingly strong upper limit on neutrino mass: C , mVa< 0.69 eV,, that is for mass degenerate neutrinos m, < 0.23 eV at 95% CL; see also the discussion of this result and of the role of primers in ref. 14. Immediately after publication of the first WMAP data, there appeared

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several papers l5 where the number of neutrino families were evaluated. Their results are, roughly speaking, N , = 1- 7 depending upon the analysis and priors. Anyhow Nu > 0 and thus CMBR confirms, independently on BBN, that CvBR (or some other relativistic background) indeed exists. The accuracy of the data is not yet good to compete with the determination of N , from BBN to say nothing about a registration of 4% addition to the neutrino energy discussed above. However the forthcoming Planck mission may be sensitive to this effect and overtake BBN in determination of N u . One should keep in mind that the impact of neutrino energy on BBN and CMBR may be different depending upon the form of the spectral distortion of electronic neutrinos f,, ( E ) . This effect,, which was calculated for massless neutrinos, depends upon the value of neutrino mass. Abundances of light elements (2H, 3He, 4He, and 7Li) produced at BBN depend upon the following quantities: 1) Number density of baryons, 7710 = 101On~/n,. In the previous century the value of this parameter was determined from BBN itself through comparison of the predicted deuterium abundance with observations. Now after measurements of CMBR angular fluctuations by MAXIMA, BOOMERANG and DASI and confirmed by WMAP l 3 this parameter is independently fixed at ~ 1 = 0 6 f0.3. 2) Weak interaction rate which is expressed through the neutron life-time, now well established, 885.71t0.8 sec 17. 3 ) Cosmological energy density at the period of BBN. The latter is usually parametrized as the effective number of additional neutrino species AN,. This type of parametrization is flawless for relativistic energy, while for another form of energy (e.g. non-relativistic or vacuum-like) its effect on the production of different light elements may deviate from that induced by neutrinos. 4) Possible non-vanishing values of neutrino chemical potentials &. While non-zero
377

der the conservative assumptions that A N < 1 and other chemical potentials are negligible was obtained in ref. 21 and reads: l ~ u w , u T l < 1.5 and /Eye 1 < 0.1. This bound would be relaxed if a conspiracy between different is compenchemical potentials is allowed and the effect of a large l&w,uTl sated by I. The best limit is presented in ref. 22 where the combined inputs from BBN and CMBR have been used: l&,u, 1 < 2.6 and I&, I < 0.2. These bounds are valid if neutrinos are not mixed. Otherwise, charge asymmetry of a certain neutrino flavor would be redistributed between all neutrino species and the bound would be determined by the most sensitive asymmetry of ve. This problem was analyzed in ref. 23 numerically and analytically in ref. where it was shown that for LMA solution of the solar neutrino deficit the transformation is quite efficient and equilibration of all chemical potentials by oscillations is achieved. This leads to the common bound for all neutrino chemical potentials: /&I < 0.07. Similar investigation both analytical and numerical was also performed in the papers 2 4 . If a new sterile neutrino (or neutrinos) mixed with active ones exists, the impact of neutrino oscillation on BBN would be more interesting. The us H u,-transformations would excite additional neutrino species leading t o an increase of the effective number of neutrinos, AN > 0 25,26, could distort the spectrum of v, and could generate a large lepton asymmetry in the sector of active neutrinos by MSW-resonance 28. In the non-resonance case, one can estimate the production rate of sterile neutrinos in the early universe through oscillations and obtain the following bounds on the oscillation parameters 29: 26727

(brntcu,9/eV2) sin4 2 0 2 2 = 3.16.

[log (1 - A N U ) l 2

(2)

(drn”,uq/eV2)sin4 Zi32:

[log (1 - ANU)l2

(3)

= 1.74.

In this result a possible deficit of u, created by the transformation of the latter into us, when refilling of v, by e+e--annihilation is already weak, is not taken into account. This effect would strengthen the bound. Numerical solution of kinetic equations governing neutrino oscillations in the early universe was performed in ref. 30 under assumption of kinetic equilibrium, so the neutrinos are described by a single momentum state with the thermally average value of the energy E = 3.15T. For the non-resonant case the obtained results are somewhat stronger than those presented above, (2,3). For the resonant case it is questionable if thermal averaging is a good approximation because the position of resonance depends upon the neutrino momentum. One more complication is that all active neutrinos are strongly mixed and their mutual transformation should be taken into

378

account together with (v, - us)-oscillations 3 1 . The active neutrino mixing noticeably changes the previously obtained cosmological limits for mixing with v,. Moreover, the solution of momentum dependent kinetic equations shows that kinetic equilibrium is strongly broken (at least for some values of the oscillation parameters) and, in particular, the spectrum of v, is distorted leading to a shift of the n l p r a t i o The calculations are complicated by the appearance of resonances if sterile neutrino is lighter than active ones. Anyhow in the resonance case the cosmological bounds on the mixing between sterile and active neutrinos are considerably stronger than those in non-resonance case. Thus if a large mixing t o v, is discovered it would mean that the lepton asymmetry of the universe is non-negligible 3 1 , because the latter might “cure” the effect of v, - v, oscillations on BBN. Thus we see that cosmology is becoming sensitive to the values of neutrino masses approaching So one may hope that neutrino will be the first particle whose mass will be measured by astronomers by the combined data from CMBR and LSS. The number of additional neutrinos at BBN is limited by 0.5 (though 1 is still not excluded) with a possibility to improve this limit down to 0.1. The observed in experiment strong mixing between active neutrinos allows cosmological lepton asymmetry to be relatively low, smaller than 0.1. This excludes, in particular, cosmological models where large chemical potential of neutrinos might be essential for large scale structure formation. A possible mixing between active and sterile neutrinos is restricted by BBN at much stronger level than by direct experiment. Planck mission may be sensitive to additional contribution to neutrino energy density at per cent level and thus will be able to trace physical processes in the universe at red shift of 1O1O. I am grateful t o F. Villante for critical comments.

m.

References 1. A.D. Dolgov, Phys. Repts. 370,333 (2002). 2. A.D. Dolgov and M. Fukugita, JETP Lett. 56 (1992) 123 [Pisma Zh. Eksp. Teor. Fiz. 56 (1992) 1291; A.D. Dolgov and M. Fukugita, Phys. Rev. D46, 5378 (1992). 3. A.D. Dolgov, S.H. Hansen and D.V. Semikoz, Nucl. Phys. B503 (1997) 426; Nucl. Phys. B543 (1999) 269. 4. A.F. Heckler, Phys. Rev. D49 , 611 (1994); R.E. Lopez, S. Dodelson, A. Heckler and M.S. Turner, Phys. Rev. Lett. 8 2 , 3952 (1999). 5 . S.S. Gerstein and Ya.B. Zeldovich, Pis’ma ZhETF, 4, 174 (1966) [English translation JETP Letters 4,120 (1966)l.

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6. R. Cowsik and J . McClelland, Phys. Rev. Lett. 29, 669 (1972). 7 . See e.g. the talks by E. Lisi, T. Schwetz, A.Y. Smirnov at this Conference. 8. R.A.C. Croft, W. Hu, and R. D a d , Phys. Rev. Lett. 83, 1092 (1999); W. Hu, D.J. Eisenstein and M. Tegmark, Phys. Rev. Lett. 80, 5255 (1998); M. Fukugita, G.-C. Liu, N. Sugiyama, Phys. Rev. Lett. 84, 1082 (2000); A.R. Cooray, Astron. Astrophys. 348, 31 (1999); E. Gawiser, Proceedings of PASCOS99 Conference, Lake Tahoe, CA 1999, astro-ph/0005475. 9. W. Hu, D.J. Eisenstein, M. Tegmark and M.J. White, Phys. Rev. D59, 023512 (1999). 10. 0. Elgaroy et al, Phys. Rev. Lett. 89, 061301 (2002). 11. S. Tremaine and J.E. Gunn, Phys. Rev. Lett. 42, 407 (1979). 12. W. Hu and S. Dodelson, Annu. Rev. Astron. and Astrophys. 40, 171 (2002). 13. D.N. Spergel et al, astro-ph/0302209. 14. 0. Elgaroy and 0. Lahav, JCAP 0304, 004 (2003). 15. P. Crotty, J . Lesgourgues and S. Pastor, astro-ph/0302337; S. Hannestad, astro-ph/0303076; E. Pierpaoli, astro-ph/0302465; V. Barger, J.P. Kneller, H.-S. Lee, D. Marfatia and G. Steigman, hep-ph/0305075. 16. A.T. Lee et al, Astrophys. J . 561, L l (2001); C.B. Netterfield et al, Astrophys. J . 571 (2002) 604; N.W. Halverson et al, Astrophys. J . 568 (2002) 38. 17. K. Hagiwara et al, Phys. Rev. D66,010001 (2002). 18. V. F. Shvartsman, Pisma Zh. Eksp. Teor. Fiz. 9, 315 (1969) [JETP Lett. 9, 184 (1969)l; G. Steigman, D.N. Schramm and J.R. Gunn, Phys. Lett. B66, 202 (1977). 19. A.D. Dolgov, Nucl. Phys., Proc. Suppl. B110, 137 (2002). 20. E. Lisi, S. Sarkar and F.L. Villante, Phys. Rev. D59, 123520 (1999); G. Fiorentini, E. Lisi, S. Sarkar and F.L. Villante, Phys. Rev. D58, 063506 (1998). 21. K. Kohri, M. Kawasaki and K. Sato, Astrophys. J . 490, 72 (1997). 22. S.H. Hansen, G. Mangano, A. Melchiorri, G. Miele and 0. Pisanti, Phys. Rev. D65, 023511 (2002). 23. A.D. Dolgov, S.H. Hansen, S. Pastor, S.T. Petcov, G.G. Raffelt and D.V. Semikoz, N u d P h y s . B632 363 (2002). 24. C.Lunardini and A.Yu.Smirnov, Phys. Rev. D64, 073006 (2001); Y.Y.Y. Wong, Phys. Rev. D66 025015 (2002); K.N. Abazajian, J.F. Beacom and N.F. Bell, Phys.Rev. D66 013008 (2002). 25. A.D.Dolgov, Yad. Fiz. 33, 1309 (1981); [English translation: Sov. J . Nucl. Phys. 33, 700 (1981). 26. R. Barbieri and A.D. Dolgov, Phys. Lett. B237, 440 (1990); K. Kainulainen, Phys. Lett. B244, 191 (1990). 27. D.P. Kirilova and M.V. Chizhov, Phys. Lett. B393, 375 (1997). 28. R. Foot, M.J. Thomson and R.R. Volkas, Phys. Rev. D53, 5349 (1996). 29. A.D. Dolgov, Surveys in High Energy Physics, 17, 91 (2002) (lectures presented at ITEP Winter School, February, 2002). 30. K. Enqvist, K. Kainulainen and M. Thomson, Nucl. Phys. B373, 498 (1992). 31. A.D. Dolgov and F.L. Villante, work in progress.

SUPERNOVA NEUTRINOS: FLAVOR-DEPENDENT FLUXES AND SPECTRA

GEORG G. RAFFELT AND MATHIAS TH. KEIL Max-Planck-Institut fur Physik (Werner-Heisenberg-Institut) Fohringer Ring 6, 80805 Munchen, Germany ROBERT BURAS, HANS-THOMAS JANKA AND MARKUS RAMPP Max-Planck-Institut fur Astrophysik Karl-Schwarzschild-Str. 1 , 85741 Garching, Germany Transporting vp and vr in a supernova (SN) core involves several processes that have been neglected in traditional simulations. Based on a Monte Carlo study we find that the flavor-dependent spectral differences are much smaller than is often stated in the literature. A full-scale S N simulation using a Boltzmann solver and including all relevant neutrino reactions confirms these results. The flavordependent flux differences are largest during the initial accretion phase.

1. Introduction

A supernova (SN) core is essentially a blackbody neutrino source, but in detail the fluxes and spectra depend on the flavor. Up to very small details ufi, u,, Dfi and D, can be treated on an equal footing and will be collectively refered t o as v f i .Numerical simulations usually find a hierarchy ( E v e )< (E,) < ( E V pand ) approximately equal luminosities. The spectral differences offer an opportunity t o observe flavor oscillations as the source fluxes will get partially interchanged. For example, it may be possible to distinguish a normal from a n inverted neutrino mass h i e r a r ~ h y ~ A full-scale numerical simulation by the Livermore group finds for the integrated signal ( E v e )= 13, (E,) = 16 and ( E v e )= 23 MeV and almost perfect equipartition of the luminosities5, results that are representative for traditional numerical simulations. Sometimes extreme spectral hierarchies of up to (E,) : (EVIL) M 1 : 2 have been stated, but searching the literature we find no support for such claims by credible simulations6. Traditional numerical simulations treat the up and v, transport somewhat schematically because their exact fluxes and spectra may not be im-

380

38 1

portant for the explosion mechanism. When a number of missing reactions are included one finds that (E,) and ( E u p )are much more similar than had been thought. The remaining spectral and flux differences are probably large enough t o observe oscillation effects in a high-statistics galactic SN signal, but the details are more subtle than had been assumed in the past.

2. Mu- and Tau-Neutrino Transport

The transport of v, and f i e is dominated by v,n ++ pe- and Fep C ) ne+, reactions that freeze out at the energy-dependent “neutrino sphere.” The flux and spectrum is essentially determined by the temperature and geometric size of this emission region. Moreover, the neutron density is larger than that of protons so that the 0, sphere is deeper than the v, sphere, explaining ( E v e )< ( E D e ) . For v,, in contrast, the flux and spectra formation is a three-step process. The main opacity source is neutral-current nucleon scattering v,N + Nv,. Deep in the star thermal equilibrium is maintained by nucleon bremsstrahlung N N H NNv,V,, pair annihilation e-e+ ++ vpV, and u,F, H v,V,, and scattering on electrons v,e- + e-v,. The freezeout sphere of the pair reactions defines the “number sphere,” that of the energy-changing reactions the “energy sphere,” and finally that of nucleon scattering the “transport sphere” beyond which neutrinos stream freely. Between the energy and transport spheres the neutrinos scatter without being absorbed or emitted and without much energy exchange, i.e. in this “scattering atmosphere” they propagate by diffusion. One may think that the v, spectrum is fixed by the medium temperature at the energy sphere so that (E,) < ( E u p )because the energy-sphere is deeper and hotter than the Ve sphere. However, the scattering atmosphere is more opaque to higher-energy neutrinos because the cross section scales as E;, biasing the escaping flux to lower energies. For typical conditions ( B u r ) of the escaping flux is 50-60% of the value characteristic for the temperature at the energy sphere7. Therefore, the final ( E y e ): ( E v p )ratio is the result of two large counter-acting effects, the large temperature difference between the u, energy sphere and the V , sphere on the one hand, and the energydependent “filter effect” of the scattering atmosphere on the other. Until recently all simulations simplified the treatment of v, transport in that energy-exchange was not permitted in vN-scattering, e-e+ annihilation was the only pair process, and v,e-scattering was the only energy-exchange process. However, it has been recognized for some time

382

that nucleon recoils are important for energy e x ~ h a n g e ~that > ~ >nucleon ~, bremsstrahlung is an important pair process6,7,8,9,10,11,12, and more recently that v,D, -+ v@gp is far more important than e-e+ + v @ , ~as@a V@V@ source reaction6J3. We have performed a detailed assessment of the relevance of the new reactions on the basis of a Monte Carlo study6. To illustrate the results we use a hydrodynamically self-consistent accretion-phase model and show in Fig. 1 (left panel) the v@ flux spectrum when using the traditional input physics (bottom curve). Then we add nucleon bremsstrahlung that increases the flux without changing much the average energy. Next we switch on nucleon recoils that depletes the spectrum's high-energy tail without changing much the overall particle flux. Finally, switching on v,V, annihilation increases the flux without affecting the spectrum much. The compound effect of the new processes is not overly dramatic, but so large that all of them should be included in serious full-scale simulations. In the right panel of Fig. 1 we compare for the same model the flux spectra of v,, f i e and v@, the latter including all reactions. In this example (EGJ almost exactly equals ( E V P )but , the fluxes differ by almost a factor of 2. This is reverse to the usual assumption of a pronounced hierarchy of average energies and nearly exact equipartition of the luminosities. We have studied a variety of stellar background models, some of them self-consistent hydrostatic models, others power-law profiles of density and temperature. For realistic cases we never find extreme spectral hierarchies,

5

I " " I ' " ' I ' J

--------

4 x

1

E3 QJ

z2 a

1 0 0

10 20 30 Neutrino Energy [MeV]

0

10 20 30 Neutrino Energy [MeV]

Figure 1. Neutrino fluxes for an accretion-phase model. Left panel, curves from bottom to top: Flux of vp with traditional neutrino interaction channels, then adding nucleon bremsstrahlung, next adding nucleon recoils, and finally adding veVe annihilation. Right panel: Fluxes for all flavors; the vp curve includes all reaction channels.

383

the differences between (ED,)and ( E V wtypically ) being 0-20%. On the other hand, the fluxes can be rather different, especially during the accretion phase when the atmosphere is quite extended. The different neutrino spheres have then rather different geometric extensions, explaining large flux differences. Later during the Kelvin-Helmholtz cooling phase the star is very compact so that any geometry effect of the radiating surfaces is small. Moreover, the relevant regions are then neutron rich so that the transport physics of V , and v p will become similar. Therefore, during the late phases one expects very similar V e and v p fluxes, while, of course, the v, flux and spectrum remain unaffected by our arguments.

3. Spectral Characteristics

To characterize the neutrino fluxes one naturally uses some global parameters such as the particle flux, the luminosity (energy flux), and the average energy ( E ) . In order to characterize the spectral shape in greater detail one may also invoke higher energy moments ( E n ) . One measure frequently given from numerical simulations is ErmS = because of its relevance for calculating average neutrino-nucleon interaction rates. Sometimes a global analytic fit to the spectra is also useful. Frequently one approximates the flux spectra by a nominal Fermi-Dirac function

d

m

772

with a temperature T and a degeneracy parameter q. This approximation allows one to fit the overall luminosity and two energy moments, typically chosen to be ( E ) and (E’). However, the Fermi-Dirac fit is not more natural than other possibilities; certainly the low- and high-energy tails of the spectra are not especially well represented by this fit. We find that the Monte Carlo spectra are approximated over a broader range of energies by a simpler functional form that we call “alpha fit,”

f ( E ) 0; E@exp [-(a

+ 1)E / E ] .

(2)

For any value of a we have ( E ) = E , a Maxwell-Boltzmann spectrum corresponds to a = 2. The numerical spectra show values of a = 2.5-5, i.e. they are “pinched.”

384 4. A Full-Scale Simulation

In the Garching SN code14 we have now implemented all relevant neutrino interaction rates, including nucleon bremsstrahlung, neutrino pair processes, weak magnetism, and nucleon recoils. Our treatment of neutrinonucleon interactions includes nuclear correlation effects. The transport part of this code is based on a Boltzmann solver. The neutrino-radiation hydrodynamics program enables us to perform spherically symmetric as well as multi-dimensional simulations, thus allowing us t o take into account the effects of convection. To explore the time-dependent properties and long-time evolution of the neutrino signal, we currently continue a state-of-the-art hydrodynamic calculation of a SN into the Kelvin-Helmholtz neutrino cooling phase of the forming neutron star. The progenitor model is a 15 M a star with a 1.28 Ma iron core (Model s15s7b2 from S. Woosley; personal communication). The period from shock formation to 480ms after bounce was evolved in two dimensions. The subsequent evolution of the model is simulated in spherical symmetry. At 150ms the explosion sets in, driven by neutrino energy deposition and aided by very strong convective activity in the neutrinoheating region behind the shock (Fig. 2). Note that a small modification of the Boltzmann transport was necessary to allow the explosion to happen15. Unmanipulated full-scale models with an accurate treatment of the microsl5Gio-2d.a 10000

-

1000

E

Y

v

LT

100

10

0

200 ,t

400

600

Lm.1

Figure 2. Trajectories of the mass shells in the core of an exploding 1 5 M g star. The explosion occurs about 150 ms after shock formation, developing a bifurcation (“bubble”) between the mass that follows the outgoing shock and the mass that settles on the nascent neutron star. Also indicated are the positions of the neutrino spheres of v,, Ye and v,.

385

physics currently do not obtain explosions16. Details of this run will be documented elsewhere; at the time of this writing the CPU expensive calculation is still on the computer. Here we show in Fig. 3 a preview of the main characteristics of the neutrino signal up to 750 ms post bounce. The neutrino signal agrees with what is expected for the standard delayed-explosion scenario. In particular, it clearly shows the prompt v, burst and a broad shoulder in all fluxes during the accretion phase that ends at 200 ms when the explosion has taken off. The average neutrino energies follow the usual hierarchy and they increase with time due to the contraction of the star. We also show the alpha parameter from a global fit according t o Eq. (2). During the accretion phase the vfl flux is least pinched, a t late times the a values of all flavors converge near 2.5. These results agree with and nicely illustrate our previous Monte Carlo findings in that the spectral hierarchy between f i e and vflis rather mild and

-

0

0

200

400

600

0

Time post bounce [ms]

200

400

600

Time post bounce [ms]

400

5

T vl

g

300

0

4

Y .-I

3 6:

-3

6

.6,

200

a

al

3 100

2

a -

0 0

200

400

600

Time post bounce [ms]

2-

0

200

400

600

Time post bounce [ms]

Figure 3. Neutrino fluxes and spectral properties for the full-scale simulation described in the text. The hydrodynamic bounce and shock formation occur at t = 0 (cf. Fig. 2). The right upper plot gives the spectral fit parameter E , the right lower one a. Note that the discontinuity in the latter at t M 480ms is caused by mapping the model from two dimensions to one.

