Fundamental interactions: proceedings of the Twentieth Lake Louise Winter Institute, Lake Louise, Alberta, Canada, 20-26 February, 2005

Proceedings otthe

Lake Louise Winter Institute

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Funda Interactions Alan Astbury

Bruce Campbell

Roger Moore

Manuella Vincter

World Scientific

Faqir Khanna

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Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

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

FUNDAMENTAL INTERACTIONS Proceedings of the Twentieth Lake Louise Winter Institute Copyright © 2006 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, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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ISBN 981-256-631-7

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PREFACE The twentieth Lake Louise Winter Institute, entitled Fundamental Interactions, was held from February 20-26, 2005 at the Chateau Lake Louise situated in the scenic Canadian Rocky Mountains. The format of the Winter Institute consisted of a mixture of pedagogical talks and short contributed presentations highlighting the latest results from experiments and new developments in theory. As usual, the sessions were held in the morning till noon and in the evening till at least 10:00 p.m. The participants had ample time for informal discussions in the afternoons or over meals. The afternoons were enjoyed by many for recreation and enjoyment of the winter wonderland in the Rockies. The pedagogical talks focused on recent developments in cosmology. Results on K- and B-decays were critically assessed to bring out the new understanding of the topic. Results that lead to an unveiling of the new phases of QCD were presented. Physics with atomic traps and its impact on fundamental physics was clearly brought out. Finally the future experiments at the LHC and their discovery potential, in particular discovery of Higgs and possibly finding supersymmetric particles, was clearly spelled out. With the complement of contributed talks, a clear view of the present status of particle physics and cosmology was available. We wish to thank Lee Grimard for a wonderful organisation of the Winter Institute with care, patience and skill. Our sincere thanks go to Suzette Chan for a masterful job of converting the contributions from the various participants into a nice proceedings. The support and help of the staff at the Chateau was available at all times, making it a rather smooth operation. Finally we wish to thank the Deans of Science at the University of Alberta and Carleton University, the Institute of Particle Physics and TRIUMF for generous financial support. The Physics Department and Theoretical Physics Institute at the University of Alberta deserve a great deal of thanks for providing the infrastructural support that makes the task of arranging the Winter Institute much easier.

Organizing Committee A. Astbury B. A. Campbell F. C. Khanna R. W. Moore M. G. Vincter v

CONTENTS Preface

v

Contents I.

II.

III.

vii

New Physics in B and K Decays R. Fleischer Physics at the Large Hadron Collider M. Lefebvre Applications of Trapped Atoms for Fundamental Symmetry Studies G. Sprouse

1

44

69

Exclusive D Semileptonic Decays at CLEO-c N. E. Adam

88

Direct CP Violation Results from T. Allmendinger

93

BABAR

Cosmic Ray Velocity and Electric Charge Measurements in the AMS Experiment L. Arruda

98

Electroweak Physics at LEP 2 P. Azzurri

104

What Can We Learn about Neutrinos at SNOLAB? A. Bellerive

109

Flavor and Chiral Oscillations with Dirac Spinors A. E. Bernardini

114

Detection and Measurement of Gamma Rays in the AMS-02 Detector J. Bolmont

119

Higgs Boson Discovery Potential at CMS J. Brooke

124

AMS Transition Radiation Detector and the Search for Dark Matter G. Carosi

129

vn

High Sensitivity B-Physics Measurements with the ATLAS Detector J. R. Catmore

134

Measurements of the CKM Angle a from C. A. Chavez

139

BABAR

Systematics of Identified Hadron Spectra at PHENIX M. Csandd

144

Deep, Dark & Directional: The DRIFT Dark Matter Experiment at Boulby Mine J. C. Davies

149

Electroweak and QCD Results from D 0 M. Eads

154

Time Dependent CP Violation in B° —> TT+TT~ Decays K. Hara

159

Modification of the Casimir Effect Due to a Minimal Length Scale U. Harbach

164

Exploring the Neutrino Universe with AMANDA and IceCube D. Hardtke

169

Jet Production at HERA and Measurements of the Strong Coupling Constant as D. Kcira

174

Parton Energy Loss, Saturation, and Recombination at BRAHMS E.-J. Kim

179

Hadron Production and Radial Flow in Au+Au Collisions at RHIC-PHENIX A. Kiyomichi

184

SUSY Searches at LEP A. C. Kraan

189

Search for New Physics at CDF II A. Lath

194

Search for Fermiophobic Higgs at LEP V. Lemaitre

199

Measurements of Proton Structure at HERA V. Lendermann

204

Top Physics at the LHC S. Lowette

209

Spatial Confinement and Thermal Deconfmement in the Compactified Gross-Neveu Model J. M. C. Malbouisson

214

Measurements of 7 in

BABAR

G. Marchiori

219

Leptogenesis from Parametric Resonance D. W. Maybury

224

Currents on Superconducting Strings in an unusual Environment M. A. Metlitski

229

Search for Technicolor at LEP N. Meyer

234

Semileptonic Decays from A. K. Mohapatra

239

BABAR

QCD Results at CDF O. Norniella

244

Hadron Spectroscopy in Electrons-Protons Collisions at HERA B. Olivier

249

Coulomb Corrections to R-Correlation in the Polarized Neutron Decay A. Pah

254

Simulating the Sensitivity of km 3 Hydrophone Arrays to Fluxes of Ultra High Energy Neutrinos J. Perkin

259

D 0 Top Physics M.-A. Pleier

264

D 0 Higgs Physics Results K. J. Rani

269

Measurements of Rb at LEPII Energies Y. Rozen

274

Quantization of Galilean Covariant Fields E. S. Santos

280

Electroweak Measurements at CDF A. Sidoti

285

Rare and Radiative B Meson Decays from the BABAR

Experiment

J. Stelzer

290

The LHCb Ring-Imaging Cherenkov Detectors J. W. Storey

295

Physics of Heavy Flavour at CDF S. Torre

300

Time-Dependent CP-Violating Asymmetries in b —• sqq and b —> sj Transitions Y. Ushiroda

305

Top Physics Results at CDF T. Vickey

310

Inclusive Branching Fraction of D —<• vX M. Weinberger

315

Integral Fluxes, Day-Night, and Spectrum Results from SNO's 391-Day Salt Phase J. Wendland

320

Jets and High pr (Di-Hadron) Correlations in PHENIX D. L. Winter

325

Resonance Production at STAR H. Zhang

330

List of Participants

335

N E W PHYSICS I N B A N D K DECAYS

R. F L E I S C H E R CERN,

Department of Physics, Theory Unit, CH-1211 Geneva 23, Switzerland E-mail: [email protected]

Flavour physics offers interesting probes for the exploration of the Standard Model and the search for new physics. In these lectures, we focus on B- and K-meson decays, introduce the concept of low-energy effective Hamiltonians to describe them theoretically, and discuss how physics beyond the Standard Model may generically affect the roadmap of quark-flavour physics. We address then both the implications of the B-factory data for the B4 —> J/ipKg channel and the prospects of Bs —> J/i/)0 modes for hadron colliders, and discuss how the Standard Model may be challenged through Bd —* 4>K§. Finally, as an example of a systematic flavour strategy to search for new physics, we analyze puzzling patterns in the B —> 7T7r, nK data and study their interplay with rare K and B decays.

1. Introduction In flavour physics, the parity and charge-conjugation operators P and C, which describe the space-inversion operation and the replacement of all particles by their antiparticles, respectively, play a key role. After the discovery that weak interactions are not invariant under parity and chargeconjugation transformations in 1957, it was believed that the product of C and P was actually preserved. It came then as a big surprise in 1964,1 when it was observed through the detection of K\, —» TT+TT~ decays that this is actually not the case! The corresponding phenomenon is referred to as CP violation, and is a central aspect of flavour physics. The manifestation of CP violation discovered in 1964 is "indirect" CP violation, which is described by a complex quantitiy ex and originates from the fact that the mass eigenstates of the neutral kaons are not eigenstates of the CP operator. After tremendous experimental efforts, also "direct" CP violation, which is caused directly at the amplitude level through the interference between different weak amplitudes, could be established in the neutral kaon system in 1999 by the NA48 (CERN) and KTeV (FNAL) collaborations, 2 thereby ruling out superweak scenarios of CP violation. 3 The world average taking 1

2

also the final NA48 and KTeV results 4 into account is given as follows: Re(e'/e) = (16.6 ± 1.6) x 1 0 - 4 .

(1)

As far as the theoretical status of this observable is concerned, the shortdistance contributions are under full control. On the other hand, the longdistance part, which is described by hadronic matrix elements of certain four-quark operators, suffers from large uncertainties. Although theoretical analyses performed within the Standard Model give results in the ball park of (1), stringent tests cannot be performed unless progress on the longdistance contributions can be made. 5 In 2001, CP-violating effects were also discovered in the B-meson system by the BaBar (SLAC) and Belle (KEK) collaborations, 6 representing the first observation of this phenomenon outside the K-meson system. The corresponding CP asymmetry arises in the "golden" decay Bj, —> J/ipKsJ and is induced through the interference between the B° —+ J/ipKg and B^ —> J/ipKg decay processes that is caused by B^-B^ mixing. In the summer of 2004, also direct CP violation could be detected by the BaBar and Belle collaborations in Ba —• ir^K^1 decays,8 thereby complementing the observation of this phenomenon in the neutral kaon system. Despite tremendous progress over the last years, we have still an incomplete picture of CP violation and flavour physics. The exploration of these topics is very exciting, as it may open a window to the physics lying beyond the Standard Model (SM), where quark-flavour physics is governed by the Cabibbo-Kobayashi-Maskawa (CKM) matrix. 9 ' 10 Indeed, in scenarios for new physics (NP), we typically encounter also new sources for flavourchanging processes and CP violation. Important examples are models with extended Higgs sectors, supersymmetric (SUSY) or left-right-symmetric scenarios for NP. In this context, it is also important to note that the experimental evidence for non-vanishing neutrino masses points to an origin beyond the SM, raising many interesting questions, which include also the possibility of CP violation in the neutrino sector. 11 Interestingly, CP violation plays also an outstanding role in cosmology, where this phenomenon is one of the necessary ingredients for the generation of the matter-antimatter asymmetry of the Universe,12 as was pointed out by Sakharov in 1967.13 However, model calculations show that the CP violation present in the SM is too small to explain this asymmetry. The required additional sources of CP violation may be associated with very high energy scales, as in the scenario of "leptogenesis", involving CP-violating decays of very heavy Majorana neutrinos. 14 On the other hand, there are

3

also several extensions of the SM with new sources of CP violation that could actually be accessible in the laboratory, as we have noted above. Before searching for NP, we have first to understand the picture of flavour physics emerging within the SM. Here the usual key problem for the theoretical interpretation is related to hadronic uncertainties, where e'/e is a famous example. In the B-meson system, the situation is much more promising: it offers various strategies to explore CP violation and flavour physics - simply speaking, there are many B decays - and we may search for SM relations, which are on solid theoretical ground and may well be affected by NP. Concerning the kaon system, the future lies on "rare" decays, which are absent at the tree level of the SM, i.e. originate from loop processes, and are theoretically very clean. A particularly important role is played by K+ —»-K+VV and K L —• it°vv, which offer poweful tests of the flavour sector of the SM. These aspects are the focus of these lectures. The outline is as follows: in Section 2, we discuss the description of CP violation in the SM and introduce the unitarity triangle (s). We then move on to the system of the B mesons in Section 3, where we classify non-leptonic B decays, introduce the concept of low-energy effective Hamiltonians, and have a closer look at the CP-violating asymmetries arising in neutral B decays. In Section 4, we turn to rare decays, and discuss Bs^ —> /x + /i _ modes as a more detailed example. After addressing the question of how NP may generically enter CP-violating phenomena and rare decays in Section 5, we are well prepared to discuss the "golden" decays Bd —> J/ipKs and Bs —• J/ip(j> in Section 6, and how we may challenge the SM through Bd —> nn, TTK data and their interplay with rare K and B decays. Finally, we conclude and give a brief outlook in Section 9. In order to complement the discussion given here, I refer the reader to the reviews, lecture notes and textbooks collected in Refs. 15-21, where many more details and different perspectives of the field can be found. There are also other fascinating aspects of flavour physics and CP violation, which are, however, beyond the scope of these lectures. Important examples are the D-meson system, 22 electric dipole moments, 23 or the search for flavour-violating charged lepton decays. 24 In order to get an overview of these topics, the reader should consult the corresponding references.

4

2. C P Violation in the Standard Model 2.1. Weak Interactions

of Quarks

In the SM of electroweak interactions, CP-violating effects are associated with the charged-current interactions of the quarks: D^UW~.

(2)

Here D G {d, s,b} and U G {«, c, t} denote down- and up-type quark flavours, respectively, whereas the W~ is the usual 5 £ / ( 2 ) L gauge boson. Prom a phenomenological point of view, it is convenient to collect the generic "coupling strengths" VUD of the charged-current processes in (2) in the form of a 3 x 3 matrix. Prom a theoretical point of view, this "quark-mixing" matrix - the CKM matrix - connects the electroweak states (d',s',b') of the down, strange and bottom quarks with their mass eigenstates (d, s, b) through the following unitary transformation :

'df\

(VudVusVub\ ] = \VcdVcsVcb\[s\= b') \Vtd Vu VtbJ

fd\ VCKM

\bj

fd\ •Is]. \bj

(3)

Consequently, VCKM is actually a unitary matrix. This feature ensures the absence of flavour-changing neutral-current (FCNC) processes at the tree level in the SM, and is hence at the basis of the Glashow-IliopoulosMaiani (GIM) mechanism. 25 If we express the non-leptonic charged-current interaction Lagrangian in terms of the mass eigenstates in (3), we arrive at Lpn? = -^=

(uh, CL, i L ) 7 " VCKM I sh \ W^ + h . c ,

(4)

where UW~ transition and its CP conjugate D —> UW+ are related to each other through VUD

^

VUD,

(5)

we observe that CP violation is associated with complex phases of the CKM matrix. Consequently, the question of whether we may actually have physical complex phases in this matrix arises.

5

2.2. Phase Structure

of the CKM

Matrix

We may redefine the up- and down-type quark fields as follows: U -> exp(i£u)U,

D -» exp(i&,)£>.

(6)

If we perform such transformations in (4), the invariance of the chargedcurrent interaction Lagrangian implies VUD -> exp(i€u)VUD exp(-i£D)-

(7)

Eliminating unphysical phases through these transformations, we are left with the following parameters in the case of a general N x N quark-mixing matrix, where N denotes the number of fermion generations: i j V ( J V - l ) +±(N-1)(N-2)

= (N-1)2.

(8)

Euler angles complex phases If we apply this expression to N = 2 generations, we observe that only one rotation angle - the Cabibbo angle #c 9 _ is required for the parametrization of the 2 x 2 quark-mixing matrix, which can be written as f

/ c o s 0 c sintfc\ \ — sin 9c cos 6c j

where sin#c = 0.22 follows from K —> n£i>e decays. On the other hand, in the case of N = 3 generations, the parametrization of the corresponding 3 x 3 quark-mixing matrix involves three Euler-type angles and a single complex phase. This complex phase allows us to accommodate CP violation in the SM, as was pointed out by Kobayashi and Maskawa in 1973. 10 The corresponding picture is referred to as the Kobayashi-Maskawa (KM) mechanism of CP violation. In the "standard parametrization" advocated by the Particle Data Group, 26 the three-generation CKM matrix takes the following form:

(

C12C13

-S12C23 S12S23 -

S12C13

Ci2S23Sl3etl513 Ci2C23Si3e

lSl3

C12C23 -C12S23 -

Si2S23S13el613 S12C23Sl3eJ'513

si3e~lSl3

S23C13 C23C13

(10) where Cij = cos % and Sij = sin 0y. If we redefine the quark-field phases appropriately, #12, #23 and #13 can all be made to lie in the first quadrant. The advantage of this parametrization is that the mixing between two generations i and j vanishes if 0j,- is set to zero. In particular, for #23 = #13 = 0, the third generation decouples, and the submatrix describing the mixing between the first and second generations takes the same form as (9).

6

2.3.

Wolfenstein

Parametrization

The charged-current interactions of the quarks exhibit an interesting hierarchy, which follows from experimental data: 26 transitions within the same generation involve CKM matrix elements of 0(1), those between the first and the second generation are associated with CKM elements of O(10 _ 1 ), those between the second and the third generation are related to CKM elements of O(10 - 2 ), and those between the first and third generation are described by CKM matrix elements of O(10 - 3 ). For phenomenological applications, it would be useful to have a parametrization of the CKM matrix available that makes this pattern explicit. 27 To this end, we introduce a set of new parameters, A, A, p and 77, by imposing the following relations: 28 s 2 3 = AX2,

sX2 = A = 0.22,

siae"" 1 3 = AX3(p - MJ).