386

in that the average energies converge at late times. Conversely, the particle fluxes differ by almost a factor of 2 during the accretion phase, but cross over shortly after the explosion. At 750 ms the differences between the fluxes continue to increase, an asymptotic value has not yet been reached.

5. Conclusions Traditional numerical SN simulations had two weaknesses regarding the flavor-dependent neutrino fluxes and spectra. First, the interaction between and the stellar medium was schematic, neglecting a number and of important processes. Second, a Boltzmann solver for neutrino transport could not be coupled self-consistently with the hydrodynamic evolution. We have performed a systematic Monte Carlo study on various stellar background models and the first SN simulation that includes all relevant interaction rates and a Boltzmann solver. While the usual relationship between the Y, and fie fluxes and spectra remains essentially unchanged, the up spectrum is much more similar to that of f i e , especially during the Kelvin-Helmholtz cooling phase. Differences of the average energies are in the range 0-20%, with 10% being a typical number. During the accretion phase the Y~ particle flux is smaller than that of Ye by up t o a factor of 2, but later the particle fluxes cross over. Our findings imply that observing neutrino oscillation effects in a SN signal is a more subtle problem than had been thought previously, but by no means impossible. However, when exploring the physics potential of a future galactic SN one should not rely on the notion of an exact flavor equipartition of the luminosities or the extreme spectral differences that have sometimes been stated in the literature.

Acknowledgments This work was supported, in part, by the Deutsche Forschungsgemeinschaft under grant No. SFB-375 and by the European Science Foundation (ESF) under the Network Grant No. 86 Neutrino Astrophysics.

References 1. A. S. Dighe and A. Y . Smirnov, “Identifying the neutrino mass spectrum from the neutrino burst from a supernova,” Phys. Rev. D 62, 033007 (2000) [hep-ph/9907423]. 2. C. Lunaxdini and A. Y. Smirnov, “Probing the neutrino mass hierarchy and the 13-mixing with supernovae,” hep-ph/0302033.

387 3. K. Takahashi and K. Sato, “Effects of neutrino oscillation on supernova neutrino: Inverted mass hierarchy,” hep-ph/0205070. 4. K. Takahashi and K. Sato, “Earth effects on supernova neutrinos and their implications for neutrino parameters,” Phys. Rev. D 66, 033006 (2002) [hepph/0110105]. 5. T. Totani, K. Sato, H. E. Dalhed and J . R. Wilson, “Future detection of supernova neutrino burst and explosion mechanism,” Astrophys. J . 496, 216 (1998) [astro-ph/9710203]. 6. M. T. Keil, G. G. RafTelt and H.-T. Janka, “Monte Carlo study of supernova neutrino spectra formation,” astro-ph/0208035. 7. G. G. Raffelt, “MU- and tau-neutrino spectra formation in supernovae,” Astrophys. J . 561,890 (2001) [astro-ph/0105250]. 8. H.-T. Janka, W. Keil, G. Raffelt and D. Seckel, “Nucleon spin fluctuations and the supernova emission of neutrinos and axions,” Phys. Rev. Lett. 76, 2621 (1996) [astro-ph/9507023]. 9. H. Suzuki, “Neutrino emission from protoneutron star with modified Urca and nucleon bremsstrahlung processes,” Num. Astrophys. Japan 2 , 267 (1991). 10. H. Suzuki, “Supernova neutrinos-Multigroup simulations of neutrinos from protoneutron star,” in: Proc. International Symposium on Neutrino Astrophysics: Frontiers of Neutrino Astrophysics, 19-22 Oct. 1992, Takayama, Japan, edited by Y . Suzuki and K. Nakamura (Universal Academy Press, Tokyo, 1993). 11. S. Hannestad and G. Raffelt, “Supernova neutrino opacity from nucleon nucleon bremsstrahlung and related processes,” Astrophys. J . 507, 339 (1998) [astro-ph/9711132]. 12. T. A. Thompson, A. Burrows and J. E. Horvath, “MU and tau neutrino thermalization and production in supernovae: Processes and timescales,” Phys. Rev. C 62, 035802 (2000) [astro-ph/0003054]. 13. R. Buras, H.-T. Janka, M. T. Keil, G. G. Raffelt and M. Rampp, “Electronneutrino pair annihilation: A new source for muon and tau neutrinos in supernovae,” Astrophys. J., in press (2003) [astro-ph/0205006]. 14. M. Rampp and H.-T. Janka, “Radiation hydrodynamics with neutrinos: Variable Eddington factor method for core-collapse supernova simulations”, Astron. Astrophys. 396, 361 (2002) [astro-ph/0203101]. 15. H.-T. Janka, R. Buras, K. Kifonidis, T. Plewa and M. Rampp, “Explosion Mechanisms of Massive Stars”, in: Core Collapse of Massive Stars, edited by C.L. Fryer (Kluwer Academic Publ., Dordrecht, 2003) [astro-ph/0212314]. 16. R. Buras, M. Rampp, H.-T. Janka and K. Kifonidis, “Improved models of stellar core collapse and still no explosions: What is missing?”, Physical Review Letters, submitted (2003) [astro-ph/0303171].

NEUTRINO FLAVOR CONVERSION INSIDE AND OUTSIDE A SUPERNOVA

C . LUNARDINI Institute for Advanced Study, Einstein drive, Princeton, N J 08540, USA E-mail: [email protected] I briefly review the effects of flavor conversion of neutrinos from stellar collapse due to masses and mixing, and discuss the motivations for their study. I consider in detail the sensitivity of certain observahles (characteristics of the energy spectra of ve and Ye events) to the 13-mixing (sin’813) and to the type of mms hierarchy/ordering (sign[AmT3]). These ohservahles are: the ratio of average energies of the spectra, T E z ( E ) / ( i ? ) , the ratio of widths of the energy distributions, T y z r/F, the ratios of total numbers of v, and Ye events at low energies, S , and in the high energy tails, Rtail. I show that regions in the space of observables T E , T y , Rtail exist in which certain mass hierarchy and intervals of sin’ 813 can be identified or discriminated.

1. Introduction and motivations The mechanism of neutrino flavor conversion due to masses and flavor mixing has been recently established by the combination of the results of solar neutrino detectors and those of the KamLand experiment’. Results from the detection of atmospheric neutrinos and the preliminary data from the K2K experiment’ strongly support the existence of this phenomenon. From the analysis of all the available data, we get a partial reconstruction of the neutrino masses mi (the label i = 1 , 2 , 3 denotes the neutrino mass eigenstates) and of the mixing matrix U , defined by v, = Uaivi, where v, ( a = e , p,T ) are the flavor eigenstates. Using the standard parameterization of the mixing matrix in terms of three angles, 812,813,823, we have:

xi

m; - ml E Am;, = (4 - 30) . lOP5eV2,

tan2812 = 0.25 - 0.85

,

(1)

from solar neutrinos and KamLand, and

m; - m;

E

Am;, = f ( 1 . 5 - 4) . 10K3eV2,

388

tan2 823 = 0.48 - 2.1 (2)

389

from atmospheric neutrinos. The sign of Am:, is unknown. The two possibilities, Am:, M Am:, > 0 and Am:, M Am:, < 0, are referred to as normal and inverted mass hierarchies/ordering respectively (abbreviated as n.h. and i.h. in the text). The mixing angle 0 1 3 , which describes the v, content of the third mass eigenstate, v3, is still unmeasured. We have an upper bound from the CHOOZ and Palo Verde experiments3,‘: sin2 d l 3

2 0.02

.

(3)

The identification of the neutrino mass hierarchy and the determination of have become the main issues of further studies.

013

To achieve these, and other important goals, thc study of neutrinos from core collapse supernovae is particulary interesting. Indeed, these neutrinos are produced and propagate in unique physical conditions of high density and high temperature, and therefore can manifest effects otherwise unaccessible. As will be discussed in the following, due t o the very large interval of matter densities realized there, the interior of a collapsing star is the only environment where two MSW resonances, associated to the two mass squared splittings of the neutrino spectrum, occur. This implies a richer phenomenology of flavor conversion, and therefore wider possibilities to probe the relevant parameters, with respect to the case of neutrinos in the solar system, where only one resonance, i.e. one mass splitting, is relevant at a time. It is important to consider, however, that the study of supernova neutrinos is not exempt of problems. The main obstacle is the absence of a “Standard Model” for supernova neutrinos, i.e. of precise predictions for the fluxes of neutrinos of different flavors originally produced in the star. The features of these fluxes depend on many details of the neutrino transport inside the star and, in general, on the type of progenitor star5. Since observables depend both on the features of the original fluxes and on the flavor conversion effects, it is clear that the extraction of information on the neutrino mixing and mass spectrum require a careful consideration of astrophysical uncertainties.

2. Properties of supernova neutrino fluxes and density profile of the star Neutrinos and antineutrinos of all the three flavors are produced in a supernova and emitted in a burst of 10 seconds duration. At a given time N

390

t from the core collapse the original flux of the neutrinos of a given flavor, v,, can be described by a “pinched” Fermi-Dirac (F-D) spectrum,

-

10 kpc for a galactic where D is the distance to the supernova (typically D supernova), E is the energy of the neutrinos, L, is the luminosity of the flavor v,, and T, represents an effective temperature. The normalization factor equals: ~ ~ ( r l , ) dz 2 3 / ( e 2 - 7 , + I). Supernova simulations provide the indicative values of the average energies5:

=

(EE) = (14-22) MeV, (Ez)/(EE) = (1.1-1.6),

(E,)/(E*) = (0.5-0.8),

-

(5) and the typical value of the luminosity in each flavor: L , (1 - 5 ) . los1 ergs s-’. The luminosities of all neutrino species are expected to be approximately equal, within a factor of two or so5. The vfi and v, (P, and oT) spectra are equal with good approximation, and therefore the two species ca,n be treated as a single one, vx (ox).The pinching parameter 7, can vary between 0 and 3 for v, and lie, while smaller pinching is expected for u p , v,: vp = vr 0 - 2. The matter density profile met by the neutrinos, at least in the first few seconds of their emission, can be approximated by that of the progenitor star6. The latter is well described by the radial power law6:

--

with C

Y

1 - 15.

3. Conversion effects Let us consider the conversion of neutrinos as they propagate from the production region outwards in the star, for the case of normal mass hierarchy (Am:, > 0). As shown in Fig. 1 (positive density semi-plane), the eigenvalues of the Hamiltonian in matter and the flavor composition of its eigenstates change with the variation of the matter density along the neutrino trajectory. At production, the mixing is suppressed due to the very large density (p 10l1 g . cmP3), therefore the eigenstates of the Hamiltonian coincide with the flavor states. At lower densities, the neutrinos undergo two MSW resonances (level-crossings). The inner resonance (H) is governed by the parameters Am;, and 013 and is realized at p lo3 g . ~ m - ~ ( l o M e V / E )The .

-

-

391

H

VX

*

/ "1

density propagation inside the ctar

U

e'

Earth matter effects

Figure 1. The level-crossing diagram for normal mass hierarchy. The solid curves represent the eigenvalues of the Hamiltonian in matter.

probability of transition between the eigenstates of the Hamiltonian (jumping probability) in this resonance, P H ,strongly depends on 813 as discussed later in this section. The second resonance, (L) is determined by Am& and 812 and happens at lower density, p (30 - 140)(10MeV/E) g . cmP3. For the values of parameters in Eq. (1) the jumping probability in this resonance is negligible (adiabatic propagation). The neutrinos leave the star as mass eigenstates and therefore do not oscillate on the way from the star t o the Earth. If they cross the Earth before detection, oscillations are restarted due to Earth matter effects7. Since they have opposite sign of the matter potential, antineutrinos do not undergo any resonance in the matter of the star (negative density semi-plane in Fig. 1). As an effect of conversion, the u, and u, fluxs in the detector, F, and F,, are combinations of the original u, and v, ( Ye and 0%)fluxes. Considering for simplicity the case of no Earth crossing, one gets:

-

F, = PH sin2 652F,O + (1- PH sin2 812)F: , FC = cos2 812 F," + sin2 812 F i .

(7)

For inverted hierarchy (Am;, < 0), the H resonance is in the antineutrino channel, while the L resonance is unaffected. In this case the fluxes

392

in the detector equal:

F, = sin2 O12F,0+ cos2 O12F,0

,

As expected, here the jumping probability PH appears in the expression of the De flux, in contrast with Eqs. (7). In summary, the supernova neutrino signal is sensitive t o the mass hierarchy and to 013 for the following reasons: (i) depending on the hierarchy the H resonance affects either neutrinos or antineutrinos; (ii) the observed u, or Ye fluxes depend on the value of 013 via the jumping probability PH. The latter can be calculated using the Landau-Zener formula and the profile (6). The result is:

It follows that three regions exist: (i) Adiabaticity breaking region: sin2 0132 10V6(E/10MeV)'I3, where P H N 1; (ii) Transition region: sin2 613. (E/10MeV)2'3, where O d P H d 1; (iii) Adiabatic region: sin2 0132 lop4 (E/10MeV)2/3,where PH 2: 0. Notice that if PH = 1 (adiabaticity breaking region) Eqs. (7) and (8) coincide. Thus, we get equal predictions for normal and inverted hierarchy and any sensitivity to the mass hierarchy is lost. Furthermore, from Eqs. (7) and (8) it is easy to see that, in the extreme case in which the original fluxes in the different flavors are equal (F: = F j , F," = F;), conversion effects cancel and one has F, = F:, FE = F,". 4. Probing 6x3 and the mass hierarchy

There are two approaches to probe the neutrino oscillation parameters and at the same time take into account the uncertainties on the features of the original fluxes. The first is to perform a global fit of the data, determining both the oscillation parameters and the parameters of the original fluxes s i m u l t a n e ~ u s l y ~However, ~~. a completely general analysis is not possible with this method, due to the large number of parameters involved. The second approach is to single out and study (numerically and analytically) specific observables which (1) have maximal sensitivity to the oscillation

393

parameters of interest and ( 2 ) whose dependence on the astrophysical uncertainties is minimal or well understood. Here I summarize some aspects of this latter method".

4.1. Observables

A good prescription to find observables which fit the criteria (1) and ( 2 ) stated above is t o consider the parameters describing the energy spectra of events induced by u, , and the same parameters for the fie-induced spectra, and take their ratios. For instance, let us consider the spectra of u, events at the SNO detector from the CC scattering on deuterium, u, +d -+ p+p+e-, and the fie events at the SuperKamiokande detector from inverse beta decay, Ve +p t n+e+. We can define the following four observables: (1)the ratio of the average energies, T E , and ( 2 ) the ratio of the widths, r r , of the u, and V,-induced spectra:

(3) the ratios of the numbers of ue and fie events in the low energy tails, S , and (4) in the high energy tails,

Here the overbarred quantities refer to antineutrino spectra, and the width r is defined as r ( ( E 2 ) / ( E ) '- l)1/2.The high and low energy cuts, E L ,E L ,EL, EL can be suitably chosen to optimize the analysis".

=

4.2. Distinguishing between extreme possibilities: scatter

plots Let us consider the three extreme cases: A. Normal hierarchy with PH = 0 (i.e. large 813, see sec. 3); B. Inverted hierarchy with PH = 0; C. PH = 1 (i.e. small 813) with normal or inverted hierarchy (recall that results do not depend on the hierarchy in this case, see sec. 3). Figure 2 shows the regions in the space of the observables T E , r y , for the cases A, B, C, obtained by scanning over the astrophysical parameters in the intervals discussed in sec. 2 . The values of the oscillation parameters JArn$,I,Am&, 8 2 3 and 8 1 2 have been taken to coincide with

394

the current best fit points with 10% error, as expected from near future measurements. To calculate Rtail the cuts E L = 45 MeV and EL = 55 have been used.

1.3 1.25 1.2 1.15 1.I 1.05 1

L'

P,=O, n.h.

A

P,=O,

0

P , = l , n.h. and i.h.

i.h.

0.95 0.9

0.85 n Q V.U

0

0.1

0.2

0.3

Figure 2. Scatter plot in the space of the observables C discussed in the text.

T E , r y , Rtazl for

the cases A, B,

The results in the figure can be easily interpreted in terms of the different size of the conversion effects in the different caseslO.They show that large regions of the parameter space exist where only one among the scenarios A, B or C is possible. Also regions appear when two of these scenarios

395

are realized. If these regions are selected by the experiments, the third possibility will be excluded. The scenarios in which 0 < PH < 1 are not shown in Fig. 2. For normal hierarchy and 0 < PH < 1 we expect the allowed region to be intermediate between the regions found for A and C. Similarly, for inverted hierarchy and 0 < PH < 1 the region of possible values of parameters is intermediate between the regions of cases B and C. For this reason, the conclusions we derived from Fig. 2 have essentially an exclusion character and not the character of establishing one of the scenarios A, B, C. It is clear that the potential of the method we have discussed depends on the statistics and therefore on the distance from the supernova. It can be checked" that for a relatively close star ( D 6 4 kpc) the error bars are substantially smaller than the field of points so that the discrimination of different possibilities becomes possible. Acknowledgments

I would like t o thank the organizers of NOON2003 for making my participation to the workshop possible with their financial support. I am also grateful for the stimulating atmosphere I enjoyed there. The research work presented in these proceedings was supported by the Keck fellowship and the NSF grants PHY-0070928 and PHY99-07949. References 1. See e.g. the review by E. Lisi, these proceedings, available at http://www-

sk.icrr.u-tokyo.ac.jp/noon2003/. 2. See e.g. the reviews by C. Yanagisawa and T. Kobayashi, these proceedings, available at http://www-sk.icrr.u-tokyo.ac.jp/noon2003/. 3. CHOOZ Collaboration, M. Apollonio et. al., Phys. Lett. B466 (1999) 415430. 4. F. Boehm et. al., Phys. Rev. D62 (2000) 072002. 5. See e.g. M. T. Keil, G. G. Raffelt, and H.-T. Janka, astro-ph/0208035, and references therein. 6. G. E. Brown, H. A. Bethe and G. Baym, Nucl. Phys. A 375 (1982) 481. 7. See e.g. A. S. Dighe and A. Y. Smirnov, Phys. Rev. D62 (2000) 033007, and references therein. 8. V. Barger, D. Marfatia, and B. P. Wood, Phys. Lett. B547 (2002) 37-42. 9. H. Minakata, H. Nunokawa, R. Tomas, and J. W. F. Valle, Phys. Lett. B542 (2002) 239-244. 10. The discussion is based on the paper by C. Lunardini and A. Y . Smirnov, hep-ph/0302033.

FUTURE DETECTION OF SUPERNOVAS

M. R. VAGINS University of California, Irvine 4129 Reines Hall Irvine, C A 92697, USA E-mail: [email protected]

Prospects for future detection of supernova neutrinos are discussed, with particular emphasis on water Cherenkov detectors. Presently under study, a novel proposed modification to the Super-Kamiokande experiment to significantly enhance its supernova detection capabilities is presented publicly for the first time.

1. Same Detectors, Different Day Table 1 contains a fairly complete list of the expected supernova responses of the world's various neutrino detectors, including those being proposed, those under construction, and those currently running. As is often the case, size matters. Now, most of these detectors or detector ideas have been around for quite a while. But is there anything new under the exploding sun? As it happens, there are a couple of new developments worth mentioning ... 0

0

A forgotten signal mode in water Cherenkov detectors is getting another chance. A possible upgrade for Super-K which could be applied to other water Cherenkov detectors is being studied.

2. The Lost Mode

In the immediate excitement after SN1987A, Wick Haxton published a paper' outlining various nuclear physics reactions which could occur in water during a galactic supernova. One of the most interesting was the charged current interaction,

396

397

v,

+Is

0 + e-

+16

F

(1)

These O(v,,e-)F events have an E,, threshold of 15.4 MeV and are somewhat backwards-peaked. They have tremendous sensitivity to the temperature of the supernova burst. Back in 1987 there were just two problems: (1) Neutrinos would have t o oscillate with near maximal mixing to get many events. (2) It was almost impossible to separate them from the more common inverse beta events.

So the idea was pretty much forgotten ... until now. Of course, sixteen years later it turns out that neutrinos do oscillate with near maximal mixing, and there may in fact be a way to tag, eventby-event, the inverse beta supernova “background.” The O(v,, e - ) F events are precious, because, as one can see in Table 2, one thing the world is currently lacking is a good SN v, detector. 3. So, What’s All This About Tagging P.,’s? In what began as a search for a new method of extracting the supernova relic neutrino [SRN] signal without background issues, for close t o a year now Fermilab’s John Beacom and I have been tossing around ideas regarding modifying the Super-K detector. It has proven t o be a very fruitful partnership: everything which follows in this paper is the result of our ongoing, combined efforts.

3.1. The Initial Goal Nearby supernovas are fairly rare events. However, all the neutrinos which have ever been emitted by every supernova since the onset of stellar formation suffuse the universe. These so-called supernova relic neutrinos, if observable, could provide a steady stream of information about not only stellar collapse and nucleosynthesis but also on the evolving size, speed, and nature of the universe itself. Super-Kamiokande has recently conducted a search for these supernova relic neutrinos’. However, this study was strongly background limited, especially by the many low energy events below 19 MeV which swamped any possible SRN signal in that most likely energy range. Consequently,

398

this study could see no statistically significant excess of events and therefore was only able t o set upper limits on the SRN flux. If it were possible to look for coincident signals, i.e., for a positron’s Cherenkov light followed shortly and in the same spot by the gamma cascade of a captured neutron, then these troublesome backgrounds could be completely eliminated. “Wouldn’t it be great if we could tag every supernova relic neutrino,” we thought. Well, the reaction we are looking for is:

So the real question is, how can we reliably identify the neutron? 3.2. The Challenge Of course, it is well known that free neutrons in water get captured by free protons and emit 2.2 MeV gammas, far below Super-K’s normal trigger threshold. However, if we could manage to see these we’d be in business! Maybe we could just lower the Super-K threshold briefly after each regular trigger ... While this would be possible, and no SK change except a new trigger board would be required, efficiency will still be fairly low. SRN’s are rare, of this signal. so what we really want is to get Hence, we need something in the water which will compete with the hydrogen in capturing neutrons. Such a competitive process is very similar mathematically to resistors in parallel, and can be exactly calculated. 3.3. The 0.1% Solution

We finally turned to the best neutron capture nucleus known: gadolinium. It has a nice 8.0 MeV gamma cascade, easily visible in Super-K. Unlike metallic Gd, the compound gadolinium (tri)chloride, GdC13, is water soluble. We found that in order to collect 50% of the neutrons on gadolinium and 50% on hydrogen you’d need to put just 9 tons of GdC13 in Super-K! That’s exactly two cubic meters. No problem! Even better, to collect >90% of the neutrons on gadolinium you’d only need to put 100 tons of GdCl3 in Super-K. That’s about twenty cubic

399

meters, or a 0.1% concentration of Gd in the tank, and with it we can tag all the SRN events. SRN models vary, but with this solute in the water Super-K should see about five SRN events each year with no background at all. Now imagine Hyper-K seeing loo+ supernova relic neutrinos every year ... But is the weird stuff in the water dangerous? The short answer is, not a t all. Both human and animal toxicology studies have been done3i415>6, and the bottom line is that you could drink at least 12 liters of this solution every day straight from the tank and suffer no detectable effects from the GdC13, even upon autopsy.

3.4. The Price of Gd in China From a physics standpoint it certainly seems like GdC13 is a nice compound to use for tagging neutrons, but can we afford 100 tons or more of it? As it turns out, there has been a dramatic revolution in the price of gadolinium over the past two decades. The opening of new mineral fields in the Gobi desert and the introduction of new rare earth refining and purification technologies have caused the price to plummet three orders of magnitude in recent years. If we had tried to use gadolinium in Super-Kamiokande from day one the raw materials alone would have added $400 million dollars to the cost of that $100 million project. Today, acquiring 100 tons of 99.99% pure GdC13 will cost us just under $330,000. The formerly high price of gadolinium could very well explain why no one has ever even proposed using gadolinium in very large detectors before. 3.5. What Else Can W e Do With G d ?

3.5.1. Solar 3, Well, once we can identify V , Is, we can dramatically improve our search for solar Fe 's. John and I estimate a two-orders-of-magnitude improvement in sensitivity over our present Super-K result7, so if there is as little as one solar F e out of 10,000 solar v,'s we will know it.

3.5.2. Galactic Supernovas Naturally, if we can do relics, we can do a great job with galactic supernovas, too. With 0.1% gadolinium in the Super-K tank,

400

(1) the copious inverse betas get individually tagged, allowing us to study their spectrum and subtract them away from (2) the directional elastic scatters, which will double our pointing accuracy. (3) The l60NC events no longer sit on a large background and are hence individually identified, and (4) the O(v,, e - ) F events’ backwards scatter can be clearly seen, providing a measure of burst temperature and oscillation angle.

3.5.3. Reactor A n t i n e u t r i n o s

If we were t o introduce a 0.1% solution of gadolinium into SuperKamiokande, we could collect enough reactor antineutrino data to reproduce KamLAND’s first published results8 in just three days of operation. Their entire planned six-year data-taking run could be reproduced by Super-K with GdC13 in seven weeks, while Hyper-K with GdC13 could collect six K a m L A N D - y e a r s of i7, data in j u s t o n e day. Super-K would collect enough reactor V,’s every day to enable it to monitor, in real time, the total reactor V , flux. This means that, unlike KamLAND, it would not be dependent on the power companies which operate the reactors accurately reporting their day-to-day power output. Although Super-K with GdC13 will not be able to extract spectral information over the entire energy range to which scintillator detectors are sensitive, it will have the unique ability to provide some i7, directional information via the emitted positrons’ Cherenkov lightg. This should, especially given the extremely high statistics involved, allow significantly tighter constraints t o be placed on the solar neutrino oscillation parameters than any other method which could conceivably become operational before the close of the present decade, and possibly far beyond. We would have these data in hand within months of the decision to introduce GdC13 into SuperKamiokande. Note that these plentiful reactor Ti, events would not be confused with the comparatively rare relic supernova V,’s or solar V,’s because of the widely differing antineutrino energy ranges and spectra of the three processes.

3.6. Gadzooks! Since John and I were focusing on the low energy side of things, we haven’t even gotten into how this solute should also allow our high energy friends to differentiate between atmospheric (or long baseline) neutrinos and an-

401

tineutrinos of all species, reduce backgrounds t o proton decay searches, and so on. We propose calling this new project “GADZOOKS!” In addition to being an expression of surprise, here’s what it stands for: Gadolinium Antineutrino Detector Zealously Outperforming Old Kamiokande, Super!

3.7. A Modest Proposal Pouring a bunch of stuff into Super-K is a big step, and not to be done lightly, no matter how promising things may look initially. Here’s what comes next: (i) Spend the next year or so exploring the chemistry, stability, and optical properties of GdC13 in detail. (ii) Understand any changes needed in the SK water system and Monte Carlo the modified detector’s response using what’s learned above as input. (iii) Build a small test tank (one supermodule) with exactly the same materials as in SK. Put in PMT’s, cables, water, and GdC13 and let it sit for two years. Check for GdC13-induced damage. (iv) If everything looks good, in mid-2005 during the last month(s) of SK-I1 put in 9 tons of GdCl3 to make sure we really understand our backgrounds. Look for reactor antineutrinos! (v) Finally, if every test still looks good, in 2006 we’ll mix 100 tons of GdC13 into SK-I11 and prepare for the bright new days of supernova and reactor neutrino data ahead! References 1. W. Haxton, Phys. Rev. D36, 2283 (1987). 2. M. Malek et al., Phys. Rev. Lett. 90, 061101 (2003). 3. T.J. Haley, K. Raymond, N. Komesu and H.C. Upham, Brit. J . Pharmacol. 17,526-532 (1961). 4. S. Yoneda, N. Emi, Y . Fujita, M. Omichi, S. Hirano and K.T. Suzuki, Fundam. A p p l . Toxicol. 2 8 , 65-70 (1995). 5. G. Bannenberg, M. Lundborg, A. Johansson, Toxicology Letters 80, 105-107 (1995). 6. A. Lieber et al., J . Virol. 71,8798-8807 (1997). 7. Y. Gando et al., Phys.Rev.Lett. 90, 171302 (2003). 8. K. Eguchi et al., Phys. Rev. Lett. 90, 021802 (2003). 9. M. Apollonio et al., Phys. Rev. D61, 012001 (2000).

402 Table 1. Total number of neutrino events expected t o be observed for a core-collapse supernova explosion at a distance of 10 kiloparsecs (32.6 lightyears) for detectors which are being proposed (*), under construction (**), and currently running (***). Detector

Total Neutrino Events

Hyper-Kamiokande (*)

~300,000

UNO (*)

~140,000

Super-K-I11 (**)

-9,700

Super-K-I1 (***)

-8,400

OMNIS (*)

-2000

SNO (***)

-1,000

KamLAND (***)

-500

Borexino (**)

-200

MiniBooNE (***)

-200

LVD (***)

-200

MOON (*)

-70

Baksan (***)

-25

Table 2. Total number of v, events expected t o be observed in existing detectors for a core-collapse supernova explosion at a distance of 10 kiloparsecs. Detector Super-K-I11 Super-K-I1

Total ve Events -700 O(v,,e-)F

+ -100

-630 O(v,,e-)F

SNO

-100

KamLAND

-30

Borexino

elastic scatters

+ -80

~ 1 5

e.s.

Session 5

Lepton Flavor Violation, Leptogenesis and Proton Decays

This page intentionally left blank

BIRTH OF NEUTRINO ASTROPHYSICS

M. KOSHIBA University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

For more details, see my review article; “Observational Neutrino Astrophysics”;Physics Report, 220 (1992) Nos.5&6,pp.229-482.

Conception There was a very important prenatal event. That was the radiochemical work of R.Davis using the reaction v , + C ~to~e-+Ar37. ~ The conclusion was that the solar neutrinos are only about 1/3 of what you expect from the Standard Solar Model of J.Bahcal1. This could be considered as the conception of the Neutrino Astrophysics and was the impetus for us to begin seriously working on the solar neutrinos

The experiments 1) KamiokaNDE; Imaging Water Cerenkov, 20% PMT coverage, 3,OOOtons, ca.3MUS$ Feasibility experiment. 2 ) Super-KamiokaNDE;the same as above, 40% PMT coverage, 50,00Otons, ca. 1OOMUS$. Full scale solar neutrino observatory. (Both 1,000m underground in Kamioka Mine) (NDE for Nucleon Decay Expenmenu Neutrino Detection Experiment))

405

406 Fish-eye View of KamiokaNDE’s Interior

50cm+ PMT which made the two detectors precision devices

Fish-Eye View of SuperKamiokaNDE’s Interior

407

Detector Performances 1) Through p in S-KamiokaNDE Shots at 50 nanosecond intervals 2) Discrimination between electron and muon

The !Ji has just elntered the dc:tector.

408

The p has reached to the bottom of the detector, while the Cerenkov light in water is still on its way.

409

The data of the outer anticounter are shown, while the inner data are moved to the top right.

The top e-event has a blurred radial distribution of Cerenkov photons, while the bottom p-event has a crisp ring image. The discriminationbetween e and p is accomplished with an error probability of less than 1%.

4 Accomplishments of KamiokaNDE 1) The astrophysical,i.e.,with D,T and E, observation of solar neutrinos by means of v,-e scattering. 2) The observation of the neutrino burst from Supernova 1987A by means of anti-v, on p producing e+ plus neutron. 3) The discovery at more than 40 of the anomaly in the atmospheric VJV, ratio. Neutrino oscillation. Non-zero masses of v’s. 4) Killed SU(5) by proton decay lifetime and SUSYSU(5) also by non-zero masses of v’s.

410 Solar Neutrinos Standard Solar Model (SSM)

~ Encru ~ (uev) t m

~

~

iw-w

Mw-m

Solar Neutdno Experimenls Target

Data / SSM 1-

' Homestake

I'CI Karniokande e- (water) .SAGE "Ga GALLEX "Ga SK e- (water)

.

. .

0.33f0.03 0.54k0.07

0.52f0.06 0.59*0.06 0.475f0.015

Solar neutrinos o(arniokandelll~ Dec. 28,1990 - Feb. 6,1995 (1036 days )

c-9,"

Y Fukuda et 81.. Phys. Rev, Len. 77 (1wB) 1683

Enerav spectrum of solar neutrino events Kamlokande II and 111 (2079 days )

7

8

8

10

11

12

13

14

20

Tolal Energy (MSV)

Based on -600 solar v events Y FuWe et a1 , Phys Rev L&

77 (le6+ltB83

41 1 The detector performance at the beginning of 1987.

The observed signal of the supernova neutrino burst. It was immediately confirmed by IMB experiment in USA. The combined results, T, of 4.5MeV and the total v energy output of 3x105'erg gave strong support to the theoretical model. 100

t

I

80

-

60

-

.

.

'

'

'

I

.

.

.

,

.

.

.

=40-

ot

-zoo

200

0

400

TIMHsec)

Atmospheric neutrinos v,/v, has to be 2 or larger

L=up to 13000 km -. = - 2 B low energy (E,c 1 GeV) ve+VI

-

3 Ylf

B highenergy

"6

Error in flux-25%, double ratio-5% Neutrino oscillations :

#1

412

The Neutrino Oscillation Consider 2 neutrino case for simplicity. The weak eigenstate v, is a superposition of vmland vd,,namely y~ = vmlcos 8 + vm2sin 8 with a parameter 8. the angik between v, and vml. The two states, vmland vm2, make beat with the ffequency proportional to E,-E, =m12-m22=Am2, since E-p+(m2/2p),thereby changing the relative intensity of vmland vm2. This causes a partial transformation of v,, to v,.

3e Allowed parameter region by the Karniokanc Karniokande atmospheric neutrino mesasurernent

lo

1

sin' ze

413

Super-KamiokaNDE Accomplished Three things so far. 1) Established the solar neutrino observation with much better statistics. 2) Firmly established, at more than 90. the non-zero masses of v's and their oscillations. 3) Non-observation of nucleon decays is giving more stringent restriction on the possible type of future grand unified theory.

Solar neutrinos (Suoer-Kamiokandel May 31,1996 -July 13,2001 (1496 days )

E, = 5.0 - 20 MeV

(14 5 eventslday)

8B flux : 2.35 i 0.02 f 0.08 [x Data

SSM(BP2WO)

lo6 /crn2/sec]

= 0.465 ' 0 0 . 0 0 5 ! ~ ~ ~(BP2wO ~ 5 0 5 x l@Jcrnzisec)

The Sun by Neutrinograph The Sun as seen by V'S

and its orbit in the Galactic coordinate.

You have to excuse the poor angular resolution because the neutrino astrophysics is still in its infantile stage.

414 Eneruv soectrum of solar neutrino events Super-Kamiokande 1496 days

O'

'

6

'

'

'

8

'

'

'10'

'

'12' ' ,14,20 Energy(MeV)

Bad fit to SMA and Just-so solutions.

Atmospheric neutrino results from SK-1 M Shwawa faUIeSKCOllab ZWZ Mmc& MayZW2

LP w n e

talkat Neublno

Down goin%

Allowed reaion combined with SNO data Super-Kamlokande 1496

Zenith Spectrum ve+vwT (95%C.L

lo4

1 0 ' ~ 10"

lo-'

I

S F u W el a1 , Phw

Ian*(Q) 102 Len B 539 (2002) 179

415

%lo4

* Rates: Homestake(Cl), GALLEX (Ga). SAGE (Cl), SK (HZO). SNO CC+NC (020) Znnith srreotra from S R energy ipectra ofo~ectronsat 7 zenith angle Mn8 + 6 nigms)

-

(dw

LMA Is the most llkely solution.

Implications of Non-zero Neutrino Masses 1) The right handed neutrinos have to exist. Standard Theory has to be modified and SU(5) is discarded as possible GUT. 2) Very low energy neutrinos will make the total reflection at very low temperature. Very nice for the future possibility of observing the 1.9K Cosmic Neutrino Background. For the sake of giving proper credit, shown here Is the author list of the supernova neutrino observation.

416

Here is the author list of the oscillation paper.

The newest result from KamLAND. The oscillation of the anti-e-neutrinos from the reactor. CPT theorem and the confirmation of S-KamiokaNDE;

sin2r =0.833, Am2=5.5x1O-kV2

First Results from KamLAND: Endeuce for Reactor Anti-Neutrino Disappearance K E g u c h i , S . E n o m o t o , K F ~ oJ.Goldman,H.Hanada,H.Ikeda,K.Ikeda,KInoue, , K.Ishihara, W Iloh, T.Iwamoto, T.Kawaychi, T.Kawashima, H.Kinoshita, Y.Kishmolo, M.Koga, Y Koseki, T.Maeda, T.Mitsui, M.Motoki, K.Nakajuna, MNakajuna,T.Nakajuna, H.Ogawa, K.Owadq T.Sakabe,I.Shirmm, J.Shirai,F.Suekane, A.Suzulu,K.Tada, O.Tajima, T Takayama, K Tamae, H.Watanabe, I.Busenitz, Z.DjuTcic, K.McKimy, D-M.Mei, A Piepke, E.Yakushev, B.E.Berger, Y.D.Chan, M.P.Decowsla, D.A.Duyer, S.J.Freedman,Y.Fu,

BK.Fujikawa,K.M.Heeger,KTLesko,K.-B.Luk,H.Murayama,D.R.Nygen,C.E.Okada, A.W.Poon,H.M.Steher, L.A.Winslow,G.A.Horton-Smith,RD.McKeowo,I klter,B.Tiploo, P.Vogel, C E Lane, T.Miletic, P Gorham, G Guillian, I.Leamed, J.Maricic, SMatsuno, S.Pakvasa,D.Dazeley, D.Hatakeyamq M Murakarm, R.C Svaboda, B.D Dieterle, M.DiMauro, J.Dehuiler, G.Gratta, K.lshii,N.Talich, Y.Uchida, M.Batygav, W.Bugg, H.Cohn, Y Efremenko, Y.Kamyshkov, A.Kozlov, Y.Nakayama, C.R.Gould, H.J.Kanuowsla, D.H.Markoff I.A.Messimore, K.Nakamura, R.M.Rohm, W.Tomaw, A.R.Youog, and Y.-F.Wang

(KamLAND Collaboration)

417

For fun : From the Am2's obtained, we can get a possible mass spectra of elementary particles using the See-saw mechanism. And if we consider a small electromagnetic mass shift occurred in one of the phase changes in the very early Universe, we get the nice regularity as seen in the last slide. Anyone of you challenge to explain this regularity?

(S)FERMION MASSES AND LEPTON FLAVOR VIOLATION - A DEMOCRATIC APPROACH *

K. HAMAGUCHI Deutsches Elektronen-Synchrotron D E SY , 0-22603, Hamburg, Germany and Department of Physics, Tohoku University, Sendai 980-8578, Japan E-mail: koichi.hamaguchi8desy. d e

MITSURU KAKIZAKI AND MASAHIRO YAMAGUCHI Department of Physics, Tohoku University, Sendai 980-8578, Japan E-mail: [email protected], [email protected]. ac.jp

It is well-known that flavor mixing among the sfermion masses must be quite suppressed to survive various FCNC experimental bounds. One of the solutions to this supersymmetric FCNC problem is an alignment mechanism in which sfermion masses and fermion masses have some common origin and thus they are somehow aligned to each other. We propose a democratic approach to realize this idea, and illustrate how it has different predictions in slepton masses as well as lepton flavor violation from a more conventional minimal supergravity approach. This talk is based on our work in Ref. 1

1. Introduction The origin of the structure of fermion masses and their mixing is a long standing puzzle in modern particle physics. This is highlighted when one sees large flavor mixing in the neutrino sector whereas the generation mixing in the quark sector is small. Supersymmetric (SUSY) extension of the standard model is very attractive not only because it stabilizes the electroweak scale against radiative corrections, but also because it may provide some crucial hints on physics *Talk presented by M. Yamaguchi

418

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at ultra high energy. In scenarios where SUSY breaking and its mediation to the Standard Model sector occurs at very high energy, the resulting soft SUSY breaking masses will carry information on physics around the mediation scale and below. On the other hand, the existence of the soft masses would raise serious phenomenological problems. Among other things, squarks and sleptons acquire gauge invariant masses which in general contain generation mixing. It is well-known that a random choice of those masses would cause large flavor changing neutral current (FCNC) which exceeds experimental bounds by a few orders of magnitude. Thus some mechanism t o suppress the flavor mixing in the supersymmetry breaking masses is requisited. There are several approaches which have been proposed to solve this notorious SUSY flavor problem. We should note that the problem is delicate because the sfermion masses are very sensitive to ultra-violet physics, presumably close t o the Planck scale physics. In any case, the attempts are classified into the following three classes: 1) decouppling sfermion masses, 2) universal sfermion masses, and 3) aligned sfermion masses. The decoupling solution requires that the sfermions in the first two generations are very heavy (of order 10 TeV) while those in the third generation do not exceed 1 TeV, which is favored as the solution of the naturalness problem. Large squark masses in the first and second generations would, however, drive the stop mass squared negative at two-loop level, resulting in undesired color breaking. This can be avoided by several ways, one of which introduce extra chiral multiplets. Though possible, a viable model would be fairly complicated. The second scenario, the universal sfermion masses, is widely considered in the literature. Minimal Supergravity (mSUGRA) scenario is a representative of this class. In this scenario, the sfermion masses are degenerate at the mediation scale of the SUSY breaking, and thus there is no flavor mixing in the sfermion masses at that scale. Flavor mixing in the Yukawa interaction in the quark and lepton sectors re-generates the flavor mixing in the sfermion masses at lower energy scale. Thus the FCNC is generally suppressed, but quite often the present and/or future experiments can have sensitivity to probe such small flavor mixing caused by various Yukawa interactions a t high energy. We should note, however, that the justification of the universality hypothesis is in general quite non-trivial. Here we would like to consider the third scenario, namely the alignment mechanism. The basic assumption is that the mechanism which controls the fermion mass structure at the same time dictates the sfermion mass

420

structure. One then expects that the sfermion mass matrix is somewhat aligned with that of the corresponding fermions and thus the SUSY flavor problem coming from the sfermion masses will be ameliorated. Furthermore, the nontrivial sfermion mass spectrum can reflect the mechanism how the fermion masses are generated, which is not the case in the universal sfermion mass approach. As we mentioned earlier, the sfermion masses are very sensitive t o ultra-violet (UV) physics one has in mind. To make a more quantitative statement, we need to make a hypothesis on a model of flavor at UV. Here we will discuss a supersymmetric extension of a democratic approach which gives phenomenologically successful masses and mixing for the quarks and leptons, including neutrino sector. The purpose of the talk is in fact two fold: 1) To propose a new alignment mechanism as a solution of the SUSY flavor problem. 2) To illustrate how predictions of alignment mechanism can be different from the conventional mSUGRA approach. We shall focus on slepton masses and lepton flavor violation.