(11)

Going back to the standard parametrization (10), we obtain an exact parametrization of the CKM matrix as a function of A (and A, p, 77), which allows us to expand each CKM element in powers of the small parameter A. Neglecting terms of 0(X4) yields the "Wolfenstein parametrization": 27 / VCKM =

I-5A2

A

-A

1 - \X2

3

2

\AX (l-p-ir1) 2.4.

Unitarity

A\3(p-ir))\

-AX

AX2

1

+ 0(X4).

(12)

/

Triangle(s)

The unitarity of the CKM matrix, which is described by ^CKM

-

VCKM = 1 = VCKM • VCKM,

(13)

leads to a set of 12 equations, consisting of 6 normalization and 6 orthogonality relations. The latter can be represented as 6 triangles in the complex plane, all having the same area, which represents a measure of the "strenghth" of CP violation in the SM. Using the Wolfenstein parametrization of the CKM matrix, the generic shape of these triangles can be explored. Interestingly, only the following two orthogonality relations correspond to the case of triangles, where all three sides are of the same order of magnitude:

vudv:b + vcdv;b + vtdvt*b = 0 V:dVtd + V:sVts + V:bVtb = 0;

(14) (IS)

in the other triangles, one side is suppressed with respect to the others by factors of 0(A 2 ) or 0(A 4 ). If we apply the Wolfenstein parametrization by

7 Im

Im

(a)

(b) (P.-n)

(P,T1)

Rb

/

a

>s

R,

A

( P \ .

- Re

Figure 1. The two non-squashed unitarity triangles of the CKM matrix, as explained in the text: (a) and (b) correspond to the orthogonality relations (14) and (15), respectively.

keeping just the leading, non-vanishing terms of the expansion in A, (14) and (15) give the same result, which is given by [(p + ir,) + (l-p-

ir,) + (-1)] AA3 = 0,

(16)

and describes the unitarity triangle of the CKM matrix. Taking also the next-to-leading order corrections in A into account, 28 as described in Subsection 2.3, we arrive at the triangles illustrated in Fig. 1. The apex of the triangle in Fig. 1 (a) is simply given by p= p 1

1

A2

V =V

H*

(17)

corresponding to the triangle sides Rb =

>4

v,, Vrcb

Rt =

Vtd A Vcb c

(18)

Obviously, this triangle is the straightforward generalization of the leadingorder case, and is usually considered in the literature. Whenever referring to a unitarity triangle (UT) in the following discussion, we shall always mean this triangle. On the other hand, the characteristic feature of the triangle in Fig. 1 (b) is that 7 = 7' + 67, with 5-y = A2T? = 0(1°).

2.5. Determination

of the Unitarity

(19)

Triangle

There are two conceptually different avenues to determine the UT: (i) In the "CKM fits", theory is used to convert experimental data into contours in the p-fj plane, where semileptonic b —-> utvi, c£&i decays and B% S-B% s mixing (see 3.1) allow us to determine the

8

Figure 2.

The current situation in the p—rj plane, as discussed in the text.

UT sides Rt, and Rt, respectively, i.e. to fix two circles in the p-fj plane. On the other hand, the indirect CP violation in the neutral kaon system described by SK can be transformed into a hyperbola, (ii) Theory allows us to convert measurements of CP-violating effects in B-meson decays into direct information on the UT angles. The most prominent example is the determination of sin 2/3 through Bd —» J/i^Ks, but several other strategies were proposed. The goal is to "overconstrain" the UT as much as possible. In the future, additional contours can be fixed in the p-fj plane through the measurement of rare decays. For example, ~BR{K+ —> K+VV) can be converted into an ellipse, and BR(K^ —• 7r°i/P) allows the determination of \fj\. In Fig. 2, we show the current situation: the shaded dark ellipse is the result of a CKM fit,29 the straight lines represent the measurement of sin 2/3 (see Subsection 6.1), and the quadrangle corresponds to a determination of 7 from Bd —» 7r+7r~, Bd —> TTTK± decays, 30 which will be discussed in Section 8. For very comprehensive analyses of the UT, we refer the reader to the web sites of the "CKM Fitter Group" and the "UTfit collaboration" . 31 The overall consistency with the SM is very impressive. Furthermore, also the recent data for B —• irp, pp as well as Bd —» D^^n* and B —> DK decays give constraints for the UT that are in accordance with the KM mechanism, although the errors are still pretty large in several of these cases. Despite this remarkably consistent picture, there is still hope to encounter deviations from the SM. Since B mesons play a key role in this adventure, let us next have a closer look at them.

9

3. System of the B Mesons 3.1. Basic

Features

In this decade, there are promising perspectives for the exploration of Bmeson decays: the asymmetric e+-e~ B factories at SLAC and KEK, with their detectors BaBar and Belle, respectively, are taking data since several years and could already produce <9(108) BB pairs. Moreover, the CDF and DO collaborations have recently reported the first results from run II of Fermilab's Tevatron. Starting in 2007, the LHC 32 at CERN will allow "second-generation" i?-decay studies through the dedicated LHCb experiment, and also ATLAS and CMS can address certain interesting aspects of B physics. For the more distant future, an e + - e ~ "super-J5 factory" is under consideration, with an increase of luminosity by two orders of magnitude with respect to the currently operating machines. 33 The 5-meson system offers also a very interesting playground for theorists, involving exciting aspects of strong and weak interactions, as well as the possible impact of physics beyond the SM. Moreover, there is an extremely fruitful interplay between theory and experiment in this field, and despite impressive progress, there are still aspects left that could not yet be accessed experimentally and are essentially unexplored.

Q

W

u, c, t\ b Figure 3.

b

u, c, t W

Q

1 u, c,t W

i i

b u, c,t

Box diagrams contributing to B°-B°

t,

W 1

mixing in the SM (q 6 {d, s}).

The B-meson system consists of charged and neutral mesons, which are characterized by the following valence-quark contents: charged:

B+ ~ ub, B ~ ub J3+~c6, B+~cb

neutral:

B°d~db,

B°d~db

The characteristic feature of the neutral Bq (q £ {d, s}) mesons is J5°B® mixing, which we encountered already in the determination of the UT discussed in Subsection 2.5. In the SM, this phenomenon, which is the counterpart of K°-K° mixing, originates from box diagrams, as illustrated in Fig. 3. Due to B°-B° mixing, an initially, i.e. at time t = 0, present B°-

10 meson state evolves into the following time-dependent linear combination: \Bq(t)) = a(t)\B°q) + b(t)\B°q).

(20)

The coefficients a(t) and b(t) are governed by an appropriate Schrodinger equation, with mass eigenstates that are characterized by mass and decay width differences A M , and A r q , respectively. The time-dependent transition rates for decays of initially present B® or B® mesons into a final state / involve cos(AMqt) and sin(AM,i) terms, describing the B^-B® oscillations.

u, c d(s)

Figure 4.

Tree diagrams (qi,?2 6

{u,c}).

W d{s) g q= Figure 5.

u,c,d,s

QCD penguin diagrams (qi = qi G {u, d, c, s}).

u, c, t

Figure 6.

3.2. Classification

Electroweak penguin diagrams (q\ = q2 &

of Non-Leptonic

B

d(s)

{u,d,c,s}).

Decays

For the exploration of CP violation, non-leptonic B decays play the key role. The final states of such transitions consist only of quarks, and they are mediated by b —> qi
11 (EW) penguins. In Figs. 4-6, the corresponding leading-order Feynman diagrams are shown. Depending on the flavour content of their final states, we may classify the non-leptonic b —> q\ qi d (s) decays as follows: •
Effective

Hamiltonians

3.3.1. General Structure For the analysis of non-leptonic B decays, we use low-energy effective Hamiltonians, which are calculated by making use of the "operator product expansion", yielding transition amplitudes of the following structure: (f\He{i\i)

= ^AcKM^Cfc^X/IQfcOOli).

(21)

Here G F denotes Fermi's constant, AQKM is a CKM factor, and fi denotes a renormalization scale. The technique of the operator product expansion allows us to separate the short-distance contributions to this transition amplitude from the long-distance ones, which are described by perturbative quantities Ck (AO ("Wilson coefficient functions") and non-perturbative quantities {f\Qk{p)\i) ("hadronic matrix elements"), respectively. The Qk are local operators, which are generated through the electroweak interactions and the interplay with QCD, and govern "effectively" the decay in question. The Wilson coefficients are - simply speaking - the scaledependent couplings of the vertices described by the Qk-

3.3.2. Illustration through an Example Let us consider the quark-level process b —+ cus, which originates from a tree diagram of the kind shown in Fig. 4, as a simple illustration. If we "integrate out" the W boson having four-momentum k, i.e. use the relation

we arrive at the following low-energy effective Hamiltonian: ffeff = ^v:sVcbQ2,

(23)

12 with the "current-current" operator 0 2 = [5Q7/*(1 - 7 s K ] fo7"(l " 7 s ) M

(24)

and the Wilson coefficient C 2 = 1; a and /3 are the SU(Z)c indices of QCD. Taking now QCD effects, i.e. the exchange of gluons, into account and performing a proper "matching" between the full and the effective theories, a second current-current operator, Oi = [5 a7M (l - 7 s M [c/37M(l - i M ,

(25)

is generated, involving a Wilson coefficient Ci(fj,). Due to the impact of QCD, also the Wilson coefficient of O2 acquires now a renormalizationscale dependence and deviates from one. The results for the Cfc(/x) contain terms of log(fj,/Mw), which become large for /x = 0{rrn,), the typical scale governing the hadronic matrix elements of the four-quark operators Ok- In order to deal with these large logarithms, "renormalization-groupimproved" perturbation theory offers the appropriate tool. The fact that (f\Heg\i) in (21) cannot depend on the renormalization scale JX implies a renormalization group equation, which has a solution of the following form: C(fi) = U(^,Mw)-C(Mw).

(26)

Here the "evolution matrix" U(fi, Mw) connects the initial values C(Mw) encoding the whole short-distance physics at high-energy scales with the coefficients at scales at the level of a few GeV. Following these lines,

H£)

(LO),

< log

M,w

(NLO),

...

(27)

can be systematically summed up, where "LO" and "NLO" stand for the leading and next-to-leading order approximations, respectively. For more detailed discussions, we refer the reader to Refs. 17, 34. 3.3.3. A Closer Look at Non-Leptonic Decays Low-energy effective Hamiltonians provide a general tool for the theoretical description of weak B- and if-meson decays, as well as Bg-B® and K°-K° mixing. Let us discuss the application to non-leptonic B decays in more detail. For the exploration of CP violation, transitions with AC = AU = 0 are particularly interesting. As can be seen from Figs. 4-6, these decays receive contributions both from tree and from penguin topologies. If we

13 apply the unitarity of the CKM matrix, we find that the corresponding CKM factors are related through

v:Tvub + v;rvcb + v;rvtb = o,

(28)

where r € {d, s}. Consequently, only two independent weak amplitudes contribute to any given decay of this kind. In comparison with our previous example, which was a pure tree decay, we have now also to deal with penguin topologies, involving - in addition to the W boson - the top quark as a second "heavy" particle. Once these degrees of freedom are "integrated out", their influence is only felt through the initial conditions of the renormalization group evolution (26). Mathematically, the penguin topologies in Figs. 5 and 6 with internal top-quark exchanges (as well as the corresponding box diagrams in Fig. 3) that enter these coefficients are described by certain "Inami-Lim functions". 35 Finally, using (28) to eliminate Vt*rVtb, we obtain an effective Hamiltonian of the following structure: 2

10

v

c

E jrVib {E * M Qi +E c* M <&} j=u,c

fc=l

r

fc=3

(29)

.

Here we have introduced another quark-flavour label j G {u, c}, and the four-quark operators Q3^ can be divided as follows: • Current-current operators: Q\r = 0% =

{rajp)v-A(Ji3ba)v-A {raja)v-A(Jpbp)V-A.

(30)

• QCD penguin operators: Ql Q\ Ql Ql

= {rabah-A^Eq'i^Qph-A. = (rQ6/3)v-AE9'(9/39a)v-A = (r»()a)v-AE,'(^yV+A = {rabp)v-AT,q'%
(31)

• EW penguin operators (the eqi denote the electrical quark charges): Ql

=

|(fa6a)v-AEg'e9'(^^)v+A

Q& = §(ra&/3)v-A E , ' Ql

Qio

eq/{q'0q'a)Y+A

= |(rQba)v-AEq'e9'(^^)v-A = Ufch)y-A E q ' V ^ D V - A -

At a renormalization scale /i = 0(mb), the Wilson coefficients of the current-current operators are Ci(/i) = O(10 _ 1 ) and C2(M) = O(l), whereas those of the penguin operators are as large as O(10 - 2 ). 3

14

The short-distance part of (29) is nowadays under full control. On the other hand, the long-distance piece suffers still from large theoretical uncertainties. For a given non-leptonic decay B —•> / , it is given by the hadronic matrix elements (f\Qk{fj)\B) of the four-quark operators. A popular way of dealing with these quantities is to assume that they "factorize" into the product of the matrix elements of two quark currents at some "factorization scale" \i = /Up- This procedure can be justified in the large-Afc approximation, 36 where NQ is the number of SU(Nc) quark colours, and there are decays, where this concept can be justified because of "colour transparency" arguments. 37 However, it is in general not on solid ground. Interesting theoretical progress could be made through the development of the "QCD factorization" (QCDF) 38 and "perturbative QCD" (PQCD) 39 approaches, the soft collinear effective theory (SCET), 40 and QCD lightcone sum-rule methods. 41 An important target of these methods is given by B —>7T7T and B —> nK decays. Thanks to the B factories, the corresponding theoretical results can now be confronted with experiment. Since the data indicate large non-factorizable corrections, 30 ' 42-45 the long-distance contributions to these decays remain a theoretical challenge. 3.4. Towards the Exploration

of CP

Violation

3.4.1. Direct CP Violation Let us now have a closer look at the amplitude structure of non-leptonic B decays. Because of the unitarity of the CKM matrix, at most two weak amplitudes contribute to such modes in the SM. Consequently, the corresponding transition amplitudes can be written as follows: A(B -+f)=

e + < V l |^i|e M l + e+iVi\A2\eiS2

A(B -+f) = e

_
\Ai\e

Ul

i,pa

iS2

+ e~ \A2\e .

(33) (34)

Here the
\Aj\eiS^YlCk(n)(f\Qi(u)\B).

(35)

fc

Using (33) and (34), we obtain the following CP asymmetry: T(B -> / ) - r ( B - / ) _ \A(B -+ / ) | 2 - \A(B -> / ) | 2 iCP T(B - / ) + T(B -+ / ) \A(B -+ / ) | 2 + \A(B -> f)\* 2|^iP 2 lsin((5i - 5 2 ) s i n ( y i - y 2 ) 2 |-4i| + 2|Ai||i4 2 |cos(«i - <52)cos(^1 - cp2) + |A 2 | 2 '

(36)

15 We observe that a non-vanishing value can be generated through the interference between the two weak amplitudes, provided both a non-trivial weak phase difference irir,irK,KK modes. (ii) In decays of neutral Bq mesons (q £ {d, s}), interference effects between B®-B® mixing and decay processes may induce "mixinginduced CP violation". If a single CKM amplitude governs the decay, the hadronic matrix elements cancel in the corresponding CP asymmeties; otherwise we have to use again amplitude relations. 3.4.3. CP Violation in Neutral Bq Decays Since neutral Bq mesons are a key element for the exploration of CP violation, let us next have a closer look at their most important features. A particularly simple - but also very interesting - situation arises in decays into final states / that are eigenstates of the CP operator, i.e. satisfy CP\f) = ±\f). a

(37)

For the calculation of Re(e'/ £ )> an approriate low-energy effective Hamiltonian with the same structure as (29) is used. The large theoretical uncertainties mentioned after (1) originate from a strong cancellation between the QCD and EW penguin contributions (caused by the large top-quark mass), and the associated hadronic matrix elements.

16 If we solve the Schrodinger equation describing Bq-Bq mixing as we noted in Subsection 3.1, we obtain the following time-dependent CP asymmetry:

r(i?°(t)-+/)-r(Bg(t)->/) r(£°(t)-/) + r(B°(i)^/) = A^(Bq

Ar„=o

-» / ) cos(AM„t) + A$?(Bq

-» / ) sin(AM,i).

(38)

Here the coefficient of the cos(AMg£) term is given by Adit

\A(B°^f)\*-\A(B°q-*f)\*

(Bq - / ) =

lAm., . / ) | 2 + W B ° - / ) | 2 '

(39)

and measures the direct CP violation in the decay Bq—*f. As we have seen in (36), this phenomenon originates from the interference between different weak amplitudes. On the other hand, the coefficient of the sin(AMg£) term describes another kind of CP violation, which is caused by the interference between B^-Bq mixing and decay processes, and is referred to as "mixinginduced" CP violation. Mathematically, it is described by A™(Bq

- /) =

2Imfj?)