2. Democratic Approach The basic idea of the democratic approach is that the 3 repetitions of quarks and leptons should be treated on an equal footing, and thus interchangeable.2 This is concisely described in terms of a permutation symmetry of three objects S3. Then the three generation fermions, which we symbolically denote by Qi ( i = 1, 2, 3), are 3 dimensional representation, 3, of the S3. It is well-known that S3 has only three irreducible representations, two of which are one dimensional and the other one is two dimensional representation. In fact, 3 is decomposed as 3 = 1 2, where 1 is a trivial representation and 2 is the two dimensional one. Now 1 is assumed to be approximately identified with the third generation. When Qi are up-type quarks, then we assume the following identification:

+

We now consider mass matrices of quarks and leptons. We assume that

s U ( 2 ) doublet ~ quarks and singlet quarks obey different 5’3, and thus on a mass matrix one S3 acts from the left and another S3 acts from the right

421

and so there is a unique invariant under the S3 x S3. We then have one massive and two massless states. To get a realistic mass spectrum, one therefore has to introduce breaking terms. Here we assume that they are of diagonal form and thus the mass matrix of, for instance, the up-type quarks becomes3

where the first matrix is the invariant mass matrix whose eigenvalues are 1, 0, 0 and the second one is the breaking term we are considering. The values of 6 and E should be properly chosen t o reproduce the realistic quark masses. A similar structure is assumed for down-type quarks and charged leptons. From this type of mass matrices, we obtain hierarchical mass structure in the quarks and charged lepton sectors, and small mixing among the quarks. The neutrino mass structure is different .4 We assume that the neutrino masses are of Majorana type, and thus only one S3 for doublet leptons is involved in the mass matrix. In this case there are two S3 invariants: one is the universal form proportional to the unit matrix, and the other one is the democratic form which is proportional to

Unlike the quark case, we shall take the universal form

with diagonal breaking terms. The choice of this form yields degenerate neutrino mass spectrum, hi-large mixing angles for solar and atmospheric neutrinos and small Ue3. We should note that a justification of the universal form was considered in the context of brane-world ~ c e n a r i o . ~ To summarize the features of the fermion masses, the democratic ansatz is very successful in fermion masses and mixing. They are dictated by S3 symmetries, whose breaking may be attributed to the nature of the Higgs sector. We now apply the idea of the democracy to the sfermion masses, which constitutes an alternative to the universal sfermion masses. Unlike the fermion masses, the Standard Model gauge invariance allows sfermion

422

masses by themselves. In fact they are originated from non-trivial coupling between visible and hidden sectors in the Kahler potential. We assume that the Kahler potential respects the S3 symmetries and so do the fermion masses. Thus for each sfermion mass matrix involves only one S3 and like the neutrino masses there are two S3 invariants. In general the sfermion mass matrix will be a linear combination of them:

where p is a parameter which is assumed to be order unity generically. It is easy to diagonalize this matrix: d i a g ( l , l , 1 p ) . Thus, if p # 0, the sfermion masses are characterized by 1)non-degeneracy and 2) flavor mixing. Since the source of the flavor mixing is a tiny breaking of the ,573, the flavor mixing of the sfermion masses is suppressed. We have checked that it basically survives various FCNC constraints from present experimental data. This is nothing but a realization of the alignment mechanism. Here we need to make an important remark on the left-handed slepton masses. The democratic part in the Kahler potential for the doublet leptons would generate non-canonical kinetic terms, which would effectively induce the democratic part in the neutrino mass matrix. It would upset the successful pattern of the neutrino mass matrix. Thus the democratic part in the doublet (left-handed) leptons should be absent. Therefore we expect universal masses for left-handed sleptons. This is a non-trivial interplay between the neutrino masses and the slepton mass spectra.

mi

+

3. Slepton Masses and Lepton Flavor Violation We have argued that in our model with the democratic ansatz the righthanded sleptons i R have non-degenerate masses and flavor mixing. On the contrary, the left-handed sleptons i L will have degenerate (and universal) masses with on flavor mixing. This mass pattern will give us unique predictions on the slepton mass spectrum as well as on the lepton flavor violation (LFV). We have the following mass spectrum for the sleptons:

mpR = mfiR# mFR, mpL = mfiL= mFL

(6)

We should note that the third generation can be either heavy or light. This is different from the renormalization group effect of the third generation Yukawa couplings, which only makes the stau lighter than the others.

423

This mass spectrum (6) should be testable in future collider experiments, especially in a linear collider. When the sfermion masses possess flavor mixing, sfermion-gaugino loop diagrams will induce LFV such as p + ey. Computation of the branching ratio of p + ey was done in Ref. 1. It should be compared with the present and expected future reach by the experimental upperbound6 of 1.2 x Here we give a rough estimate. The present MeG experiment7 N experimental bounds constrain the flavor mixing in the sfermion masses as

( ~ 4 5~(a few) ) ~ x 1~ 0 - ~ (612)RR5 (a few) x 1 0 - ~ (612)LR,RL

for the slepton mass mi find

M

-

< (a few) x

(7)

low6

100 GeV. On the other hand, in our model we

Thus we expect that our model generically predicts the branching ratio just around the experimental bound, and within the reach of the future experiment. In fact, in Ref. 1, we have shown that 1) p + ey does not exceed the present bound and 2) in a wide region of the parameter space the branching ratio can be larger than the expected future reach, as far as the sparticle masses are around the electroweak scale. Here it is interesting t o compare our case with the conventional mSUGRA scenario where LFV occurs due t o possibly large renormalization group effects from right-handed neutrino Yukawa coupling^.^^^ In the mSUGRA, the sfermion masses are assumed t o be universal at the Planck or GUT scale. Of course they are subject to radiative corrections. In fact the effect can be compactly evaluated by using renormalization group. Contribution from gauge interaction is generation blind, on the other hand, Yukawa interaction may discriminate generation. When the right-handed neutrino Yukawa couplings are fairly large, they will give flavor dependent contribution to the left-handed sleptons. Thus unlike the democratic case we are considering the degeneracy will be broken in the left-handed slepton masses. Furthermore flavor mixing in the lepton sector arises through the left-handed sleptons, and thus the chirality structure of the magnetic

424

moment type operators which generate LFV is different between the two scenarios. The difference may be observable if polarized muon beam is available in p. + ey decay experiment," by looking the angular distribution N (1f PFcos O ) , where PF is the muon polarization. 4. Summary SUSY Standard Model has more than 100 parameters for sfermion masses and their mixing. Generic parameter choice would predict too large FCNC problem, which is the referred to as the SUSY FCNC problem. In this talk, we have proposed the democratic approach t o fermion and sfermion masses as an alignment solution to the SUSY FCNC problem. It turned out that the model has unique predictions on slepton masses and lepton flavor violation such as p -+ ey, which will be testable in future experiments. In particular our model can be distinguished from the universal scalar mass approach with renormalization group effects from righthanded neutrino Yukawa couplings. A more general conclusion which was illustrated in our study is that collider experiments and LFV processes may provide crucial hints to discriminate the theory of flavor. References 1. K. Hamaguchi, M. Kakizaki and M. Yamaguchi, arXiv:hep-ph/0212172. 2. H. Harari, H. Haut and J. Weyers, Phys. Lett. B 78 (1978) 459; H. Fritzsch, Phys. Lett. B 73 (1978) 317. 3. Y. Koide, Phys. Rev. D 28 (1983) 252; Phys. Rev. D 39 (1989) 1391. 4. H. Fritzsch and Z. Z. Xing, Phys. Lett. B 372 (1996) 265; M. Fukugita, M. Tanimoto and T . Yanagida, Phys. Rev. D 57 (1998) 4429; M. Fujii, K. Hamaguchi and T. Yanagida, Phys. Rev. D 65 (2002) 115012. 5. T. Watari and T. Yanagida, arXiv:hep-ph/0205090. 6. M. L. Brooks et al. [MEGA Collaboration], Phys. Rev. Lett. 83 (1999) 1521. 7. L. M. Barkov et al., Research Proposal for experiment at PSI. 8. F. Borzumati and A. Masiero, Phys. Rev. Lett. 57 (1986) 961. 9. J. Hisano, T. Moroi, K. Tobe, M. Yamaguchi and T. Yanagida, Phys. Lett. B 357 (1995) 579; J. Hisano, T. Moroi, K. Tobe and M. Yamaguchi, Phys. Rev. D 53 (1996) 2442; Phys. Rev. D 53 (1996) 2442; J. Hisano, D. Nomura and T. Yanagida, Phys. Lett. B 437 (1998) 351; J. Hisano and D. Nomura, Phys. Rev. D 59 (1999) 116005. 10. Y. Kuno and Y. Okada, Phys. Rev. Lett. 77 (1996) 434.

pe CONVERSION EXPERIMENTS: TESTING CHARGED LEPTON FLAVOR VIOLATION

ANDRIES VAN DER SCHAAF Physak-Instatut der Unaversitat Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland E-mail: [email protected]

The recent evidence for neutrino mixing shows that lepton flavor is not a conserved quantity. Due to the smallness of the neutrino masses effective flavor changing neutral currents among charged leptons remain negligible in the Standard Model. Whereas b --t s y has a probability of O(10W4) ,u --t ey is expected with a branching ratio around Observable rates would be an unambiguous signal for physics beyond the Standard Model and indeed, many extensions of the model are constrained best by the present experimental limits on charged lepton flavor violation. In this talk I will discuss experimental searches for charged lepton flavor violation with emphasis on ,ue conversion in muonic atoms.

1. Introduction

.W-.. .

W .--\ \

I

P

'ew

t

I

t

I

b

e

r

,

S

u.c.t

0 u,d

K'(892) u,d

b+sy

P+ey

Figure 1. 2nd order weak contributions to ,u --t ey and b + sy.

v-Oscillations directly lead to finite rates for rare muon decays (see Fig. 1). Such second-order charged weak interactions result, however, in negligible contributions to the branching ratios since they are strongly sup-

425

426

pressed dynamically:

Note that the corresponding mechanism in the quark sector leads to b + sy with a branching ratio of 0(10-4) due to the large top mass. The observation of charged lepton number violation would thus be an unambiguous sign of new physics and indeed, a number of Standard Model extensions are probed sensitively112. 2. Present constraints on charged lepton flavor violation Table 1. Upper limits on branching ratios of particle decay modes that do not conserve lepton flavor. Decay

Limit

p+-+ e+y

1.2.10-11

[Ref] Exp./Lab. MEGA

Decay

Limit

r+ 2pe

1.8. 10V6

[Ref] Exp./Lab. l4

1.0. lo-"

SINDRUM r+ p2e

1.5.

l4

8.3. lop1'

SINDRUM r-+ 3e

2.9. 10V6

l4

p-Ti+e-Ti

6.1.10-13

SINDRUM K + - + n + p e 2.8. 10-l'

l5

BNL

p-Ti+

e+Ca*

3.6.

SINDRUM K;+

p-Pb+

e-Pb

4.6.

p-Au+ e-Au

1.9.

p++

e+e+e-

p+e-

tf

p-e+

lo-''

4.7.

l6

BNL

SINDRUM K;+ nope 4.4.

l7

Fermi

SINDRUM Bo+ pe

1.2.

l8

BaBar CLEO

pe

T+

ey

2.7. l o p 6

lo

CLEO

Bo+ r e

5.3. l o p 4

l9

T+

by

1.1.10-6

11

CLEO

Bo+rp

8.3.1OW4

l9

1.0.

l2

Belle

Zo+ep

1.7.1OP6

2o

2.0. l o p 6

l3

BaBar

Zo+ e r

9.8.

2o

1.9.10W6

l4

CLEO

Zo+ p r

1.2.1OW5

2o

r+ 3p

OPAL

Table 1lists the present limits on processes forbidden by charged lepton flavor conservation. Best constraints come from the forbidden p and K decays where dedicated experiments have been performed. One should keep in mind, however, that couplings to the third generation could be enhancedl in which case the T limits start to become interesting as well.

3. p e conversion versus p

--+ ey

Which limit from Table 1 gives the best constraint on charged lepton flavor violation not only depends on the experimental sensitivities but also on the

427

mechanism of the violation. In many scenarios, for example, the branching ratio for pe conversion is lower by a factor of O ( a ) compared to p + ey. In other cases, i.e. when the violations are mediated by leptoquarks’l or R-parity violating couplings to SUSY particles”, the situation is reversed. In neutrino-less p e conversion leaving the nucleus in its ground state the nucleons act coherently, which boosts the conversion probability relative t o the rate of nuclear muon capture which is the dominant competing process for medium and heavy nuclei. For the same reason transitions to the ground state are enhanced relative to other final states which are expected to occur with a probability below 10 % for all nuclear systems. Experiments have been performed on a variety of nuclei (see Table 1). Several authors have studied the nuclear physics aspects of the process, unfortunately with conflicting resultsZ4J5. From an experimental point of view coherent pe conversion has many nice features. Whereas the sensitivity to p + ey is limited by the performance of large-solid-angle high-resolution photon detectors giving rise to background from accidental ey coincidences already at present beam intensities, pe conversion would fully benefit from future high-intensity muon beams.

4. Background sources in searches for pe conversion The signature for pe conversion is a single mono-energetic electron with an energy (depending on the muon binding energy) around 100 MeV. There is a variety of processes that may result in the emission of electrons in the region of interest. Electrons resulting from pe conversion in muonic atoms are emitted at the kinematic endpoint of muon decay in orbit which constitutes the only intrinsic background. Since the decay rate drops steeply above m,c2/2 (see Fig.2 for muonic gold) the set-up may have a large geometrical acceptance and still the detectors can be protected against the vast majority of decay and capture events. The rate at the endpoint scales with the energy resolution to the 5th power and a resolution around 1%is sufficient to keep it below Other potential background involves cosmic rays or beam contaminations. Radiative T - capture followed by y + e+e- produces electrons with energies around 100 MeV with a probability of O(10-6/MeV). Such prompt beam related background can be suppressed by beam pulsing, a beam veto counter, or beam purity.

428

Figure 2. Electron spectrum for muon decay in orbit in the case of muonic gold obtained by scaling the lead spectrum from Ref.26.

5 . MECO

MEC027, an approved BNL experiment, aims at a single-event sensitivity of 2 x for conversion on aluminum (see Fig. 3). To achieve this large

ector solenoid /-I bea

stop

cryst calor

Figure 3. MECO set-up. Pions are produced by 8 GeV/c protons on a W target situated in a graded solenoidal field. Negatively charged particles of
gain in sensitivity a novel beam concept has been developed. Secondary beam particles from the interactions of 4 x s-l 8 GeV/c protons in a tungsten target are collected and transported t o the experimental target by superconducting solenoids. The overall length of the solenoid system including the detection solenoid is 27 m. Both the production target and the

429

experimental target are situated in regions of diminishing field strength. As a result many particles originally moving backward are reflected resulting in increased solid angles. MECO uses beam pulsing to fight prompt beam induced background. After a bend solenoid particles get charge separated. With the help of a slit system halfway the s-shaped transport solenoid a wide momentum band of one charge polarity can be transmitted. During the 700 ns wide observation window starting M 600 ns after a proton bunch the beam load has dropped by 2-3 orders of magnitude. Due to the 26 ns pion lifetime the 7 1 - rate drops much faster, to about one per minute after 600 ns which is sufficiently low to keep the background from radiative pion capture under control. Since muonic atoms at medium 2 have lifetimes of several 100 ns a large fraction of them is still "alive" when the time window opens. For aluminum which is the first choice for the target 50% of the muonic atoms decay in the time window. Assuming a measuring time of lo7 s the expected single-event sensitivity is 2 x

6 . SINDRUM 11: a new limit for pe conversion on gold

In the past decade in a series of searches with the SINDRUM I I spectrometer limits on the conversion rates on medium and heavy nuclei have improved significantly (see Table 1). This program was finished in the year 2000 with an effective 81 days measurement on gold. Figure 4 shows a vertical cross section through the spectrometer. Pions are removed with the help

1

A exit beam Solenoid

F inner dnfl chamber

B gold target G outerdrifl chamber C vacuum wall H superconducting coil D ~CintiIIairhodoscope I helium bath I E Cerenkov hodoscope J magnet yoke

I

1111

I 111 -

'

'

'

'

'

' lm '

'

'

'

'

Figure 4. SINDRUM II; typical trajectories of a beam p- and a hypothetical conversion electron are indicated.

430

of an 8 mm thick CH2 degrader at the entrance of a 9 m long solenoid ( Libearnsolenoid” in Fig.4) which is coupled directly to the spectrometer. At 50 MeV/c pions stop in the degrader and muons go through. The range distributions depend mainly on the momentum distribution of the beam. By carefully adjusting the fields in the various beam elements the required steeply falling range distribution was obtained. 4.37 f 0.32 x 1013 muonic gold atoms were formed in the target as monitored by observing muonic X-rays with a Ge(Li) detector positioned outside the spectrometer coil. Given the overall detection efficiency for pe conversion (including the 97% capture probability) of 7.0% this leads to a single-event sensitivity of 3.26 f 0.22 x

70

80 ETOT (MeV)

90

1

100

Figure 5 . The measured energy distribution is compared with simulated distributions for muon decay in orbit and pe conversion. No events are found above 100 MeV.

Nw

Figure 6. L ( N w eand )

max

.f”‘ L(N,,)dN,,.

Figure 5 shows the resulting e- energy distribution. The steep drop below 74 MeV reflects the requirement that the electron moves at least 46 cm from the spectrometer axis. The measured spectrum is in reasonable agreement with the prediction for decay in orbit. One event is observed around 96.4 MeV which is marginally compatible with the energy distribution expected for pe conversion. We performed a likelihood analysis of the energy distribution including a flat background from cosmic rays and radiative pion capture in addition to the distributions shown in Fig. 5. Figure 6 shows the resulting likelihood function L(N,,) for the expectation value of the number of pe conversion events. The 90% C.L. upper limit is N Y ( 9 0 % C.L.) = 2.45 deduced from Jl.45L(N,e)/JrL(N,,) =90% . Combined with the single event sensitivity quoted above this leads to:

BE:’d < 8 x

9001oC.L.