(40)

"i+i^r

where £<«)

=

±e -ie<j>

'A(B°q^jy A(B° ^ /)_

(41)

!>(«) that is associated with Bq~Bq involves the CP-violating weak phase @)^' mixing. In the SM, it is related to the CKM phase of the box diagrams with internal top-quark exchanges shown in Fig. 3 as follows:

e ^ - 7 r = 2arg(TO
= 4>q = {

+2/3 = 0(47°) -2*y = 0 ( - l ° )

(q = d) (q = s),

(42)

where /3 and Sj were introduced in Figs. 1 (a) and (b), respectively. If we use (33) and (34), we may rewrite (41) as follows:

e?) = +-e-

'e+i^\Ai\eiSl +e+i^2\A2\eiS2' 5 e-^IAile" ! +e-^2|A2|ei52J '

(43)

and observe - in analogy to the discussion of direct CP violation in 3.4.1 that this quantity suffers, in general, also from large hadronic uncertainties However, if one CKM amplitude plays the dominant role, we arrive at -e+^//2[M/|e%Ai) -1(0,-0/) (44) i,5 +e +e /_ e -^//2|M/|e

17 Consequently, the hadronic matrix element \Mf\elSf cancels in this special case. Since the requirements for direct CP violation are obviously no longer satisfied, the observable A^{Bq —• / ) vanishes. On the other hand, we may still have mixing-induced CP violation. In particular, A $ ? ( B , ^ / ) = ±sin0

(45)

is now governed by the CP-violating weak phase difference = 4>q — <j>f and is not affected by hadronic uncertainties. The corresponding timedependent CP asymmetry takes then the simple form

r(B"(t)^/)-r(B»(t)->/) r(B°(t)-»/) + r(i?o(t)-/)

= ±sinsin(AM g i),

(46)

Ar„=o

and allows an elegant determination of sin^. In Sections 6 and 7, we will see that this formalism has powerful applications for the search of NP. 4. Rare Decays 4.1. General

Features

The exploration of flavour physics through CP violation can nicely be complemented through "rare" decays. In the SM, these processes do not arise at the tree level, but can originate through loop effects. Consequently, rare B decays are mediated by FCNC processes of the kind b —* s or b —> d, whereas rare K decays originate from their s —» d counterparts. Prominent examples of rare B decays are the following exclusive channels: B - • K*-y, B --> fry, ... B -f K*n+yT , B -> P/J.+/J,

Bs,d -> M V - While the B8+H~, which are therefore more promising from the theoretical point of view, but are unfortunately more difficult to measure; the cleanest rare B decays are given by B —» Xs^vv processes. A tremendous amount of work went into the calculation of the branching ratio of the prominent B —• Xs^ decay,46 and the agreement of the experimental value with the SM expectation implies important constraints for

18 the allowed parameter space of popular NP scenarios. The phenomenology of the kaon system includes also interesting rare decays: 16 ' 29 • KL - • 7r°e+e-, Kh — T T W

4.2. Theoretical

-

Description

For the theoretical description of rare decays, low-energy effective Hamiltonians are used, in analogy to the analysis of non-leptonic B decays. The structure of the corresponding transition amplitudes is therefore similar to the one of (21), i.e. the short-distance physics is described by perturbatively calculable Wilson coefficient functions, whereas the long-distance dynamics is encoded in non-perturbative hadronic matrix elements of local operators. It is useful to rewrite the rare-decay implementation of (21) as follows:47,48 A(decay) = P 0 (decay) + ^

Pr{deca,y)Fr(xt

= m2t/M^).

(47)

r

Here /x = no = O(Mw) was chosen, and the Wilson coefficients Ck(no) were expressed in terms of "master functions" Fr(xt). These quantities follow from the evaluation of penguin and box diagrams with heavy particles running in the loops, i.e. top and W in the SM, and are related to the Inami-Lim functions.35 On the other hand, the term PQ summarizes the contributions from light internal quarks, such as the charm and up quarks. It should be noted that PQ and Pr are process-dependent quantities, i.e. depend on the hadronic matrix elements of the operators Qk for a given decay, whereas the Fr(xt) are process-independent functions. In Section 5, we will return to this formalism in the context of NP. Rare decays have many interesting features, as discussed in several reviews and the references therein. 16 ' 34 ' 46,49 Let us here choose BStd —> M+M~ modes as a representative example, since these decays allow a compact presentation, belong to the cleanest representatives of the field of rare decays, and are an important element of the B-physics programme at the LHC. 50 4.3. Example:

B S) d —* l^+l^~

In the SM, Bq —* /J + /X~ modes (q 6 {s,d}) originate from Z° penguins and box diagrams, as can be seen in Fig. 7. The corresponding low-energy effective Hamiltonian is given as follows:

HeS =

GF

"71

27rsin 0\y

Vi*bVtqT}YY0(xt){bq)v-A(M)v-A

+ h.c, (48)

19

Figure 7.

b

!>•

6

W

M

W

M

Decay processes contributing to Bs(i —• £ i + / i - in the SM.

where a denotes the QED coupling, G\y is the Weinberg angle, and the short-distance physics is described by Y(xt) = VYYo(xt).

(49)

Here rjy = 1.012 is a perturbative QCD correction, 51-53 and the Inami-Lim function Yo(xt), which can be written to a good approximation as ,1.56

Y0(xt) = 0.98 x

mt .167 GeV J

(50)

describes the top-quark mass dependence. 54 We observe that the matrix element of (48) between a (/x~/z+| final state and a |B°) initial state involves simply the "decay constant" / B , which is defined through b

{0\halsq\B°{k))=ifBqka.

(51)

Consequently, we encounter a very favourable situation with respect to the hadronic matrix elements. Since, moreover, NLO QCD corrections were calculated, and long-distance contributions are expected to play a negligible role, 51 the Bq —• n+n~ modes belong to the cleanest rare B decays. In the SM, their branching ratios can be written as'55 BR(B S

4.1 x 10

M"V

h

T2

0.24 GeV BR{Bd

V,ts\

2

x

0.20 GeV

Ba

0.040

H+fj,-) = 1.1 x 10

n3.12 mt 167 GeV

T

1.5ps

(52)

10 2

f \Vtd\ 1 0.008

'

T

Bd

r

mt

i3.12

1.5 ps L167 GeV J

(53)

which should be compared with the current experimental upper bounds: BR(B S -> n+V~) < 5-0 x 10" 7 [DO @ 95% C.L.56] 8

(54) 57

BR(Bd -f fi+fj,-) < 8.3 x 10" [BaBar @ 90% C.L. ]. b

Note that (0\hyaq\B°(k))

= 0, since the B° is a pseudoscalar meson.

(55)

20

If we use the relation Vtd

*

S

A

vcb

1 Vtd [1 + 0(A 2 )], ~ A Vts

(56)

we observe that the measurement of the ratio

BR(B d ->/i + AO

'TBd

BR(B,-»JKV)

JB,.

\MBd] fBd [MB A JB,.

2

Vd Vts

(57)

would allow a determination of the UT side Rt- This strategy is complementary to the one addressed in Subsection 2.5, which is offered by AMd AM,

\MBd] [MB A

BBA .BB,.

2

fBd JBB.

Vd Vs

(58)

where the BB„ are non-perturbative "bag" parameters arising in B®~B® mixing. These determinations rely on the following 5f/(3)-breaking ratios: JBS

p _

IBA

BsfBs

(59)

BdfBd

which can be obtained from QCD lattice studies or with the help of QCD sum rules, and are an important target of current research. 58 Looking at (57) and (58), we see that these expressions imply the relation

BR(Bs^fi+Li-) BR(Bd^n+»-)

~TBA ~BBd~

'AM/

jBd.

[AMJ

B

. Bs.

(60)

which suffers from theoretical uncertainties that are smaller than those affecting (57) and (58) since the dependence on ( / s d / / B s ) 2 cancels and BBd/BBs = 1 up to tiny 5?7(3)-breaking corrections. 59 Moreover, we may also use the (future) experimental data for AM(S)
fi+fi')

BR(Bd

M"V

= (3.42 ±0.53) x

AM, 18.0 p s " 1

(1.00 ±0.14) x 10" 1 0 .

x 10"

(61) (62)

In view of these tiny branching ratios, we could only hope to observe the Bq —> n+n~ decays at the LHC, should they actually be governed by their SM contributions. 50 However, as these transitions are mediated by rare FCNC processes, they are sensitive probes of NP. In particular, as was recently reviewed,15 the Bq —> \x+yT branching ratios may be dramatically enhanced in specific NP (SUSY) scenarios. Should this actually be the

21 case, these decays may be seen at run II of the Tevatron, and the e+e~ B factories could observe Bd —> fi+fJ.~. The interpretation of the present and future experimental constraints on Bs —> fi+[i~ in the context of the constrained minimal extension of the SM (CMSSM) with universal scalar masses was recently critically discussed.60 5. How Could N e w Physics Enter? 5.1. Twofold Impact

of New

Physics

In order to address the question of how NP affects flavour physics, we use once agian the language of the low-energy effective Hamiltonians introduced above. There are then two possibilities for NP to manifest itself:15 (i) NP may modify the "strength" of the operators arising in the SM. In this case, we obtain new short-distance functions that depend on the NP parameters, such as masses of charginos, squarks, charged Higgs particles and tan/3 = t^/wi in the MSSM. The NP particles enter in new box and penguin diagrams and are "integrated out" as the W and top, so that we arrive at initial conditions for the renormalization-group evolution (26) of the following structure: Ck{ti = Mw)^CfA

+ C^,

(63)

p

where the NP pieces C ^ may also involve new CP-violating phases that are not related to the CKM matrix, (ii) NP may lead to an enlarged operator basis:

{Qk}^{QlM,Qfp},

(64)

i.e. operators that are absent (or strongly suppressed) in the SM may actually play an important role, thereby yielding, in general, also new sources for flavour and CP violation. 5.2. Classification

of New

Physics

After these general considerations, NP can be divided into the following classes, as was done by Buras 15 Class A: this class describes models with "minimal flavour violation" (MFV), which represent the simplest extension of the SM. Here the flavourchanging processes are still governed by the CKM matrix - in particular there are no new sources for CP violation - and the only relevant operators

22

are those present in the SM. If we use v as an abbreviation for the set of parameters involved, the Fr(xt) introduced in (47) are simply replaced by generalized functions Fr(v), which involve only seven "master functions", S(v), X{v), Y(v), Z(v), E(v), D'(v), E'(v). In (48), we encountered already one of them, the function Y, which characterizes rare K, B decays with d.+£~ in the final states. Concerning Bq —* /U+/i~ decays, the NP effects can hence be included through the simple replacement Y(xt) —> Y(v). A similar procedure applies to the expressions for AMq, where a function S(v) is involved. Since the same functions enter in the Bs- and Bd-meson cases, relations (57), (58) and (60) hold not only in the SM, but also in the whole class of MFV models, thereby providing an interesting test of this NP scenario. Examples are the THDM-II and constrained MSSM if tan /3 is not too large, as well as models with one extra universal dimension. Class B: in contrast to class A, new operators arise, but still no new CP-violating phases are present. Examples of new Dirac structures are (V - A) ® (V + A), (S - P) ® (S ± P),
on the Roadmap

of Quark-Flavour

Physics

The B-meson system offers a variety of processes and strategies for the exploration of CP violation. 61 Looking at Fig. 8, where we have collected prominent examples, we see that there are processes with a very different dynamics that are - within the framework of the SM - sensitive to the same

23 7T7T (isospin), B — pn, B —• pp

Rt (B»-B» mixing)

Rl, (b —• u,

B

rvK (penguins)

7?* • K^n) B only trees B;±: • [)t:D

Bd -» il>Ks (Bs — M : 4>3 ss 0) Bfi —> 4>K§ (pure penguin)

Bd - • D W * ^ : "• + 2/31

Figure 8.

only trees

A brief roadmap of B-decay strategies for the exploration of CP violation.

angles of the UT. Moreover, rare B- and if-meson decays, which originate from loop effects in the SM, provide complementary insights into flavour physics and interesting correlations with the CP-B sector. In the presence of NP, the subtle interplay between different processes is expected to be disturbed, so that discrepancies should emerge. There are two popular avenues for NP to enter the roadmap of flavour physics: (i) Bq-B® mixing: NP may enter through the exchange of new particles in the box diagrams, or through new contributions at the tree level, thereby modifying the mixing parameters as follows: A M , = AMqSM

A M NP

4>q = 4^ + 4^.

(65)

Whereas A M ^ P would affect the determination of the UT side Rt, the NP contribution qF/4>^M ~ 1 m a y ~~ m principle - be possible for a NP scale ANP in the TeV regime; such a pattern may also arise in specific NP scenarios. However, thanks to the B-factory data, the space for NP is getting smaller and smaller in the .B^-meson system. On the other hand, the Bs sector is still essentially unexplored, and leaves

24

a lot of hope for the LHC era. In Section 6, we will discuss the corresponding "golden" decays, Bd —• J/tpKs and Bs —• J/ip<j>. (ii) Decay amplitudes: NP has typically a small effect if SM tree processes play the dominant role, as in Bd —• J/ipKs decays. On the other hand, there are potentially large effects in the FCNC sector. For instance, new particles may enter in penguin diagrams, or we may encounter new FCNC contributions at the tree level. Sizeable contributions may arise generically in field-theoretical estimates with ANP ~ TeV, 64 as well as in specific NP models. Interestingly, there are hints in the current B-factory data that this may actually be the case. In particular, Belle results for the Bd —• wK decays show a puzzling pattern which may indicate NP in the EW penguin sector. These hot topics will be discussed in Sections 7 and 8, respectively. Let us emphasize that also the D-meson system provides interesting probes for the search of NP: 2 2 D°-D° mixing and CP-violating effects are tiny in the SM, but may be enhanced through NP. Concerning model-dependent NP analyses, in particular SUSY scenarios have received a lot of attention; for a selection of recent studies, see Refs. 6570. Examples of other fashionable NP scenarios are left-right-symmetric models, 71 scenarios with extra dimensions, 72 models with an extra Z', 7 3 little Higgs scenarios, 74 and models with a fourth generation. 75 6. " G o l d e n " Decays of B Mesons Let us now have a closer look at Bd —> J/ipKs and Bs —> J/tp
Bd^J/iJ>Ks

6.1.1. Amplitude Structure and CP-Violating Observables This decay has a CP-odd final state, and originates from b —> ccs quarklevel transitions. Consequently, as we have seen in the classification of Subsection 3.2, we have to deal both with tree and with penguin topologies, so that the decay amplitude takes the following form:76

A(B°d - JI^KS) = AW ( 4 + A{) + WA$ + A| s ) 4.

(66)

25

In this expression, the

\is)

vq,v;b

(67)

are CKM factors, A^ is the CP-conserving strong tree amplitude, while the Ap describe the penguin topologies with internal g-quark exchanges (q € {u, c, t}), including QCD and EW penguins; the primes remind us that we are dealing with a b —* s transition. If we eliminate now \[s' with the help of (28) and apply the Wolfenstein parametrization, we arrive at A{B°d - • J/ipKa) oc [1 + A 2 ae*V 7 ] ,

(68)

where ae^ =

Rb 1-A2

u

A Zip

•4

-riq-i "T -'T-p

(69) "^-P

is a hadronic parameter. Using now the formalism of Subsection 3.4.3 we obtain c(d) _ *ipKs =

+e"

1+ A W V 1 + A 2 ae w e + i T

(70)

Unfortunately, ae1^, which is a measure for the ratio of the Bd —> J/tpKs penguin to tree contributions, can only be estimated with large hadronic uncertainties. However, since this parameter enters (70) in a doubly Cabibbosuppressed way, its impact on the CP-violating observables is practically negligible. We can put this important statement on a more quantitative basis by making the plausible assumption that a = 0(A) = 0(0.2) = O(A), where A is a "generic" expansion parameter:

A&(Bd^J/^Ks)=0A®?(Bd

J/^KS)

0(A 3 )

(71) 3

S

3

= - s i n 0 d + 0(A ) = - s i n 2 £ + 0(A ).

(72)

Consequently, (72) allows an essentially clean determination of sin 2/3.7 6.1.2. Experimental

Status

Since the CKM fits performed within the SM pointed to a large value of sin 2/3, Bd —> J/ipKs offered the exciting perspective of large mixinginduced CP violation. In 2001, the measurement of A™™(Bd —• J/tpKs) allowed indeed the first observation of CP violation outside the i-f-meson

26

system. 6 The most recent data are still not showing any signal for direct CP violation in Bd —> J/tpKs decays, as is expected from (71), but yield f 0.722 ± 0.040 ± 0.023 (BaBar 77 ) s i n 2 0 - | o.728 ±0.056 ±0.023 (Belle 78 ),

. . '

[

which gives the following world average:79 sin 2/3 = 0.725 ±0.037.