(2)

431

7. Summary and Outlook Forty years after Pontecorvo’s original proposal of neutrino oscillations2* (and five years after his death) Super-Kamiokande found strong evidence for oscillations in the signals from atmospheric neutrinos2g. When neutrinos oscillate lepton flavor is not conserved just as quark flavor isn’t. Still, due to the tiny neutrino mass splittings on the scale of rnw neutrino mixing can not be observed in processes involving charged leptons such as p+ t e+y, pe conversion or K + pe. This situation changes dramatically in many extensions of the Standard Model, such as supersymmetry or left-right symmetry and in many cases experimental bounds on charged lepton flavor violation give the best constraints. The sensitivities reached in experimental searches for muon number violation ha.ve improved steadily in the past fifty years. Presently, the upper limits on the branching ratios are 0(10-12) and even better searches have been initiated recently. After a first signal would be found “precision” experiments (i.e. 2-dependence of pe conversion, decay asymmetries of p+ -+ e f y and p + 3e relative to the p spin direction) would be needed to discriminate between the various options. Such program would require both better detection systems and better muon beams, like those discussed within the framework of Neutrino Factories30. References 1. Aysto et al., CERN Stopped Muons Working Group, Preprint CERN-TH/2001-231, hep-ph/0109217 (2001). 2. Y. Kuno and Y. Okada, Rev. Mod. Phys. 73, 151 (2001). 3. M. Ahmed e t al., MEGA Collaboration, Phys. Rev. D65, 112002 (2002). 4. U. Belgardt et al., SINDRUM Collaboration, Nucl. Phys. B229, 1 (1988). 5. L. Willmann et al., Phys. Rev. Lett. 82, 49-52 (1999). 6. P. Wintz, Proc. Lepton-Baryon 98 (Trento), eds. H.V. Klapdor-Kleingrothaus and I.V. Krivosheina (Bristol and Philadelphia: Institute of Physics Publishing), p 534 (1998). 7. J. Kaulard et al., SINDRUM II Collaboration, Phys. Lett. B422, 334-38 (1998). 8. W. Honecker et al., SINDRUM II Collaboration, Phys. Rev. Lett. 76, 200 (1996). 9. F. Riepenhausen, Myon-Elektron-Konversion in Gold, Ph. D thesis Zurich University (1999). 10. K.W. Edwards et al., CLEO Collaboration, Phys. Rev. D55, R3919-23 (1997). 11. S. Ahmed et ak., CLEO Collaboration, Phys. Rev. D61, 071101(R) (2000). 12. K. Abe et al., Belle Collaboration, Search for 7 + p~ydecay at Belle, LP 01

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(Rome), KEK-PREPRINT-2001-79 (2001). 13. M. Roney, Search for T + py at BaBar, ICHEPU2 (Amsterdam), July 24-31 2002, to appear in the proceedings (2002). 14. D.W. Bliss et al., CLEO Collaboration, Phys. Rev. D57,5903-07 (1998). 15. R. Appel et al., Phys. Rev. Lett. 85,4482 (1999). 16. D.Ambrose et al., Phys. Rev. Lett. 81, 5734 (1998). 17. L. Bellantoni, KTEV Collaboration, Proc. 36th Rencontres d e Moriond (Les Arcs, France), 10-17 Mar 2001, hep-ex/0107045 (2001). 18. G. Tong G, Lepton flavour violation at e'e- colliders, ICHEPO2 (Amsterdam), July 24-31 2002, to appear in the proceedings (2002). 19. R. Ammar et al., CLEO Collaboration, Phys. Rev. D49,5701-04 (1994). 20. R. Akers et al., 2.Phys. C67, 555 (1995). 21. E. Gabrielli, Phys. Rev. D62,055009 (2000). 22. A. de Gouv&aet al., Phys. Rev. D63,035004 (2001). branching ratio, 23. L. Barkov et al., Search for p+ + e+y down to available at http: //www .icepp. s .u-tokyo .ac .jp/meg. 24. T.S. Kosmas, Progress in Particle and Nuclear Physics 48,307-16 (2002). 25. R. Kitano et al., Phys. Rev. D66,096002 (2002). 26. R. Watanabe et al., Atom. Data and Nucl. Data Tab. 54,165 (1993). 27. M. Bachman et al., MECO, BNL proposal E 940 (1997). 28. B. Pontecorvo, Sou. Phys. JETP 6,429 (1958). B. Pontecorvo, Sov. Phys. JETP 7,172 (1958). B. Pontecorvo, Sov. Phys. JETP 26,984 (1968). 29. Y . Fukuda et al., Super-Kamiokande Collaboration, Phys. Rev. Lett. 81, 1562 (1998). 30. http://muonstoragerings.web.cern.ch/muonstoragerings/

NEUTRINO BI-LARGE MIXINGS AND FAMILY Masako BAN DO^ and Midori O B A R A ~ Aichi University, Mzyoshi ! $Aichi 470-0296, Japan Graduate School of Humanities and Sciences, Ochanomizu University, Tokyo 112-8610, Japan After a brief review of quark-lepton relations in grand unified theories (GUT), we show that the Pati-Salam relation with only one type of Higgs field configuration with "four zero symmetric texture" can reproduce two large neutrino mixings as well as observed mass differences. This is quite in contrast to the case of S U ( 5 ) where bi-large mixings essentially come from the charged lepton sector with nonsymmetric charged lepton mass matrix.

1. Neutrino Masses and GUT Recent results from KamLAND together with the neutrino experiments by Super-Kamiokande 2 , 3 and SNO have confirmed neutrino oscillations with two large mixing angles 5,6,7,8. with the mass squared differences are

5 sin2 21312 5 0.86, 5.1 x lop5 5 Am:, 5 9.7 x lop3 eV2, (1.1) 0.4 5 tan21312 5 3.0. 1.4 x 10K3 5 Am;, 5 6.0 x 10K3 eV2, (1.2)

0.29

As we can express the neutrino mixings in terms of MNS matrix ', which are further divided into two terms, Ul and U,, the unitary matrices which diagonalize the 3 x 3 charged lepton and neutrino mass matrices, Ml and M,; UMNS =

U/MK

ul u: U!MvUv = diag(m,,,m,,,m,,),

= diag(m,,m,,m,),

(1.3) (1.4)

in analogous to CKM matrix derived from quark mass matrices, Md and Mu;

t UCKM = UuUd, ULMuVu = diag(mu,m,,mt),

U J M d V ,= diag(md,m,,mb),

(1.5) (1.6)

where U and V are unitary matrix acting on left- and right-handed fermions, respectively and diag(m1, m2, m3) are mass eigen values of fermions. The observed tiny neutrino masses are most naturally explained if tree mass terms "E-mail address: bandoQaichi-u.ac.jp bE-mail address: [email protected]

433

434

are forbidden by some symmetry and they come only from the higher dimensional operator (the so-called see-saw mechanism), which we adopt in this paper. Then the neutrino mass matrix M , is derived from huge right-handed Majorana masses ( M R )and the Dirac masses (Mu,) of EW scale;

M, =

M T M~ ; M~

~

~

.

(1.7)

In the SUSY standard model, the following Yukawa terms, which has family indices 3 x 3, Y , , j , connect s U ( 2 ) 2, ~ Q and L t o 1 fermions, U R , ~ R , ~ R , U R ; w y

= QL(Y,uRH, f YddRHd) f L ( x e R H u f Yu,VRHd) -k YRVRVRHR.(1.8)

The S U ( 2 ) doublet up- and down-type Higgs fields, H,, Hd with VEVs, v U ,vd give mass matrices + Mu = Y,v,, Md = Y d V d , MUD= Y,, Y,, Ml = x 2 ) d after the standard symmetry is broken down to S U ( 3 ) x U ( l ) e m . The Majorana mass term (the last term of Eq. (1.8) including S U ( 2 ) singlet Higgs field H R gives neutrino right-handed mass term, M R = YRVRwhere the VEV YR is expected to be much larger than EW scale. 2. Hierarchy Problem Before going to the discussion of neutrino masses, we make comments on the hierarchy problems whose origin may indicate something to the family structure. If one wants t o construct unified theory, it is governed by the scale Mp which is far higher than electroweak scale. We know that the GUT scale, MG is near below the Planck scale, M p which is usually taken as the reduced Planck mass, l / d m . This huge discrepancy between two scales, M p and M w is called ”strong hierarchy problem”. The introduction of supersymmetry (SUSY) provides a good solution for solving strong hierarchy. The GUT itself needs several energy scales appearing in the steps of GUT breakings into standard symmetry GI -+ Gz . . . G M ,with each of scales actually expressed as AnMp. There we use the typical hierarchical parameter X 0.2 (the Cabibbo mixing angle). Especially recent neutrino small masses indicates some intermediate scales of order GeV, which is roughly equal to AsMp. Thus we here recognize ”mild hierarchy” appearing as AnMp in terms of the typical hierarchical parameter X 0.2 (the Cabibbo mixing angle). The intermediate scale M R is of order GeV corresponds to AsMp. On the other hand, the hierarchical fermion masses are also controlled by the same A; the electron mass, the smallest Dirac fermion mass is almost X8Mt,in terms of the top quark mass, mt = 170 Gev.. It is interesting that both in high and law energy regions (at Mp and M w scales) common the power law, Anmild hierarchy structure, which may give a hint of the origin of family. Indeed the simplest example

-

-

435

to explain this is to introduce the anomalous U ( l ) x family quantum number: the power structure comes from the Froggatt-Nielsen mechanism according to which Yukawa couplings come from higher dimensional operators A" = ( &)" with n determined to compensate the U ( l ) x symmetry by Froggatt Nielsen field O(X = -1). This simplest example of family symmetry has a characteristic feature; If we assume the strength of all coupling constants of order 1, the Froggatt Nielsen mechanism produces the power hierarchical coefficients of A" where n is solely determined by the U(1) charges of relevant fields and so such power structure is always of factrizable form. Within the framework of GUT the X charge is assigned to the each GUT multiplet. Also this U ( l ) x explains the "mild hierarchies" of symmetry breaking scales by assigning X charges t o Higgs fields. We could also introduce more complicated family symmetries beyond abelian case. In the following we shall examine how such family quantum numbers can be consistent with recent neutrino experimental data.

3. GUT and Family symmetry Now if we assume some GUT and that the family structure is the same for all the members of a multiplet. Two types of relations are derived between the unitary matrices U,,d,l,,, according to the different kinds of symmetries of the system. In the following sections we investigate how the unitary matrices, Ud, U,, Ul and U,,, , are mutually related with each other if we assume some grand unified gauge theory or some family symmetry. First, within the standard model, there is no relation between them since the up and down fermions couple to different Higgs fields. If the hierarchical mass structure comes from the Froggatt Nielsen mechanism, then the power factor is determined merely from the X charges of relevant left-handed fermions. Then, since we have already s U ( 2 ) in ~ standard model, the S U ( 2 ) doublets, Q and L have common charges, 41,q 2 ,43 and 1 1 , 1 2 , 1 3 , respectively. yie1ding

UCKM with

2

?

ud -2u,, UMNs ? ul

21

u ~ , u,,, ?

(3.9)

indicating the same power structure. Second, in the Georgi-Glashow

S U ( 5 ) symmetry ( S ( 3 ) ,x s U ( 2 ) ~x U ( 1 ) y c S U ( 5 ) ), where ( Q L , ~ R , u R ) belong to the same multiplet, 10, while ( L , ~ R t)o, 5 * . Note that S U ( 5 ) GUT never provides new relations for M C K M and M N M S ,although we have a familiar relation, A41 t) M Z , once we fix the representations of Higgs field, Md t)M T , where tt means that they are mutually related by accompanying some CG coefficients according to the representations of coupled Higgs field.

436

Thirdly, the Pati-Salam symmetry S U ( 4 ) p s conibines UL with z q into FL and d L with I L into FR, so we have UCKM 21 U, N u d Y U M N SN ul 2 u,. Thus we see that the Pati-Salam symmetry with X-charge power law does predict the same hierarchical mixing matrix both for UCKM and U M N S . Thus in order to reproduce neutrino large mixing angles within Pati-Salam symmetry, we should discard simple Froggatt Nielsen mechanism and give up factrizable property of power law structure. The simplest example of such possibilities is to introduce "zero texture" which has been extensively investigated by many authors'l. Note that even in such case we have the relation of mass matrices, MUDH Mu, Ml H Md. For larger GUT, SO(10), the situation is essentially the same, so far as they include the subgroups above mentioned. In SO(10) all the fermions of a family may form a single multiplet 16, and so if the Froggatt Nielsen mechanism works, all the components of Q(l6) do have common X charge. So if we take Gi(l6) to i-th family, and since Pati-Salam symmetry dictates small neutrino mixing angles. Thus we must introduce twisted family structure by introducing new fermions $(lo) and Qi(l6) must not be identified to i-th family (non-parallel family structure), which is most naturally implemented in Es GUT?. Leaving the discussion of S U ( 5 ) symmetry to Kugo's talk, I here show an example of the Pati-Salam symmetry in the next section. 4. Pati-Salam Symmetry with Symmetric Four Zero Texture The model we introduce here is the following example'' of symmetric "four zero" texture which has been extensively investigated by many authors''. Under the Pati-Salam symmetry ( we name this "up-road option" because the neutrino large mixing angle is related to up-quark mass matrix M , as mentioned in the previous section). We show that the following configuration of the representation of Higgs field for up-quark mass matrix

0 126 0

0

10 126

('7 0) 0

Mu = (126 10 1 0 ) , M R =

ThfR

0

(4.10)

.

which may be compared with the Georgi-Jahrscog of down-type mass matrix. Now MvD is obtained by multiplying Clebsch-Gordan coefficient, 1 or -3;

0 -3a

OaO MuYmt(::;)

H'uD=mt(-ia

0 :3),

. = ~

a=-

mt

b = " mt c '

'

(4.11)

Then M vare easily calculated. In order to get large mixing angle 1923, the of 2-3 element of Mu should be of the same order of magnitude as 3-3 element, namely,

437

h

2:

-

1+ r

- JGmgmc

called ”seesaw enhancement”

M” =

(T

lop7. Such kind of enhancement mechanism is

12,13,8

7)

o $ o

With tiny r , M,, is approximately given,

m: = -

‘ P o 9m: h = -ac/3r, (w) , a = 2hb/c,

(4.12)

p = -3ha/c,

-

-

where sin2 2823 can be made large when h O(1). However it is non-trivial to reproduce both the experimental bound sin2 2012 and mass ratio rnvlz/mvz3 and we should not stay in order-of-magnitude calculation. Since all the matrix elements of M,, are now expressed in terms of up-quark masses with the parameter r or h, the neutrino masses and mixing angles at GUT scale are obtained straightforwardlylO. The obtained formula at GUT scale is to be compared with the neutrino experimental data at GUT scale. Here we estimate the RGE evolution of neutrino mass matrix at M Z by using the approximate formula obtained by Haba and Okamura14. the transformed expression of a , and h of Eq. (4.11) from M E to mz scale are given as,

where the RGE factors 6’s is estimated as at most 0.1, We compare the corrected values of neutrino masses and mixing angles at M z scale and the experimental data and found that within the error only the small region of h near around 1 is consistent with the observed mass ratio and two mixing angles, for which case the final expressions of neutrino masses and mixing angles at GUT scale is,

with x =

6,E. y =

We leave the detailed calculations in our full

paperlo>?.and here note that our model predicts not only the order of magnitudes but the exact vales of all neutrino masses and mixing angles. This is remarkable and enables us to predict Ue310.1irrespectively of CP phase. It is remarked that our neutrino mass matrix has been determined with almost uniquely determined within error bars of up-quark masses, it can make the prediction of leptgenesis calculation once we fix the CP phase, which are now under calculation by Obara, Kaneko Tanimoto and Bando15. In conclusion we

438

have seen that the up-road option can reproduce the present neutrino experimental data very well. However also down-road option may be also worthwhile t o be investigated , in which case the Nature may show ”twisted family structure”. On the contrary in the case of up-road option it requires ”parallel family structure”. We thank t o M. Tanimoto, A. Sugamoto and T. Kugo and S. Kaneko and the members attending the Summer Institute 2002 held a t Fuji-Yoshida and at the research meeting held in Nov. for instructive discussions. M. B. is supported in part by the Grant-in-Aid for Scientific Research No. 12640295 from Japan Society for the Promotion of Science, and Grants-in-Aid for Scientific Purposes (A) “Neutrinos” (Y. Suzuki) No. 12047225, from the Ministry of Education, Science, Sports and Culture, Japan. References 1. KamLAND report hep-ex/0212021 to be submitted to Phys. Rev. Lett. 2. SK Collab., Phys. Lett. B433 (1998) 9;ibid.436,33(1998);ibid. 539,179(2002). 3. Super-Kamiokande Collaboration, Phys. Rev. Lett. 86 (2001) 5651; ibid.86,5656(2001). 4. SNO Collaboration, Q.R. Ahmad et al., Phys. Rev. Lett. 8 9 (2002) 011301; ibid. 89, 011302 (2002). 5. M. Maltoni, T. Schwetz and J.W.F. Valle, arXiv:hep-ph/0212129. 6. G.L. Fogli et al., arXiv: hep-ph/0212127. 7. J.N. Bahcall, M.C. Gonzalez-Garcia, and C. Pena-Garay, arXiv:hep-ph/0212147. 8. A. Yu. Smirnov, Phys. Rep. D48 (1993) 3264. 9. Z. Maki, M. Nakagawa and S. Sakata, Prog. Theor. Phys. 28 (1962) 870. 10. M. Bando and M. Obara, arXiv: hep-ph/0212242;M. Bando and M. Obara, in preparatin. 11. P. Ramond, R.G. Roberts and G.G. Ross, Nucl. Phys. B406 (1993) 19; J. Harvey, P. Ramond and D. Reiss, Phys. Lett. B 9 2 (1980) 309; Nucl. Phys. B199 (1982) 223; S. Dimopoulos, L.J. Hall and S. Raby, Phys. Rev. Lett. 6 8 (1992) 1984; Phys. Rev. D45 (1992) 4195; Y. Achiman and T. Greiner, Nucl. Phys. B443 (1995) 3; D. Du and Z.Z. Xing, Phys. Rev. D48 (1993) 2349;H. Fritzsch and Z.Z. Xing Phys. Lett. B353 (1995) 114; K. Kang and S.K. Kang, Phys. Rev. D 5 6 (1997) 1511; J.L. Chkareuli and C.D. Froggatt, Phys. Lett. B450 (1999) 158; P.S. Gill and M. Gupta, Phys. Rev. D57 (1998) 3971; M. Randhawa, V. Bhatnagar, P.S. Gill and M. Gupta, Phys. Rev. D 6 0 (1999) 051301; S.K. Kang and C.S. Kim, Phys. Rev. D 6 3 (2001) 113010; M. Randhawa, G. Ahuja and M. Gupta, arXiv: hep-ph/0230109. 12. M. Bando, T. Kugo and K. Yoshioka, Phys. Rev. Lett. 80 (1998) 3004. 13. M. Tanimoto, Phys. Lett. B345 (1995) 477. 14. H. Haba and N.Okamura, hep-ph/9906481. 15. M. Bando, S. Kaneko, M. Obara and M. Tanimoto, in preparation.

LEPTOGENESIS AND NEUTRINO MASSES

M. PLUMACHER Theory Division, CERN, CH-1211 Geneva 23, Switzerland Thermal leptogenesis explains the baryon asymmetry of the universe by the out-ofequilibrium decays of heavy right-handed neutrinos. In the minimal seesaw model this leads to interesting implications for light neutrino properties. In particular, quasi-degenerate light neutrino masses are incompatible with leptogenesis. An upper bound on light neutrino masses of 0.1eV can be derived, which will be tested by forthcoming laboratory experiments and cosmology.

1. Introduction The observed baryon asymmetry of the universe is one of the most intriguing problems of particle physics and cosmology. The precision of measurements of the asymmetry has significantly improved with the observation of acoustic peaks in the cosmic microwave background (CMB). The WMAP ) error experiment has measured the baryon asymmetry with a ( 1 ~standard of 5% 1,

-

which is consistent with the results of standard primordial nucleosynthesis (BBN), obtained from the measurements of relic nuclear abundances. A simple and elegant explanation of the observed baryon asymmetry is offered by neutrino physics. During the past years data on atmospheric and solar neutrinos have provided strong evidence for neutrino masses and mixings. In the seesaw mechanism the smallness of these neutrino masses is naturally explained by the mixing of the left-handed neutrinos with heavy Majorana neutrinos. Further, the connection between baryon and lepton number in the high-temperature, symmetric phase of the standard model due to rapid sphaleron transitions is by now firmly established '. As in classical GUT baryogenesis 5 , out-of-equilibrium decays of the heavy Majorana neutrinos can then generate a lepton asymmetry which, by sphaleron processes, is partially transformed into a baryon asymmetry '.

439

440

A beautiful aspect of this ‘leptogenesis’ mechanism is the connection between the cosmological baryon asymmetry and neutrino properties. This , very much connection is established by standard kinetic calculations like in big bang nucleosynthesis 5 , where light nuclei play the role analogous to leptons in leptogenesis. The requirement of ‘successfulbaryogenesis’, i.e. the existence of neutrino masses and mixings for which the predicted and the observed value of the baryon asymmetry are in agreement, constitutes a severe test for models of neutrino masses, which has been extensively explored during the past years lo. The dynamical generation of a baryon asymmetry requires that the particle interactions do not conserve baryon number, C and CP. In leptogenesis these conditions are realized by the couplings of the heavy Majorana neutrinos Ni. Their decays can generate an asymmetry in the number of leptons and antileptons, and therefore in B - L. The crucial departure from thermal equilibrium is provided by the expansion of the universe. At temperatures T N O ( M i ) the abundance of heavy neutrinos exceeds the thermal abundance due to their weak interactions with the thermal bath. In the following we shall assume that the dominant contribution to the baryon asymmetry is given by decays of N1, the lightest of the heavy Majorana neutrinos. This assumption is well justified in the case of a mass hierarchy among the heavy neutrinos, i.e. M I << Mz,M3, and it is also known to be a good approximation, if M2,3 - M I = O(M1). A quantitative description of the generation of a baryon asymmetry is obtained by means of two kinetic equations, one for the number of heavy neutrinos N1 and one for the B - L asymmetry 7,8,9: 71839

d“l-

-

dz

~NB-L --

-(D

+ S ) (NN1

-

-EI D ( N N ~ N Z )-WNB-L, (3) dz where z = M l / T and ~1 is the CP asymmetry in the decay of the righthanded neutrinos. Ni is the particle number in a comoving volume element R?(t),chosen to contain one photon at a time t , before the onset of leptogenesis. For a massless boson with QB degrees of freedom in thermal equilibrium one has N B = g B / 2 , whereas for a fermion with g F degrees of freedom N F = 3 g ~ / 8 The . final baryon asymmetry is conveniently expressed in terms of the baryon-to-photon ration ~ B = O N B ( z ) / N ? ( z ) .In the simple case of isentropic expansion of the universe one obtains 7 ~ N0 0.036N~o. The relevant processes in the thermal plasma contributing to the equations are: decays and inverse decays of N1 into leptons and Higgs bosons

441

Nl H 14, and anti-leptons and anti-Higgs bosons, N1 c--) ?4, A L = 1 scatterings of N1 off top-quarks and A L = 2 processes mediated by the exchange of all heavy right-handed neutrinos, The first three contribute all together to modify the Nl abundance. Denoting thermally averaged reaction rates by ri, the term D s I ' D / ( H z ) accounts for the decays and inverse decays, where H is the Hubble parameter. Similarly, the term S E r s / ( H z ) accounts for the AL = 1 scatterings. The decays are also the source term for the generation of the B - L asymmetry, the first term in the second equation, while all the other processes contribute to the washout term W = r w / ( H z) that competes with the decay source term. The contribution to W from AL = 2 scatterings can conveniently be separated into two parts. The first part, W,,,, comes from the resonance contribution from N1, which typically dominates in the temperature range from z N 1 down to z Y 10. The remaining part, Wnon-res, is dominant at low temperatures, z 5 10, where the scattering amplitudes with Ni exchange are proportional to the light neutrino mass matrix m,. In order to understand the dependence of the solutions of the rate equations ( 2 ) and (3) on the neutrino parameters, it is crucial to note that the reaction rates are all dimensionless functions of the inverse temperature z, proportional to

where u is the vacuum expectation value of the standard model Higgs field. The effective neutrino mass G I is given by

where mg is the Dirac neutrino mass matrix. Further, E2 = tr(rn~m,),is the quadratic mean of light neutrino masses, up to a factor l/& Eq. (4) implies that, as long as Wn,n-r,s can be neglected, the generated lepton asymmetry is independent of M I . 2. Constraints on neutrino parameters

In this section we shall compare the predicted baryon asymmetry with the value measured from CMB (cf. eq. (1)).From eq. (3) it is easy to see that the final asymmetry NB-L has to depend linearly on the CP asymmetry El:

3 4

N B - L = --ElKO.

(6)

442

Figure 1. Iso-KOcurves for -

m = 0.05 eV

N

FAmatm.

Pigl = 0 (thick lines) and NFl

= 3/4 (thin lines) assuming

Here we have neglected a possible initial B - L asymmetry present before leptogenesis. This usually is a good approximation, since AL = 2 processes mediated by heavy neutrinos are strong enough at high temperatures, z << 1, to washout an initial asymmetry 13. The efficiency factor K O is normalized to be 1 in the limiting case where an initial thermal abundance of heavy neutrinos decays far out of equilibrium, where all washout scattering processes can be neglected, i.e. in the case W = 0. In thermal leptogenesis this yields the maximal asymmetry, and one always has KO 5 1. In general, K O depends only on three parameters: the effective neutrino mass 6 1 , the quadratic mean of light neutrino masses m and the heavy neutrino mass M I . In Fig. 1 we plot the dependence of the baryon asymmetry on the parameters 6 1 and M I by means of iso-KO curves of the efficiency factor, for the choice m = 0.05eV. We have performed the calculations both for an initially vanishing iV1 abundance (thick lines) and for a thermal initial N1 abundance, NEl = 3/4 (thin lines). For vanishing initial N1 abundance the enclosed domains have a finite extension in 61; for thermal initial abundance there is no boundary at small 61.

443

Figure 1 clearly shows the existence of two different regimes: the domain of ‘small’ N1 masses, M I < 1013 GeV(O.l eV/m)2, and the domain of ‘large’ N1 masses, M I > 1013 GeV(O.l eV/m)2. The dependence of the boundary on m is determined by the behaviour of the non-resonant washout rate, Wnon-re, M1m2. In the small M I regime the non-resonant part Wnon-,e, of the washout rate is negligible to a very good approximation, and there is only a small dependence on M1 and m in the final asymmetry. Hence, the efficiency factor 60 depends approximately only on 61. For an initially vanishing Nl abundance the suppression of the final asymmetry for small GI is due to the fact that Yukawa interactions are not strong enough to create an initial thermal distribution of right-handed neutrinos. On the other hand, assuming an initial thermal abundance, the neutrinos decay far out of equilibrium and one approaches the limit 6 0 4 1. For large GI, the Yukawa interactions become strong enough to create an initial thermal distribution of heavy neutrinos, i.e. one becomes independent of initial conditions. The suppression of the baryon asymmetry is now due to the washout processes W . In the large M I regime the non-resonant washout rate Wn,,-,,, dominates, leading to an exponential suppression of the produced baryon asymmetry. Here the iso-KO curves become almost independent of 6 1 . Hence, in the most general case, the final baryon asymmetry depends on only four parameters: E I , 6 1 , M I and m.

3. The maximal baryon asymmetry Up to now we have treated the CP asymmetry ~1 as an independent parameter. However, it can be shown that the CP asymmetry satisfies an upper bound l 3

where mi are the light neutrino masses. For hierarchical light neutrino masses, in the limit m l 4 0, this simplifies to l 1

The maximal baryon asymmetry produced by N1 decays is therefore given by: r ) g ? ( G l , M l , E ) !Y

10- 2 Emax l (Ml,Gl,E)60(Gl,Ml,~ . )

(9)

444

Figure 2.

Isc-r/l;oax curves for NEl = 0 (thick lines) and NEl = 3/4 (thin lines) for

the case of hierarchical light neutrino masses ( E = 0.05 eV N J ~ l n & ~ ) The . region within the dashed lines is currently allowed by the CMB constraint (cf. eq. (9)) for the ( 3 0 ) lower value.

r/gyB

7l;;Oax has to be larger than the observed baryon asymmetry (cf. eq. (1))for this mechanism to be successful. This yields a lower bound on M I ll. For zero (thermal) initial Nl abundance one obtains ',

MI

2 2.4 (0.4) x

lo9 GeV (2.5 x 1yev2) Amatrn

This is illustrated in Fig. 2, where iso-qgr curves in the ( 6 1 , MI)-plane are shown for m = 0.05 eV. For values fil and M1 enclosed by these curves the baryon asymmetry q g f B can be obtained. In the case of NEl = 0, the allowed regions are closed domains; for Nkl = 3/4 there is no lower limit on 6 1 . 4. A bound on light neutrino masses

It can be shown that the effective neutrino mass 6

is bounded from below by the lightest neutrino mass ml and from above by m3 12,'. Hence, for large 5, corresponding to quasi-degenerate light neutrinos, one has 6 1 2~ m. 1

445 10.~

10.~

10.~

10"

10.'

1 oo

10'

10l6

1 0l6

1015

1 015

10l4

1 014

1013

1 013

lo1*

10l2

10"

10''

-rnmln=0.051 eV

1 O'O

10'

1 O'O 10'

Figure 3. Curves in the %l-M1-plane of constant T$F = (thin lines) and @Oax = 3.6 x l o p l o (thick lines) for the indicated values of m. The filled regions for vggx 2 3 . 6 10-l' ~ are the allowed regions from CMB. There is no allowed region for 5i = 0.20 eV.

Increasing E leads to a suppressed baryon asymmetry, since the bound (8) on the CP asymmetry becomes stronger, and because the washout rates become more effective. Hence, there is a maximal value of E above which the observed baryon asymmetry cannot be produced in N1 decays. This is illustrated in Fig. 3, where we have displayed the curves defined by @r(%l,M I ,E ) = for different values of E and assuming a normal hierarchy of light neutrino masses. For E = 0.20 eV successful baryogenesis is no longer possible 13. In terms of light neutrino masses this corresponds to the limits m3 < 0.12eV and ml e m2 < 0.11 eV.

qgyB

5 . Conclusions

We have shown that in the minimal version of thermal leptogenesis, where the lightest of the heavy Majorana neutrinos N1 is the source of the baryon asymmetry, the final baryon asymmetry is determined by only four param, heavy neutrino mass M I , the effective eters: the CP asymmetry ~ 1 the light neutrino mass 6 1 and the quadratic mean m of light neutrino masses. The observed baryon asymmetry can only be explained if M I , and there-

446

fore the baryogenesis temperature TB M I , is above 2 x 109GeV and if light neutrino masses are not too large, m3 < 0.12eV and m l 21 m2 < 0.11 eV. Using the unitarity of the leptonic mixing matrix, IUeiI2 = 1, one then obtains for the mass measured in tritium P-decay, mVe< 0.12 eV. This value is smaller than the sensitivity aimed a t by the KATRIN collaboration The same bound as for mveone also finds for the Majorana mass measured in neutrinoless double P-decay, mee < 0.12 eV. This prediction can be tested by the GENIUS project 15. Cosmological bounds on neutrino masses will also improve, and the Sloan Digital Sky Survey combined with CMB data from the WMAP experiment is expected t o reach the sensitivity of the leptogenesis bound, m i 5 0.34 eV 16. N

xi

xi

Acknowledgments I would like to thank W. Buchmuller and in P. Di Bari for an enjoyable collaboration on the topic of this review. Further, I would like t o thank the organizers of NOON 2003 for organizing a stimulating and fruitful meeting.

References 1. D. N. Spergel et al., astro-ph/0302209. 2. T.Yanagida, in Workshop on Unified Theories, KEK report 79-18 (1979) p. 95; M. Gell-Mann, P. Ramond, R. Slansky, in Supergravity (North Holland, Amsterdam, 1979) eds. P. van Nieuwenhuizen, D. Freedman, p. 315 3. V. A. Kuzmin, V. A. Rubakov, M. E. Shaposhnikov, Phys. Lett. B 155 (1985) 36 4. D. Bodeker, G. D. Moore, K. Rummukainen, Phys. Rev. D 61 (2000) 056003 5. E. W. Kolb, M. S. Turner, The Early Universe, Addison-Wesley, New York, 1990 6. M. Fukugita, T. Yanagida, Phys. Lett. B 174 (1986) 45 7. M. A. Luty, Phys. Rev. D 45 (1992) 455 8. M. Plumacher, Z. Phys. C 74 (1997) 549 9. W. Buchmuller, P. Di Bari and M. Plumacher, Nucl. Phys. B 643 (2002) 367 10. For a review and references, see W. Buchmuller, M. Plumacher, Int. J. Mod. Phys. A 15 (2000) 5047 11. S. Davidson and A. Ibarra, Phys. Lett. B 535 (2002) 25 12. M. Fujii, K. Hamaguchi and T . Yanagida, Phys. Rev. D 65 (2002) 115012 13. W. Buchmuller, P. Di Bari and M. Plumacher, hep-ph/0302092. 14. KATRIN Collaboration, A. Osipowicz et al., hep-ex/0109033 15. H. V. Klapdor-Kleingrothaus, Nucl. Phys. Proc. Suppl. 100 (2001) 350 16. W. Hu, D. J. Eisenstein, M. Tegmark, Phys. Rev. Lett. 80 (1998) 5255

LEPTOGENESIS AND C P VIOLATION OF NEUTRINO OSCILLATION

TAKUYA MOROZUMI Graduate School of Science, Hiroshima University, 1-3-1, Kagami-yama, Higashi-Hiroshima, Japan 739-8526 E-mail: [email protected]

After brief introduction to mechanism of leptogenesis, I review our recent work on CP violation for leptogenesis and its impact on neutrino oscillation and neutrinoless double beta decay.

1. Introduction Low energy observables such as C P violation in neutrino oscillation, neutrinoless double p decay, and (Ue31measurements in neutrino sectors may give important hint on the mechanism generating Baryon number asymmetry. [l]

In the seesaw mechanism, they have strong connection with physics of origin of baryon asymmetry through leptogenesis.[2] Outline of this talk is: (1) I show how C P violating phase in lepton number asymmetry contributes to the neutrinoless double beta decay in a toy model for leptogenesis. (2) In realistic model, we show the C P violating phase which generates the lepton number asymmetry induces the mixing of neutrino oscillations and C P violation of neutrino oscillations. [3] (3) We give a specific example in which correlation of C P violation of high energy and CP violation of low energy. How large the effect in neutrino physics is shown. [3]

447

2. Toy model for leptogenesis and neutrinoless double beta

decay First I illustrate how lepton number is generated. We start with a simple seesaw model for leptogenesis. The model has one generation (electron family only Ng = 1) and two heavy Majorana neutrinos N = 2, i.e., ( N g ,N ) = (1,2) model. The lagrangian for this model is given by,

L

-a(=$'* - =$-)Nl - b(=$O* 1- #yRM1NlR KM2N2R).

=

-

-

e ~ $ - ) N 2+ h.c.

+

(3)

where N1 and N2 are two heavy Majorana neutrinos and one doublet of electron family is introduced. There is a CP vioalting phase in the model, which is given as a relative phase of two yukawa couplings a and b,

Arg.(a*b) = YR.

(4)

The Feynman diagrams which generate lepton number asymmetry are shown in Fig.1. To generate CP violation for matter and anti-matter asymmetry tree and one-loop diagram must interfere.

a* Fig. I

d+

3 Mi Amp.(Nl + e+$-) = a* + i--ab*2 3 2 M2 ~

(5)

The primordial lepton (electron) number asymmetry is given as:

Thus, cosmological lepton number asymmetry is proportional to s i n ( 2 y ~ ) . L will be washed out and the present baryon number Anomalous B

+

449 L)primordial. Furthermore, if, Bprimordial = 0: B,,, i(-L)primordial. In the toy model, baryon number is proportional to the CP violating phase 7~ in the leptonic sector. The leptognesis process occurs in the symmetric phase in electroweak theory. eve

is proportional to ( B N

4+

4-

\

/

c.

In Fig.2, we show how the physical quantity in the broken phase is related to the leptogenesis. Because the lepton number asymmetry occurs as interference of tree and one loop diagrams in Fig.1, we can look at the lepton asymmetry as the diagram shown in (a) in Fig.2. In two parts of(a), we replace eleccron (positron) with neutrino (anti-neutrino) and also replace charged higgs with vaccum expectation value. Then we obtain the diagrams in (b) and (c). They are just two contribution to light effective Majorana neutrino mass m , f f . Because ( m e f f ) e iserelated to the neutrinoless double beta decay, the lepton number asymmetry and the double beta decay rate are closely related to each other. The neutrinoless double beta decay is CP conserving quantity and it depends upon a leptogenesis CP phase Y R as COS(2YR).

450 3. Neutrino oscillation and leptogenesis

To explore the relation between neutrino oscillation and leptogenesis, we must extend the toy model to model including three flavors: Ng = 3 . How many heavy Majorana neutrino must be included ? Because there are two mass scales for light neutrinos, i.e., Am:tm,,Am:ol.,a t least, there are two heavy Majorana neutrinos, i.e., N = 2. In the (3,2) model, seesaw matrix is 5 x 5 matrix given as;

Let’s look at the low energy side. The light neutrino mass matrix for (v,,v p , vT) are given as: ‘ T -mD-mD. M

By diagonalizing m e f f we , can obtain mixing MNS matrix U.

Utm,ffU*= Diag.(O, Amsol.Amatm).

(9)

The model predicts one massless neutrino. From the MNS matrix, we can determine CP violation in neutrino oscillation. (See Eq.( l).) In cosmological side, the lepton number asymmetry is the sum of the three family asymmetry and is given as:

For comparison, we also show the electron family asymmetry in the toy 1 generation Model. Let’s look at the correlation between high energy CP violation ( E ) and low energy CP violation P - P . There are three CP violating phases in the (3,2) seesaw model: First we parametrize Dirac mass term mD ( 3 x 2),[3]

mD

=

UL

(1 2 m2 0 m

VR,

(11)

451

where UL and VR are unitary matrices given as,

We denote three C P violating phases as S L , ~ L , ~ Among R. them, a C P violating phase Y R contributes to leptogenesis.

How leptogenesis phase contributes to CP violation in low energy is more complicated. We observe that if light neutrinos were Dirac fermion, U = UL. However, in the seesaw, U # UL.We parameterize U = ULKR. Below we show KR has an angle 8 and two phases 4 and a.

1 0 0 0 cose s i n 8 e r . i ) ) 0 - sin 8ei4 cos

1 0 0 ( 0 eicv 0 o o e-ia

)

.

(15)

K R can be determined. To be explicit, we substitute the parametrization mD, m,ff = -mo=rng 1 = -UL(~VR&VR T rnT )ULT . The equation for KR is. of

where Zij are:

452

A similar formulae for 2 3 3 is obtained. Thus the induced mixing 8 and CP phases $, a in K R are obtained as functions of Y R , 8 ~M,I ,M2, m2, m3.

With double arrows, we show which quantities of the cosmological CP phase and heavy Majorana mixing have impacts on the induced angle and CP phases in low energy. Now we are ready see how three CP phases contribute to CP violation in neutrino oscillations [3]P - P J, N

J

= Im[U,lU,*lU,*,U,2].

J

1 8

= - sin 2

8 sin~2 1 ~3 ~ ~~ ~ cos [c~ 281sin 3 SL sin 2 8 ~ 2 3

+ c ~ 1 sin 2 28 sin(SL

- Y L - $) cos 2 8 ~ 2 3 1 - - S L ~ ~ Ssin L 2~8 s~i n 2 8 ~ 2 3 s i n ( 2 6 ~- y~ - $)] 2 1 - sin 28 sin 28L23 sin(yL $)(sin 2 8 ~ 1 2 ~ ~ 8 sin 2eL13sL13cL12)

+

+

13 ~ ~ 1 2

(19)

It is useful to map our MNS matrix U on the standard parameterization of MNS matrix. If ~ ~ in1 UL3 and the induced mixing sin 8 is small compared with ~ ~ 1~ 2~ , 2 we 3 ,obtain the following relations,

453

Then the angles and phases of the standard parameterization are given as:

We can get b 513 from Ue3 and CP violation of neutrino oscillation and a1 from the neutrinoless double beta decay. We may be able to fix all the parameters ~ ~ 1b 3 ~,and , 7~once the induced mixing angle 8 and CP violation 4 and Q are known from the requirement of leptogenesis. This was done in [3]. There, 6' and 4,01 are determined from (1) high energy physics input (MI, M2 , ri,r2) (2) neutrino mass eigenvalue eq. det.(meffm!ff - n2) = 0, ,/= 7 x 10-3(eV), 723 = ,/= = 5 x loA2.

722

=

With the input we can determine (m2, m3, Y R ,8,) which leads to the prediction of 0, 4 and also lepton number asymmetry €1. The range of (8,4) which is consistent with baryogenesis obtained in thie way is limited. (See for details [3]). Typical size for the induced mixing angle 8 is given below. sin 0

5 1 = O.Ol(eV),

-- 0.066,

5 1 = 0.03(eV),

sin 0 0.15 < -

Jz

Jz

o.2.

The lower bound of M I is obtained from lepton number asymmetry It is about 1011(GeV).

454

4. Model with the correlation between CP violation of neutrino oscillation and leptogenesis Here we give an example for the model in which J is determined by leptogenesis phase YR.[3]Suppose UL is a real orthogonal matrix as UL = 023012. MNS matrix U has the following form; Taking 8 ~ 2 3= 7r/4, 8 ~ 1 2= 7r/4, we have;

;(

cos 0

1

sin 0 exp[-i+]

Jz

U= -

2

cos0-fisinBexp[id] sin f ? e x p [ - a d ] + f i c o s ~ 2 - cosf?+fisinBexp[i#~] -sin 6 exp[-z+]+ficos e 2 2

X P . ( l , a!, -a!),

J

=

sin 28 sin 4-

1

YR # 0

# 0.

@

J

5. Summary 0

0

0

0

I review the recent work of C P violation aspect of leptogenesis [3] and show how the leptogenesis C P violating phase has impact on the low energy observables such as neutrinoless double beta decay, C P violation of neutrino oscillation and MNS matrix element J u e 3 J . leptogenesis phase ( Y R ) certainly affects the neutrino oscillation CP violation through (4) In the most general case, we can not distinguish the phase coming from leptogenesis ( 4 )and the other phases Y L SL in UL unless the precise determination of neutrinoless double beta decay is obtained. A specific case in which the correlation between leptogenesis CP phase and C P violation of neutrino oscillation is given and numerically the size of low energy CP asymmetry J is estimated. ~ 1 3 e ~ p ( - i 6=) exp(-iq5) Typically the following ranges 0.01 < fi J < 0.04, 0.07 < IUe31 < 0.2 are obtained.

References 1. Sakharov, Pisma Zh.Eksp. Teor.Fiz. 5,32-35 (1967). 2. M.Fukugita and T. Yanagida PhysLett. B174,45 (1986). 3. T. Endoh, S. Kaneko, S. K. Kang, T. Morozumi,

Phys.Rev.Lett.89:231601,2002

M. Tanimoto,

EXPERIMENTAL REVIEW OF PROTON DECAYS

MASATO SHIOZAWA Institute for Cosmic R a y Research, Univ. of Tokyo, Higashi-Mozumi, Kamioka-cho, Yoshiki-gun, Giju, 506-1205, JAPAN E-mail: [email protected] Experimental results on baryon number violated proton decay searches are reviewed in this article. The Super-Kamiokande detector that is the largest proton decay detector gives lower limit on nucleon partial lifetime for various decay modes. From the full Super-Kamiokande-I data (1489 days livetime or 91.6 kton,year exposure), the obtained experimental limit is 5.4 x years for p + e+r0 mode and 2.2 x years for p t DK+ mode at 90% confidence level.