(74)

The theoretical uncertainties are below the 0.01 level (a recent analysis finds even smaller effects80), and can be controlled in the LHC era with the help of the Bs —» J/tpKs channel. 76 6.1.3. What about New Physics? The agreement of (74) with the CKM fits is excellent.31 However, despite this remarkable feature, NP could - in principle - still be hiding in the mixing-induced CP violation observed in Bd —> J/ipKs- The point is that the key quantity is actually the B^-B^ mixing phase

cf>d = TA + T = W + 4>r,

(75)

where the world average (74) implies 0d = ( 4 6 . 5 i ^ r

V

(133.5i33;°)°.

(76)

Here the former solution would be in excellent agreement with the CKM fits, yielding 40° <; 2/3 <; 50°, whereas the latter would correspond to NP. 6 3 , 8 1 Both solutions can be distinguished through the measurement of the sign of cos (f>d, where a positive value would select the SM case. Performing an angular analysis of Bd —• Jl^\—• t+£~]K*[-+ ir°Ks] processes, the BaBar collaboration finds82 cos
(77)

thereby favouring the SM. Interestingly, this picture emerges also from the first data for CP-violating effects in Bd —> D^^TT^ modes, 83 and an 42 analysis of B —> irir, irK decays, although in an indirect manner. As far as NP contributions at the amplitude level are concerned, they have to compete with SM tree-diagram-like topologies, which play the dominant role in the B —> J/ifrK modes. Consequently, the NP contributions to the decay amplitudes are generically at most at the 10% level; these effects could be detected through appropriate observables, exploiting direct CP violation and charged B*1 —> J/tpK± decays. 62 Since the current B-factory

27

data do not give any indication for NP of this kind, we eventually arrive at the situation in the p-fj plane shown in Fig. 2. The space for NP contributions to B°d-B°d mixing is therefore getting smaller and smaller. However, there is still hope for NP effects in B°-B° mixing, which can nicely be probed through Bs —» J/ip(p, the £?s-meson counterpart of Bd —> J/ipKg. 6.2. Ba ->• J/tpcp 6.2.1. Preliminaries: Characteristic Features of B®-B® Mixing At the e+e~ B factories operating at the T(45) resonance, no Bs mesons are accessible, whereas we obtain plenty of Bs mesons at hadron colliders, i.e. at Tevatron-II and the LHC. The Bs system has interesting features: • In the SM, the B®-B® oscillations are expected to be much faster than their S^-meson counterparts, and could so far not be observed. The current lower bound for the mass difference of the Bs mass eigenstates is given as follows:79 AM S | S M > 14.4 p s " 1 (95% C.L.),

(78)

and plays an important role in the CKM fits.58 • In contrast to the B^-meson system, the width difference AT S is expected to be sizable in the Bs case, 84 and may therefore allow interesting studies with the following "untagged" Bs rates: 85 ' 86 (T(Bq(t) -+ / ) ) = T(B°q(t) - / ) + T(B°q(t) - / ) .

(79)

Recently, the first results for ATS were reported from the Tevatron, using the Bs —» J/ip(/> channel: 87 88 | A r s | _ / 0.65to i ± 0.01 (CDF 89 )

,. -{a2i+°ir^(So ).2lj£2jj (DO )/ ). 89

(8o)

Finally, let us emphasize again that s is negligibly small in the SM, whereas 4>d takes the large value of 2/3 = (46.5t|;o)°. 6.2.2. CP Violation in Bs -+ J/ip(j> This channel is simply related to Bd —> J/tpKs, through a replacement of the down spectator quark by a strange quark. Consequently, the structure of the Bs —• J/ip(j) decay amplitude is completely analogous to (68). On the other hand, the final state of Bs —> J/ip<j> is an admixture of different CP eigenstates, which can, however, be disentangled through an angular

28

analysis. 87 ' 90 The corresponding angular distribution exhibits tiny direct CP violation, and allows the extraction of sin
= sin 4>s + 0(1(T 3 )

(81)

through mixing-induced CP violation. Since s = —2X2r] = O(10~ 2 ) in the SM, the determination of this phase from (81) is affected by hadronic uncertainties of 0(10%), which may become an important issue for the LHC era. These uncertainties can be controlled with the help of flavoursymmetry arguments through the decay Bd —• J/tpp0.91 Because of its nice experimental signature, Bs —> J/tp(j> is very accessible at hadron colliders, and can be fully exploited at the LHC. Needless to note, the big hope is that sizeable CP violation will be found in this channel. Since the CP-violating effects in Bs —• J/ipcp are tiny in the SM, this would give us an unambiguous signal for NP. 92 As the situation for NP entering through the decay amplitude is similar to B —> J/ipK, we would get immediate evidence for NP contributions to B®-B® mixing, and could extract the corresponding sizeable value of 4>s . 93 Such a scenario may generically arise in the presence of NP with ANP ~ TeV, 61 as well as in specific models (see, e.g., Refs. 66, 68). In such studies, also correlations with CP-violating effects in Bd —• Ks are typically investigated, which is our next topic. 7. Challenging the Standard Model through Bd —• 0-K"s 7.1. Amplitude

Structure

and CP-Violating

Observables

Another important probe for the testing of the KM mechanism is offered by B° —> (j>Ks, which is a decay into a CP-odd final state, and originates from b —• sss transitions. Consequently, it is a pure penguin mode, which is dominated by QCD penguins. 94 Because of the large top-quark mass, EW penguins have a sizeable impact as well. 95 ' 96 In the SM, we may write A(B°d -> 4>Ks) - \{:]Ai

+ \isU£

+ X^A'p,

(82)

where we have applied the same notation as in Subsection 6.1. Eliminating once more the CKM factor A^s) with the help of (28) yields A(B°d -» 4>KS) oc [1 + A 2 6e ie e i7 ] ,

(83)

where Ac' — A*' P

P

(84)

29

Consequently, we obtain

The theoretical estimates of bez& suffer from large hadronic uncertainties. However, since this parameter enters (85) in a doubly Cabibbo-suppressed way, we obtain the following expressions:97 + O(\2)

A%P(Bd->(f>Ks)=0

(86) 2

A%P*(Bd - j>Ks) = - sin
(87)

where we made the plausible assumption that b = 0(1). On the other hand, the mixing-induced CP asymmetry of Bd —> J/ipKs measures also — sind, as we saw in (72). We arrive therefore at the following relation: 9 7 - 1 0 0 A£P*(Bd -> Ks) = A™(Bd

- J/i,Ks)

+ 0(A 2 ),

(88)

which offers a very interesting test of the SM. Since Bd —* cpKs is governed by penguin processes in the SM, this decay may well be affected by NP. In fact, if we assume that NP arises generically in the TeV regime, it can be shown through field-theoretical estimates that the NP contributions to b —> sss transitions may well lead to sizeable violations of (88); in order to trace the origin of NP systematically, a combined analysis of the neutral and the charged B —> <j)K modes would be very useful.64 7.2. Experimental

Status

It is interesting to have a brief look at the time evolution of the S-factory data. At the LP '03 conference,101 the picture was as follows: A**, o _ ,K x _ J -0-38 ± 0.37 ± 0.12 (BaBar) ACP{Bd - 4>KS) - | + Q J 5 ± Q 2 Q ± 0Q7 ( B e U e ) A™{R

_ ,K

x _ / -0-45 ± 0.43 ± 0.07 (BaBar)

^CP(^-^S)-|

+ 0 - 9 6 ± 0 - 5 0

+O.II

(Belle).

(89)

(90)

In the summer of last year, the following situation emerged at ICHEP '04: 102

A^ (R ->rhK)-$ ACP(Bd

- 4>KS) - | _ Q

A™(B ^,hK\-[ ACP (Bd^

+0M

±

o g ± Q 2 2 ± Q Q9 ( B e l l e i 0 4 )

~ ° - 5 0 ± °- 25 -° °07

4>KS\ - | _ 0 ( ) 6

= -(sin2/3)^s

°- 23 ± °-° 5 ( B a B a r l ° 3 ) (BaBarl°3)

± Q 3 3 ± Q Q9 ( B e l l e i o 4 )

(qi)

(91)

(o2] (92)

30

Step 1.

; : H->nn Decays • described within SM

mrX: B :

T

Si/able Departures from QC1JI'. 1'QCT)

(LM -Puiguius small)

Step 2.

d, 8, x, A ; + SU(3)F

Step 3.