1. Introduction Most of Grand Unified Theories (GUTS) allow baryon number violated transitions between leptons and quarks and proton decay channels into lighter leptons and mesons become open. Therefore, the decay of the proton is one of the most dramatic predictions of various GUT models 4,6. It has been noted that there are several indirect evidence of GUT such as the observed family-structure of elementary particles and the meeting of the three gauge couplings. Moreover, recent discovery of finite, small neutrino mass also suggests the physics at the energy scale far beyond the standard model '. Proton decays would provide the window for viewing the new physics and it is important to push up the experimental sensitivity for this processes.

2. Nucleon Decay searches in the Super-Kamiokande detector 2.1. The Super-Kamiokande detector Super-Kamiokande (SK) is a large water Cherenkov detector holding 50 ktons of ultra-pure water. Details of the detector can be found elsewhere '. The fiducial volume is 22.5 kiloton and total detector livetime for physics

455

456

analysis is finally 1489 days corresponding to 91.6 kt.year exposure. 2.2. p

+e+r0

mode

This decay mode has a characteristic event signature, in which the electromagnetic shower caused by the positron is balanced against the two showers caused by the gamma rays from the decay of the TO. This signature enables us to discriminate the signal events clearly from atmospheric neutrino background. To extract the p + e+T0 signal from the event sample, these selection criteria are defined ',lo: (Al) the number of rings is 2 or 3, (A2) all rings have a showering particle identification (PID), (A3) 85 MeV/c2 < 7ro invariant mass < 185 MeV/c2, (A4) no decay electron, (A5) 800 MeV/c2 < total invariant mass < 1050 MeV/c2 and total momentum < 250 MeV/c. Criterion (A2) selects e* and y. Criterion (A3) only applies to 3-ring events. Criterion (As) checks that the total invariant mass and total momentum correspond to the mass and momentum of the source proton, respectively. From p + e+7ro Monte Carlo sample, detection efficiency is estimated as 40%. Expected number of backgrounds from atmospheric neutrino interactions is estimated from atmospheric neutrino Monte Carlo sample as 0.3 events. Finally, there is no candidate events found in data sample. From these results, the lower limit on partial lifetime of proton is obtained as 5.4 x years at 90% confidence level (CL).

+ O K + mode The p + fiK+ mode is generally favored by GUT models implemented with 2.3. p

supersymmetry 1>8>11.Because produced K+ is expected to have momentum below Cherenkov threshold, the K f is generally invisible in a water Cherenkov detector. Therefore, experimental searches are performed by looking for decay products of the K+. There are two prominent decay channels of K+; K+ + p+u and K+ + 7r+7ro and three search methods for p + OK+ have been developed '. In the first method, K+ decays into p+ are looked for. The p+ is expected to have monochromatic momentum of 236 MeV/c. Selection criteria for this decay mode are defined as: ( B l ) the number of rings is one, (B2) the ring has a nonshowering PID, (B3) one decay electron, (B4) 215 MeV/c < muon momentum < 260 MeV/c, (B5) the ring is not proton Because we found no significant excess in the signal region, we applied spectrum fitting to obtain upper limit of signal events. From this analysis, we obtained the partial lifetime limit for p + DK+ decay mode as 4.2 x years at 90%

457

CL. In the second method, additional criterion is required to eliminate the remaining backgrounds. This criterion requires nuclear deexcitation y from the residual 15N nucleus. We expect the y to be observed proceeding to the K f decay with the time difference corresponding to the K+ lifetime (TK+ = 12 nsec). By this criterion along with criteria (Bl-B5), expected number of backgrounds is reduced to 0.7 events while detection efficiency including the kaon decay branching ratio is 8.6%. Candidate events are looked for in the data sample but no candidate is found. Obtained partial lifetime from this method is 11.4 x lo3’ years at 90% CL. In the third method, K+ decays into two pions are used. Selection criteria for this method are: (Cl) the number of rings is 2, (C2) all rings have a showering PID, (C3) 85 MeV/c2 < 7ro invariant mass < 185 MeV/c’, (C4) 175 MeV/c < 7ro momentum < 250 MeV/c, (C5) 40 p.e.s < photo electrons emitted by 7r+ < 100 p.e.s, (C6) residual charge < 70 p.e.s (C7) one decay electron. The criteria (ClGC4) select desired 7ro and the criteria (C5C7) are defined for produced 7r+. Detection efficiency including the kaon branching ratio is 6.0% and expected number of backgrounds is 0.6. Again, there is no candidate remaining after these criteria and partial lifetime limit is 7.9 x lo3’ years at 90% CL. In summary, we cannot find any candidate events for p + OK+ decay mode in three methods. Combined lifetime limit years at 90% CL. from the three methods is obtained as 2.2 x 2.4. Other Decay modes

We have also performed searches for nucleon decays to other combinations of a lepton and a meson: p+ 7 r o , e+ 7,/*+ 7,Y 7,e+ p, e+ w , and ef 7. Other kaon modes have been also looked for: proton decays t o e+ KO and p+ KO, and neutron decays to v KO. In all searches, we have found no significant excess of signals. Obtained nucleon lifetime limits are summarized in Figure 1.

+ +

+

+

+

+

+

+

+

+

3. Soudan 2 3.1. The Soudan 2 Detector

The Soudan 2 detector is a time projection, modular iron tracking calorimeter with a total mass of 974 tons and fiducial mass of 770 tons”. 1 m long drift tubes fill the spaces in the stacked steel sheets with 1.6 mm thick to detect ionization electrons of charged particles.

458

mode

(%r

ex osure EB observed B.G. &yr) event 0.2 54 40 0 32 0 0.2 43 0.2 17 0 23 0.2 13 9 0 5 9 21 5.6 4.2 0 0.4 5.6 0.5 2.9 0 3.8 0.1 73 0 98 61 0 0.2 82 22 3 4 -

-

4.2 11 7.9

8.6 6.0

0

0

0.7 0.6

6.9 5.5

14 20

19.2 11.2

9.2

1

1.1

8.7

7.9 1.3

5 0

3.6 0.1

4.0 1.7

*

0.4

7.0 2.8

3 0

3.2 0.3

t

r

f

3

4 f

I *

t f

e17

t

.IE:

.1 f

n..

*

3.0 0.8

.

0

t

*L

n *

10.7

0

*

a

n

2.0

5.4

.. .

*

u iD

1

. a

t

13.9 7.1

KAM

4.9 3.7

1

lo3'

Soudanl

lo3' 10 33 lifetime limit (years)

10 34

Figure 1. The obtained lifetime limit of nucleons from SK-I (left figure) and their comparisons with other experiments (right figure).

3.2. p

-+

PKf search

One of advantages of the Soudan 2 detector is that K+ track from the proton decay can be imaged. Proton decay searches via p + DK+ mode have been performed using two K+ decay channels 3.56 kt.year exposure data are used for the p + DK+ searches 1 3 . Selection criteria for K+ -+ p+v channel are: ( D l ) two charged tracks with common vertex (no proton), (D2) K+ range < 50 cm, (D3) 28 cm < muon range < 58 cm, (D4) decay electron. Detection efficiency after all criteria is estimated as 9.0% and expected backgrounds is 0.4 events and one candidate event was found. Moreover, selection criteria K+ -+ n+no channel are defined: (El) two charged tracks and two showers, (E2) K' range < 50 cm, (E3) 100 MeV/c2 < invariant K+ mass < 660 MeV/c2, (E4) 80 MeVlc < n+ momentum < 400 MeV/c, (E5) 40 MeV/c < no momentum < 390 MeV/c, (F5) 10 MeV/c2 < invariant no mass < 290 MeV/c2, Detection efficiency after all criteria is estimated as 5.5% and expected backgrounds is 1.1 events

459

and no candidate event was found. From two methods, combined lower limit is obtained as 4.3 x 1031 years at 90% CL.

4. Invisible Decay Searches

So far, nucleon decay searches using visible secondary particle are reviewed. It is also important to look for nucleon decays into invisible particles. Recently, proton decays in Deutron into invisible state has been looked for using residual neutron signal in the SNO detector l4 and gives the limit of 3.5 x lo2' years at 90% CL. Similar invisible decay have been looked for in the old Kamiokande detector using deexcitation gamma signal from residual nuclei and gave limit of 1.8 x 1031 years a t 90% CL. 5. Future Proton Decay Detector There are several proposed detector for future nucleon decay searches. One is ICARUS, liquid Ar detector that has excellent tracking and particle identification capabilities. It is planned that 600ton detector will be in operation in the underground soon and expected proton lifetime sensitivity is around T x E x years where T is lifetime in year and E is detection efficiencies. Another detector is proposed in Japan which is lMton size water Cherenkov detector called Hyper-Kamiokande. Expected sensitivities of Hyper-Kamiokande are 2 x years and 3 x 1034 years for p t e+xo and p t pK+, respectively. 6. Summary

In this article, proton decay searches via various decay modes are presented. The obtained experimental limit from full SK-I data is 5.4 x years for p -+ e+xO mode and 2.2 x years for p -+ pK+ mode at 90% CL. Figure 1 shows obtained lifetime limits for these decay modes from SK, IMB3, Kamiokande, and Soudan 2. In conclusion, there is no evidence for nucleon decays so far. However it should be noticed that the background level in SK is still low in many decay modes and we can expect further improvements beyond the current experimental limits by increasing statistics. We need to keep watching nucleons t o open new physics beyond the standard model.

7. Acknowledgments The author appreciates the Super-Kamiokande collaborators for much help in preparing the latest results and his talk.

460

References

J. Ellis et al., Nucl. Phys. B202,43 (1982). Y.Fukuda et al., Phys. Rev. Lett. 81,1562 (1998). Y.Fukuda et al., Nucl. Instr. Meth. A501, 418 (2003). H. Georgi and S. L. Glashow, Phys. Rev. Lett. 32,438 (1974). Y. Hayato et al., Phys. Rev. Lett. 83,1529 (1999). 6. Jogesh C. Pati and Abdus Salam, Phys. Rev. Lett. 31,661 (1973). 7. For example, Jogesh C. Pati, hep-ph/0005095. 8. N. Sakai and T. Yanagida, Nucl. Phys. B197, 533 (1982). 9. M. Shiozawa et al., Phys. Rev. Lett. 81,3319 (1998). 10. M. Shiozawa, PhD thesis, University of Tokyo (1999). 11. S. Weinberg, Phys. Rev. D26, 287 (1982). 12. W. W. M. Allison et al., Nucl. Instr. Meth. A376, 36 (1996); W. W. M. Allison e t al., Nucl. Instr. Meth. A381, 385 (1996). 13. W. W. M. Allison et al., Phys. Lett. B427, 217 (1998). 14. Yu.G.Zdesenko and V.I.Tretyak, Phys. Lett. B553. 135 (2003).

1. 2. 3. 4. 5.

IMPACT AND IMPLICATION OF BI-LARGE NEUTRINO MIXINGS ON GUTS*

TAICHIRO KUGO+ Yukawa Institute for Theoretical Physics, K y o t o University, K y o t o 606-8502, Japan E-mail: [email protected]

Under the assumptions that 1) the quark/lepton mass matrices take FroggattNielsen’s factorized power form A + ~ + + J with anomalous U(1) charges $;, and 2) the U(1) charges $; respect the S U ( 5 ) GUT structure, we show that the quark mass data necessarily implies the large 2-3 mixing in the MNS mixing matrix UMNS. If we further add the data of the mass squared difference ratio of solar and atmospheric neutrinos, then, it implies that the 1-2 mixing in UMNS is also large, so explaining the bi-large mixing. This analysis also gives a prediction that ( U M ~ J should S ) ~ ~ be of order X (0.1 - 0.5). Ue3

-

1. Introduction

Existence of a certain grand unified theory (GUT) beyond the standard model is guaranteed by i) the anomaly cancellation between quarks and leptons and ii) the unification of the gauge coupling constants at energy 1015-16GeV. The strongest candidate for the unified scale around p gauge group is E6, which is not only suggested by string theory but also unique in the property that it is the maximal safe simple group allowing complex representations in the E-series; E3 = S U ( 3 )x S U ( 2 ) ,E4 = S U ( 5 ) , E5 = SO(IO), E 6 , E7, E8.l The purpose of this talk is to analyze the implications of the neutrino data on the possible GUTS. This is based on a work2 in collaboration with Masako Bando. The particular facts of the neutrino data are:3,4i5,6 N

*Talk presented at NOON2003 held at Kanazawa, Feb. 10 -14, 2003. t Work partially supported by Grant-in-Aid for Scientific Research No. 13640279 from Japan Society for the Promotion of Science, and Grants-in-Aid for Scientific Research on Priority Area “Neutrinos” (Y. Suzuki) No. 12047214 from the Ministry of Education, Science, Sports and Culture, Japan.

461

462

(1) Bi-large mixing

sin2 2eI2

N

(0.86 - 1.0),

sin22&

N

1.

(1)

(2) Mass-squared difference ratio

Am& Am:,,

N

7 x 10-5 eV2 3 x 10-3ev2

N

~ 2 - 3

where X defined below is a quantity of magnitude X

(2) N

0.22.

These show a sharp contrast to the quark sector, in which the mixings are very small and the mass spectrum is hierarchical. The mutual relations of masses and mixing angles between quarks and leptons/neutrinos will be great clues for the GUTS. As an working hypothesis we here assume an supersymmetric SU(5) GUT and the Froggatt-Nielsen mechanism7 to generate effective Yukawa coupling matrices of the form

where the Yukawa couplings y can in principle depend on the generation label i , j but are assumed to be all order 1 and so are denoted by y collectively. O is the Froggatt-Nielsen field carrying the U(1)x charge -1 and the U(1)x charges of the other Higgs field H and matter fields Q i (i = 1,2,3) are denoted by the corresponding lower-case letters:

X ( O ) = -1,

X ( H ) = h,

X(!$i) = $i ( 2 0).

(4)

After the Froggatt-Nielsen field O develops a vacuum expectation value (VEV) (0),which is assumed to be smaller than the Planck scale by a factor of Cabibbo angle Bc

the effective Yukawa couplings induced from Eq. (3) are given by ye! = y x A $ i + $ j + h = 0 (1) x X$i+&+h. 23 That is, the mass matrix M takes the form

5

(6)

463

?,hi

with ( H ) = u. +p and are the U ( l ) x charges of the right-handed and !J and @,: respectively. Thus, in this Froggattleft-handed matter fields T Nielsen mechanism, the hierarchical mass structure can be explained by the of the matter fields. Note that this difference of the U ( l ) x charges type of ‘factorized’ mass matrix can be diagonalized as

V M U t = Mdiag.

(8)

by unitary matrices V and U taking also a similar power forms:

2. U ( l ) x charge assignment

I assume SU(5) structure at least for the U ( l ) x charge assignment. Then, first, we consider the Yukawa coupling responsible for the up-quark sector masses. In order for the effective Yukawa coupling @,i(lO)+@j(lO)+hu

YU@Z(~O)@j(~O)~U(5)

+

yu;; = y , x

x$ ‘ i ( l O ) + $ j

(10)+h,

(10)

to reproduce the observed up-type quark mass hierarchy structure mt : m, : mu = 1 : x 4 : x 7 ,

(11)

we are led to choose the following values for the U ( l ) x charges of three generation Q ~ ( 1 0fermions ) taking h, = 0 for simplicity:* (+1(10),+ 2 ( 1 0 ) , + 3 ( 1 0 ) ) = ( 3 , 2, 0 )

( 12)

Next we consider the mass matrices of down-type quarks and charged leptons which come from the couplings

+

yd;; = y d x

$i(lO)+@j(S*)+hd

(13)

Note that this yields the transposed relation between the down-type quark mass matrix Md and the charged lepton one Ml: MdT Adz. This is because the @ i ( 5 * )multiplets contain the right-handed component d“ for the

-

464

down-type quarks while the left-handed component 1 for the charged leptons. Therefore the unitary matrices for diagonalizing those mass matrices, satisfy the relations

so that we have

That is, the mass matrix takes the form

In order for this quarks

M d

to reproduce the mass ratio of the top and bottom

we take q3(5*)= 2 - h d . Further, t o reproduce the down-type quark mass hierarchy m b : m , : m d

exp. =

=1:X2:x4,

we take G 2 ( 5 * )= 2 - h d and $1(5*) = 3 - h d ; thus, we have

and the mass matrix (16) now reduces to

This form of mass matrix is called lopsided.

(18)

465

3. Mixing matrices

Mixing matrices in the quark sector and lepton sector are called CabibboKobayashi-Maskawa (CKM) and Maki-Nakagawa-Sakata (MNS)' matrices and they are given by UCKM = u ~ u ~U, MNs = U l u J . (21) In our case both U, and Ud takes the form U, Ud (Al$~(lo)-$j(lo)l), so that the CKM matrix, generally, also has the same form N

UCKM= UJJJ

pv

N

pv

:

( :) 1

(~l~i(w-~~(1o)l)

3;

(i 1;)

A2

.

(22)

This is all right. For the charged lepton sector we have

ul

N

(Al$<(5*)-$J(5*)l)

N

(23)

If the mixing matrix U, in neutrino sector is 1, this beautifully explains the observed large 2-3 neutrino mixing! However, this alone fails in explaining the large 1-2 mixing. We thus have to discuss the neutrino mixing matrix U , now. N

4. Neutrino mass matrix and mixing

Generally in GUTS, there appear some right-handed neutrinos XPl(1) = (I = 1 , . . . , n ) ;for instance, n = 3 in SO(10) and n = 6 in EG.They will generally get superheavy Majorana masses denoted by an n x n mass matrix ( M R ) I J and , also possesses the Dirac masses (R-L transition mass terms)

(M&

N

yvvAh" x

(A$45*)+@

)

(24)

induced from

(25) Here 11," denotes the U ( l ) x charges of the right-handed neutrinos 91(1). The Majorana mass matrix M v of (left-handed) neutrino is induced from these masses M R and MD by the see-saw mechanismlo and evaluated as

1ij

(Mv

( M a 21 (MK

1I J P f D 1J j c(

A$;(5*)+$J(5*) (26)

466

Note here that the dependence on the U ( l ) x charges $? of the right-handed neutrinos has completely dropped off." Plaguing the values (19) for & ( 5 * ) , we thus have

This neutrino mass matrix happens to take the same form as one of the models that have been proposed by Ling and Ramond." This form is very interesting. First, this matrix implies the large 2-3 mixing in the diagonalization matrix U,. The 2-3 mixing is also large in the charged lepton mixing matrix Ul as we have seen above, and so is it generally in the MNS matrix UMNS= UlUi unless a cancellation occurs between Ul and U,. Second, it is natural to assume that three neutrino masses are not so degenerate accidentally. Then, the mass squared difference ratio (2) of solar and atmospheric neutrinos implies the mass ratio of the second and third neutrinos :

In order for the Mu to reproduce this mass ratio, the 2 x 2 bottom-right submatrix of this Mu should not be naturally-expected order 1, but should be O(X); that is, it is diagonalized by an 2 x 2 unitary matrix uu as

If this is the case, the mass matrix Mu takes the following form after the diagonalization of this 2 x 2 bottom-right submatrix:

If we note the 2 x 2 top-left submatrix of this matrix

(^x" i), "We should however take it account that this occurs only for a generic case and may be broken in particular cases in which ( M g ) i I brings about correlation between the left-handed neutrino index i and right-handed one 1.'

467

we see that this also gives the large mixing in the 1-2 sector so that it explains the bi-large mixing. Therefore, the experimental fact (32) necessarily implies the bi-large mixing! We note that a very similar neutrino mass matrix Mu to ours (27) was also proposed by Maekawa:12 ~2

M v cx

(y:

~ 1 . 5 x1

.

,At5

(33)

5 . Prediction on Ue3

We should note that there is one more prediction in our framework, that is, the magnitude of the Ue3 (UMNS)13: Ue3

-

=

O(X1)

N

- 0.1 ) ( - 0.5 v ~0.5 xi.5

(34)

This is seen as follows. First, we have

which have resulted from down-type quark masses and a n S U ( 5 ) relation. Second, we have for the matrix elements of U,,, (u,,)31

-

A$1(5*)-@3(5*)

=

,

(Uv)32

and

(Uv)33

-

- O(1).

(36)

These clearly give rise t o Ue3 ( U M N S ) p , = ( ~ l Q ) 1 3 O(X). This prediction gives a crucial test for the idea of Froggatt-Nielsen mechanism.

6. Conclusion

I have shown the following points in this paper: (1) If we assume Froggatt-Nielsen’s factorized form for the quark/lepton mass matrices and the S U ( 5 ) structure for the U(1)x charges, an input of up- and down-type quark masses necessarily implies that the 2-3 mixing is large in the MNS matrix UMNS.

468

-

(2) If we further add the data ~ A m & / A m ~ t , A, then, it implies that the 1-2 mixing in U M Nis~ also large, so leading to bi-large mixing. (3) The measurement of Ue3 will confirm or kill the basic idea of Froggatt-Naelsen mechanism for explaining the hierarchical mass structures of quarks and leptons.

Acknowledgments

I would like t o thank Masako Bando for collaborations in the work which this talk is based on. I also thank N. Maekawa for valuable discussions. I was also inspired by stimulating discussions during the Summer Institute 2001 and 2002 held at Fuji-Yoshida. References 1. Lie Algebras in Particle Physics, (Westview Press, 1999) 2. M. Bando and T. Kugo, in preparation. 3. Y. Fukuda et al. [Super-Kamiokande Collaboration], Phys. Lett. B 433, 9 (1998) [arXiv:hep-ex/9803006]; Phys. Lett. B 436, 33 (1998) [arXiv:hepex/9805006]. 4. S. Fukuda et a2. [Super-Kamiokande Collaboration], Phys. Lett. B 539, 179 (2002) [arXiv:hep-e~/0205075];Phys. Rev. Lett. 86,5651 (2001) [arXiv:hepex/0103032]; Phys. Rev. Lett. 86,5656 (2001) [arXiv:hep-e~/0103033]. 5. Q. R. Ahmad et al. [SNO Collaboration], Observatory,” Phys. Rev. Lett. 89, 011301 (2002) [arXiv:nucl-ex/0204008]; Phys. Rev. Lett. 89,011302 (2002) [arXiv:nucl-ex/0204009]. 6. K. Eguchi et al. [KamLAND Collaboration], Phys. Rev. Lett. 90, 021802 (2003) [arXiv:hep-ex/0212021]. 7. C. D. Froggatt and H. B. Nielsen, Nucl. Phys. B 147,277 (1979). 8. M. Bando and T. Kugo, Prog. Theor. Phys. 101 (1999) 1313 [arXiv:hepph/9902204]. 9. Z. Maki, M. Nakagawa and S. Sakata, Prog. Theor. Phys. 28 (1962) 870. 10. T.Yanagida, in Proceedings of the Workshop on Unified Theory and Baryon Number of the Universe, eds. 0 . Sawada and A. Sugamoto (KEK, 1979); M. Gell-Mann, P. Ramond and R. Slansky, in Supergravity, eds. P. van Nieuwenhuizen and D.Z. Freedman (North Holland, Amsterdam, 1979). 11. F. S. Ling and P. Ramond, Phys. Lett. B 543 (2002) 29 [arXiv:hepph/0206004]. 12. N. Maekawa, Prog. Theor. Phys. 106 (2001) 401 [arXiv:hep-ph/0104200]; Prog. Theor. Phys. 107 (2002) 597 [arXiv:hep-ph/0111205]. M. Bando and N. Maekawa, Prog. Theor. Phys. 106 (2001) 1255 [arXiv:hepph/0109018].

Scientific Programme

KamLAND Results

K. Inoue

Tohoku U.

SNO Update

M. Chen

Queen’s U.

11:lO - 11:35

Super-K Solar neutrinos

M. Smy

UCI

11:35 - 12:05

Borexino & Future LE solar neutrino

S. Shoenert

Max-PlanckInstitut

12:05 - 12:45

Neutrino oscillations and the shining of the sun

C. GonzalezGarcia

CERNI Stony Brook/ IFIC

14:15 - 14:30

Supernova relic neutrino results from Super-Kamiokande

M. Malek

SUNY

14:30 - 1455

Relic Supemova Neutrinos and Neutrino Oscillations

S. Ando

U. of Tokyo

1455 - 15:25

Solar and reactor neutrino analysis: Results and desiderata

E. Lisi

INFN Ban

1555 - 16:25

Can 4 neutrinos explain global oscillation data including LSND?

T. Schwetz

Technical U.

16:25 - 1650

Universal Texture of Quark and Lepton Mass Matrices

Y. Koide

u. of

1650 - 17:15

Neutrino Masses and Beyond from Supersymmetry

0. Kong

National Central University, Taiwan

17:15 - 18:OO

Neutrino Physics after KamLAND

A. Y. Smimov

International Center for Theoretical Phvsics

9:30 - 10:15 10:15 - 10:40

Break

Lunch

Break

469

Shizuoka

470

Reception

***** 1l-Feb ( n e ) ***** 09~15- 09:40

Results in K2K and future

T. Kobayashi

KEK

09~40- 10:05

BooNE at Six Months

E. Zimmerman

u. of Colorado

10:05 - 1030

Status of MINOS

M. Messier

Indiana U.

1030 - 10155

Status of OPERNCNGS

M. Nakamura

Nagoya U.

Status of ICARUS

A. Ereditato

INFN Napoli

11:50 - 12:15

NuMI OFFaxis Experiment

S. Wojcicki

Stanford U.

12:15 - 12:40

JHFnu (phase I) neutrino oscillation experiment

A. Ichikawa

KEK

F. Suekane

Tohoku U.

T. Lasserre

CENSaclay

Break 11:25

-

11150

Lunch 1490 - 14~25 Theta13 measurement by

Japanese reactors 14~25- 14~50 Future prospect for reactor

neutrino experiment in Europe 1450 - 1 5 1 5

Using Reactors to Measure Theta 13

M. Shaevitz

Columbia U.

15:15 - 15:45

Impact of Ue3 on neutrino models

M. Tanimoto

Niigata U.

CPV in JHFnu (phase 11)

T. Nakaya

Kyoto U.

16:40 - 17:05

Parameter degeneracy (overview) and JHF/NuMI complementarity

S. Parke

Fermilab

17:05 - 17:30

Parameter degeneracy and e

A. Donini

Univarsidad Autonoma Madrid

17:30 - 17:55

Parameter degeneracy and reactor

0. Yasuda

Tokyo Met. U.

Break 16:15

-

16140

+ tau

47 1

***** 12-Feb (Wed) ***** 09:15 - 09~40 Results from L3+C

P. Le Coultre

CERN

K. Abe

U. of Tokyo

The calculation of atmospheric neutrino flux

M. Honda

ICRR

10:55 - 11:20

Progress in analysis of high energy primary cosmic-ray spectra measured in BESS-02

S. Haino

U. of Tokyo

11120- 11:45

Atmospheric neutrinos

C. Yanagisawa

SUNY

11145- 12110

Initial Results from HARP

C. Wiebusch

CERN

M. Sakuda

KEK

09:40

- 1O:OO

A measurement of mu,p and He

energy spectra at the small atmospheric depth 1000 - 1025

Break

12~10- 12~35 Study of neutrino interaction for neutrino oscillations

Self-Guided Tour in Kanazawa

***** 13-Feb (mu)***** 09115 - 09150

Heidelberg-Moskow (Present and Future)

H. V. Klapdorl Max-PlanckI. V. Krivosheina Institut

09:50 - 1015

CUORICINO and CUORE: results and prospects

A. Giuliani

INFN

S. Jullian

u. Paris

11~10- 11~3.5 Double beta decay constraints

H. Sugiyama

Tokyo Met. U.

11:35 - 12~00 Implication of the next generation double-beta-decay experiments

S. Petkov

SISSATriestd INFN Trieste

12:OO - 12~25 MAJORANA

H. Miley

Pacific Northwest National Laboratory

12125- 12~50 MOON

R. Hazama

Osaka U.

10~15- 10~40 NEMO

Break

472

Lunch 14~10- 14:35

EX0

C. Hall

SLAC

1435 - 15:OO

CANDLES

T. Kishimoto

Osaka U.

15:OO - 15:25

CAMEO/GEM

Y. Zdesenko

Inst. For Nuclear Research

15:25 - 15:50

XMASS

S. Moriyama

ICRR

A. Dolgov

INFN FerrardTEP

G. Raffelt

MPI Physik

17110- 17~35 Neutrino Flavor conversion inside and outside supernova

C. Lunardini

Inst. Advanced Study

17~3.5- 18~00 Detectors, future detection of SN

M. Vagins

Irvine

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Supernova neutrinos: Flavordependent fluxes and spectra

Banquet

09:15

- 1O:OO

Birth of Neutrino Astrophysics

M. Koshiba

U. of Tokyo

1O:OO

- 10:25

Lepton flavor violation and SUSY GUT

Y. Shimizu

Nogoya U.

(S) fermion Masses and Lepton flavor Violation

M. Yamaguchi

Tohoku U.

10:25 - 1O:SO

Break 11:20 - 11:45

mu

+ egamma experiment(MEG)

D. Nicolo’

INFN Pisd Pisa, Scuola Normale Superiore

11:45 - 12:lO

mu

+ e conversion experiment

A. Van der Schaaf

Zurich U.

12:lO - 12:35

Hints of Family Structure from Neutrino Oscillation

M. Bando

Aichi U.

473

Lunch 1400 - 14:25

Leptogenesis

M. Pluemacher

CERN

14:25 - 1450

Leptogenesis and CP violation in neutrino oscillations

T. Morozumi

Hiroshima U.

1450 - 15:15

Experimental review of proton decay

M. Shiozawa

ICRR

1515 - 15x40

Theoretical review of proton decay

J. Hisano

ICRR

1540 - 16:25

Impact and Implication on GUTS of Large Neutrino Mixings

T. Kugo

Kyoto U.

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List of Participants

Koh ABE Univ. of Tokyo [email protected]. u-tokyo.ac.jp

Hiro EJIRI JASRI.-Spring8/RCNO-Osaka ejiri @spring8.oKjp

Shin’ichiro AND0 Department of Physics School of Science, Univ. of Tokyo [email protected]. u-tokyo.ac.jp

Tomohiro ENDOH Faculty of Science University of Hiroshima [email protected]

Ken-Ichi AOKI Kanazawa University [email protected]

Antonio EREDITATO INFN Napoli antonio.ereditato @cern.ch

Mayumi AOKI Theory Group, KEK rnayurni.aoki @ kek.jp

Yoshiyuki FUKUDA Faculty of Education Miyagi University of Education [email protected]

Masako BAND0 Aichi University bando @aichi-u.ac.jp Mark CHEN Queen’s University rnchen @post.queensu.ca Alexander DOLGOV I”, Ferrara, Italy and ITEP, Moscow, Russia dolgov@fe. infn. it Andrea DONINI Dep.Fisica Teorica Universidad Autonoma Madrid [email protected]

Takeshi FUKUYAMA Ritsumeikan University [email protected] Yoshihito GANDO Research center for neutrino science Univ, of Tohoku gando @awa.tohoku.ac.jp Andrea GIULIANI Universita‘ dell’lnsubria Dipartimenfo di Scienze [email protected] Concha GONZALEZ-GARCIA CERNETONY BROOWIFIC concha @rnail.cern.ch 475

476

Sadakazu HAINO School of Science Univ. of Tokyo haino @ icepp.s.u-tokyo.ac.jp

Serge JULLIAN NEMO LAL,University Paris Sud jullian@lal. in2p3.fr

Carter HALL SLAC [email protected]

Takaaki KAJITA ICRR, Univ. of Tokyo [email protected]

Ryuta HAZAMA Department of Physics Osaka University hazama @ km.phys.sci.Osaka-u.ac.jp

Mitsuru KAKIZAKI Tohoku Univ. [email protected]

Junji HISANO ICRR, Univ. of Tokyo hisano@icrr:u-tokyo.ac.jp

Yuki KAMO Department of Physics Kumamoto Univ. kamo @sci.kumamoto-u.ac.jp

Morihiro HONDA ICRR, Univ. of Tokyo [email protected]

Satoru KANEKO Niigata University [email protected] p

Atsuko ICHIKAWA IPNS, KEK ichikawa @neutrino.kek.jp

Tokufumi KATO State University of New York at Stony Brook fumi @superk.physics.sunysb. edu

Kunio INOUE Reseach Center for Neutrino Science Tohoku University inoue @awa.tohoku.ac.jp Masaki ISHITSUKA Neutrino center ICRR, Univ. of Tokyo ishi @ suketto.icrr:u-tokyo.ac.jp Yoshitaka ITOW Karnioka Observatory ICRR, Univ. of Tokyo itow @suketto.icrr:u-tokyo.ac.j p

Tsuyoshi KIMURA Institute of Theoretical Physics Univ. of Kanazawa tuyosi @ hep.s.kanazawa-u.ac.j p Tadafumi KISHIMOTO Department of Physics Osaka University [email protected] Teru yuki KITABAYASHI Accelerator Engineering Center Mitsubishi Electric System & Service Engineering Co.Ltd. tekita @dream.com

477

Hans Volker KLAPDORKLEINGROTHAUS Max-Planck-Institut fuer Kernphysik HEIDELBERG klapdo r @ g ustav. mpi-hd. mpg.de Takashi KOBAYASHI IPNS, KEK ta kashi.kobayashi @ kek.j p Yoshio KOIDE Dept of Physics Univ. of Shizuoka koide @ u-shizuoka-ken.ac.jp Otto KONG Department of Physics National Central University, Taiwan Otto @phy.ncu.edu.t w Masatoshi KOSHIBA University of Tokyo mkoshiba C3icepp.s.u-tokyo.ac.jp Yusuke KOSHIO Kamioka Observatory ICRR, Univ. of Tokyo koshio@icr,:u-tokyo.ac.jp Irina Vladimirovna KRIVOSHEINA Max-Planck-Institut fuer Kernphysik and Radiophysicsl Research Institute HEIDELBERG and Nishnii-Nowgorod irina @ gustavmpi-hd. rnpg.de Jisuke KUBO Kanazawa Inst. f. Theor. Physics, Kanazawa U [email protected]. kanazawa-u.ac.jp

Takahiro KUBOTA Department of Physics Osaka University kubota @ het.phys.sci. Osaka-u.ac.jp Taichiro KUGO Dept. of Physics Kyoto University kugo @gauge.scphys.kyoto-u.ac.jp Yoshitaka KUNO Department of Physics Graduate School of Science Osaka University kuno @phys.sci.Osaka-u.ac.j p Thierry LASSERRE CEA/Saclay/DAPNIA./SPP [email protected] r Pierre LE COULTRE Laboratory of High Energy Physics ETH Zurich Pierre. Le. [email protected] Serge LIKHODED Boston University [email protected] Eligio LISI Istituto Nazionale di Fisica Nucleare INFN, Bari eligio. h i @ba.injk. it Dawei LIU Dept. of Physics & Astronomy Univ. of California, Irvine dwliu @hep.ps.uci.edu Cecilia LUNARDINI Institute for Advanced Study [email protected]

478

Matthew MALEK State University of New York at Stony Brook [email protected]

Chikaori MITSUDA High energy laboratory Univ of Niigata mitsuda @ hep.sc.niigata-u.ac.jp

Koichi MATSUDA Department of Physical Sciences Ritsumeikan Univ. sph30101 @se.ritsumei.ac.jp

Kohei MIZUTANI Department of Physics Saitama University [email protected]

Satoshi MATSUDA Kyoto University matsuda @phys.h.kyoto-u.ac.jp

Shigetaka MORIYAMA Kamioka Observatory ICRR, Univ. of Tokyo moriyama @icrr:u-tokyo.ac.jp

Masahisa MATSUDA Dept. of Physics Aichi Univ. of Education mmatsuda @ auecc.aichi-edu.ac.j p

TAKUYA MOROZUMI HIROSHIMA UNIV. moroz,umi@ hiroshima-t4.ac.jp

Mark MESSIER Indiana University [email protected]

Yorikiyo NAGASHIMA Osaka University nagay @snow.dti2.ne.jp

Shouichi MIDORIKAWA Faculty of Engineering Aomori University midori @aomori-u.ac.jp

Masayuki NAKAHATA Kamioka Observatory ICRR, Univ. of Tokyo nakahata @suketto.icrr:u-tokyo.ac.jp

Harry MILEY Pacific Northwest National Laboratory harry miley @pnl.gov

Mitsuhiro NAKAMURA F-lab., Department of Physics Nagoya University nakamura @jlab.phys.nagoya-u.ac.j p

Hisakazu MINAKATA Department of Physics Tokyo Metropolitan University minakata @phys.metro-u.ac.jp

Hiroaki NAKANO Niigata Univ. nakano @muse.sc.niigata-u.ac.jp

Akihiro MINAMINO Kamioka Observatory ICRR, Univ. of Tokyo minamino esuketto. icrr.u-tokyo.ac.jp

Tsuyoshi NAKAYA Physics, Faculty of Science Kyoto University nakaya @scphys.kyoto-u.ac.jp

479

Shoei NAKAYAMA Kamioka Observatory ICRR, Univ. of Tokyo [email protected]

Stephen PARKE Theoretical Physics Department Fermi National Accelerator Laboratory parke @fnal.gov

Toshio NAMBA Kamioka Observatory ICRR, Univ. of Tokyo namba @suketto.icrr. u-tokyo.ac.jp

Denis PERRET-GALLIX CNRS (Centre National de la Recherche Scientifique) [email protected] r

Ryousuke NAMBU Kamioka Observatory ICRR, Univ. of Tokyo [email protected]:u-tokyo.ac.jp

SERGUEY PETCOV Elementary Particle Physics Sector SISSA petcov @ he.sissa.it

Donato NICOLO’ Physics Department University of Pisa [email protected]

Michael PLUEMACHER CERN Theory Division Michael,[email protected]

Yoshihisa OBAYASHI Kamioka Observatory ICRR, Univ. of Tokyo ooba@ icrr.u-tokyo.ac.jp Tommy OHLSSON Mathematical Physics Department of Physics Royal Institute of Technology (KTH) tommy @theophys.kth.se Hideaki OHSUMI Faculty of Culture and Education Saga University [email protected] p Yuichi OYAMA IPNS, KEK [email protected]

Georg RAFFELT MPI Physik [email protected] Makoto SAKUDA IPNS, KEK makotosakuda @ kek.jp Tomoyuki SANUKI Graduate School of Science Univ. of Tokyo sanukiC3phys.s.u-tokyo.ac.jp Stefan SCHOENERT Max-Planck-Institut for Nuclear Physics, Heidelberg Stefan.schoenert @mpi-hd.mpg.de Thomas SCHWETZ Physik Department Technical University Munich schwetz @ph.tum.de

480

Mike SHAEVITZ Columbia University shaevitz @nevis.Columbia.edu Yasuhiro SHIMIZU Department of Physics Nagoya University shimizu @eken.phys.nagoya-u.ac.jp Tetsuo SHINDOU High energy theory group Fac. of Sci. Osaka Univ. shindou @ het.phys.sci.Osaka-u.ac.jp Masato SHIOZAWA Kamioka Observatory ICRR, Univ. of Tokyo masato @ icrkm4.icrr.u-tokyo.ac.jp Junpei SHIRAI Research Center for Neutrino Science Tohoku University [email protected] Alexei SMIRNOV. International Center for Theoretical Physics smirnov @ ictp.trieste.it Michael SMY University of California, Irvine smy @solar1.ps.uci.edu Fumihiko SUEKANE RCNS, Tohoku Univ. suekane @awa.tohoku.ac.jp Hiroaki SUGIYAMA Dept. of Phys. Tokyo Metropolitan Univ. [email protected]

Yoichiro SUZUKI Kamioka Observatory ICRR, Univ. of Tokyo suzuki @suketto.icrr.u-tokyo.ac.jp Eiichi TAKASUGI Dept. of Physics Osaka University [email protected] Morimitsu TANIMOTO Department of Physics Niigata University tanimoto @muse.sc.niigata-u.ac.jp Kikuchi TATSURU Department of Physics Ritsumeikan University [email protected] Tadayuki TESHIMA College of Engineering Chubu University teshirna @ isc.chubu.ac.jp Shoji TORI1 Institute of Physics Kanagawa University toriiC3phu2.n.kanagawa-u.ac.jp Sheng-Yi TSAI Institute of Quantum Science College of Science and Technology Nihon University tsai @phys.cst.nihon-u.ac.j p Mark VAGINS University of California, Irvine [email protected]

481

Andries VAN DER SCHAAF Ph ysik-Institut Zurich University [email protected]

Chiaki YANAGISAWA Department of Physics and Astronomy University at Stony Brook chiaki @superk.physics.sunysb. edu

Seiichi WAKAIZUMI Center for Univeristy Extension Univ. of Tokushima wakaizwn @cue.tokushima-u.ac.jp

Osamu YASUDA Physics Department Tokyo Metropolitan University yasuda @phys.metro-u.ac.j p

Wei WANG Boston University [email protected]

Masaki YASUE Department of Physics Tokai University [email protected]. u-tokai.ac.jp

Christopher WIEBUSCH CERN christopher.wiebusch @cern.ch Stanley WOJCICKI Stanford University sgweg @slac.Stanford. edu

Masashi YOKOYAMA Kyoto Univ. yokoyama @ hep.phys.s.u-tokyo.ac.jp

Zhaohua XIONG Hiroshima University xiongzh @ theo.phys.sci.hiroshima-u.ac.j p

Tetsuya YOSHIDA Institute of Particle and Nuclear Studies High Energy Accelerator Research Organization (KEK) tetsuya.yoshida @ kek.jp

Tetsuo YABUKI Univ.Rakuno Gakuen yabuki@ rakuno.ac.jp

Motohiko YOSHIMURA ICRR, Univ. of Tokyo yoshim@ icrr:u-tokyo.ac.jp

Shuei YAMADA Kamioka Observatory ICRR, Univ. of Tokyo [email protected]:u-tokyo.ac.jp

Joanna ZALIPSKA Soltan Institute for Nuclear Studies jzal @neutrino.kek.j p

Masahiro YAMAGUCHI Department of Physics Tohoku University yama @ tuhep.phys. tohoku.ac.jp Akira YAMAMOTO Cryogenics Science Center, KEK akira.yamarnoto @ kek.jp

Yuri ZDESENKO Lepton Physics Department Institute for Nuclear Research zdesenko @ kimkiev.ua Eric D ZIMMERMAN University of Colorado edz @pizero.colorado.edu