Correlation* between . 11 - •> nK, Rare K and U : Decays and other Processes 1

Implications lor Rare K. and 13 Decays .sensitive In GWI*

F i g u r e 9. T h e logical s t r u c t u r e of a s y s t e m a t i c s t r a t e g y t o a n a l y z e t h e B p u z z l e s a n d t o e x p l o r e t h e i r i m p l i c a t i o n s for r a r e K a n d B d e c a y s .

mr,nK

Because of -(sm2/3)^Ks = A^{Bd -> J/ipKs) = -0.725 ± 0.037, the Belle data may indicate a violation of (88) through CP-violating NP contributions to b —> sss transitions, which has already stimulated many speculations about NP effects in the decay B& —* 4>Ks-66'68 However, the new Belle data moved towards the SM, and the BaBar data - though also somewhat on the lower side - are in accordance with the SM. Consequently, it seems too early to get too excited by the possibility of having a violation of the SM relation (88). It will be very interesting to observe how the B-factory data will evolve, and to monitor also similar modes, such as Bj, —> rj'Ks. However, it is questionable to perform averages over many decays of this kind to argue for NP in b —+ s penguin processes, as is frequently done in the literature. The point is that we encounter different hadronic uncertainties in the SM, and that also NP is generally expected to affect these decays differently. 8. T h e B —• 7T7T, TTK Puzzles a n d t h e i r Implications for R a r e K a n d B Decays

8.1.

Preliminaries

For the search of NP signals and the exploration of their specific nature, it is crucial to exploit as much experimental information as possible, and to make also use of the interplay between CP-violating phenomena and rare decays. As an example, let us discuss a strategy, which was recently proposed to analyze puzzling patterns in the data for B —> TVIT and B —> -KK decays, and to investigate their implications for rare K and B decays. 42 Its

31 starting point is the SM, with

4>d = ( 4 6 . 5 i ^ ) ° (see (76)),

7 = (65 ± 7)° (CKM fits),

(93)

and it consists of three interrelated steps, as illustrated in Fig. 9:

• In step I, we perform an isospin analysis of the currently available B —> mr data, allowing us to extract a set of hadronic parameters characterizing the B —> TTTT system, and to predict the CP-violating Bd —• 7r°7r° observables. We find large non-factorizable effects, but arrive at a picture which is consistent with the SM. • In step II, we use the hadronic B —> TTTT parameters from step I to determine their B —> TTK counterparts with the help of the 5(7(3) flavour symmetry, allowing us to predict the B —> nK observables in the SM. We find agreement with the B-factory data in the case of those decays that are only marginally affected by EW penguins. Moreover, we may extract 7, in excellent accordance with (93), and can perform a couple of other internal consistency checks, which also support our working assumptions. On the other hand, in the case of the B —> irK decays with a significant impact of EW penguins, we obtain predictions which are not in agreement with the current data. This feature is a manifestation of the "£? —» irK puzzle", which was already pointed out in 2000, 105 and received considerable attention in the recent literature (see, for instance, Refs. 81, 106-110). It can be resolved through NP in the EW penguin sector, which enhances the corresponding contributions and introduces a new CP-violating phase. • In step III, we assume that NP enters in the EW penguin sector through Z° penguins, and explore the interplay of such a scenario with rare K and B decays. Interestingly, spectacular NP effects would arise in several processes, in particular in K^ —* TT°I/P and Bs,d —* At+At~ modes, thereby leading to a specific pattern which can be tested experimentally.

Let us now have a closer look at these three steps, where the numerical results refer to a recent update. 30

32

8.2. Step I: B ->

TTTT

8.2.1. Input Observables The B —> 7T7T system offers three channels, £?+ —» 7r+7r°, B° —• 7r+7r~ and B° —> 7r°7r°, as well as their CP conjugates. Consequently, two independent ratios of the corresponding CP-averaged branching ratios are at our disposal, which we may introduce as follows: BR(B±

TyTTTV

- * T^TT 0 )

B R ( B d ->• 7T+7T-) •n-00

=

*

BR(Bd T,T,/r,

- ^ - = 2.20 ± 0.31

(94)

TB+

- + 7r°7r°) J. N =0.67 ±0.14.

(95)

.BR(.B d ->7r+7r-)J The branching ratios for Bd —+ 7r+7r_ and B^ —• 7r°7r° are found to be surprisingly small and large, respectively, whereas the one for B*" —> •K±IT0 is in accordance with theoretical estimates. This feature is reflected by the pattern of R\*_ ~ 1.24 and B$ ~ 0.07 arising in QCDF. 106 In addition to the CP-conserving observables in (94) and (95), we may also exploit the CP-violating observables of the Bd —»7r+7r~ decay: A^(Bd

- • TT+TT") = - 0 . 3 7 ± 0 . 1 1

(96)

A%£(Bd -> TT+TT") = +0.61 ± 0.14.

(97)

The experimental picture of these CP asymmetries is not yet fully settled. 79 However, their theoretical interpretation discussed below yields constraints for the UT in excellent agreement with the SM. 8.2.2. Hadronic Parameters Using the isospin flavour symmetry of strong interactions, the observables in (94)-(97) depend on two (complex) hadronic parameters, del6 and xelA, which describe - sloppily speaking - the ratio of penguin to colour-allowed tree amplitudes and the ratio of colour-suppressed to colour-allowed tree amplitudes, respectively. It is possible to extract these quantities cleanly and unambiguously from the data: c d = 0.5li°;220,

0 = +(14Oii 4 8 )°,

* = 1.15+°0;i86,

A = - ( 5 9 ± £ ) ° ; (98)

a similar picture is also found by other authors. 4 3 - 4 5 In particular the impressive strong phases give an unambiguous signal for large deviations from C

EW penguin topologies have a tiny impact on the B —• mr system, but are included in the numerical analysis. 3 0

33

"factorization". In recent QCDF 1 1 1 and PQCD 1 1 2 analyses, the following numbers were obtained: d\QCuF = 0-29 ±0.09, <*IPQCD

= 0.23t£o5>

0| Q C D F = -(171.4 ±14.3)°, +139° <

^IPQCD

< + 14 8°>

(99) (100)

which depart significantly from the experimental pattern in (98). 8.2.3. CP Violation in Bd -»ir°ir 0 Having the hadronic paramters of (98) at hand, the CP-violating asymmetries of the Bd —> 7r°7r° channel can be predicted: 4 & ( i k - ^ V ) | S M =-0.28±2;£ A$?{Bd - 7 r V ) | S M = -0.63±g;«,

(101) (102)

thereby offering the exciting perspective of large CP violation in this decay. The first results for the direct CP asymmetry were recently reported: 4dirrR

0 7 r 0x_

f - ( 0 - 1 2 ± 0 . 5 6 ± 0 . 0 6 ) (BaBar 113 )

^cp(^-»*)-(_(0.43±0.5llg:IJ)

(Belle114),

(1 3)

°

and correspond to the average of A^(Bd -*• 7r°7r°) = -(0.28 ± 0.39),79 which shows an encouraging agreement with (101). In the future, more accurate input data will allow us to make much more stringent predictions. 8.3. Step II: B -»• nK 8.3.1. Ingredients of the B —> TTK Analysis In contrast to the B —> irw modes, which originate from b —> d processes, we have to deal with b —• s transitions in the case of the B —> wK system. Consequently, these decay classes differ in their CKM structure and exhibit a very different dynamics. In particular, the B —> nK decays are dominated by QCD penguins. Concerning the EW penguins, the B —• ITK decays can be divided as follows: • B°d -> ir~K+, B+ -> n+K° (and CP conjugates): EW penguins are colour-suppressed and expected to play a tiny role; • B+ -> n°K+, B°d -> TT°K° (and CP conjugates): EW penguins are colour-allowed and have therefore a significant impact.

34

The starting point of our B —> TTK analysis are the hadronic B —» -KIT parameters determined in Subsection 8.2, and the values of 4>d and 7 in (93), which correspond to the SM and are only insignificantly affected by EW penguins. We use then the following working hypothesis: (i) SU(3) flavour symmetry of strong interactions; (ii) neglect of penguin annihilation and exchange topologies. It is important to stress that internal consistency checks of these assumptions can be performed, which are nicely satisfied by the current data and do not indicate any anomalous behaviour. We may then determine the hadronic B —»• -nK parameters through their B —> inr counterparts, allowing us to predict the B —>• TTK observables in the SM. 8.3.2. Observables with a Tiny Impact of EW Penguins Let us first have a look at the observables with a tiny impact of EW penguins. Here the direct CP asymmetry in Bd —• ir^K^ modes, which could be observed last summer, plays an important role. The average of the corresponding BaBar and Belle results 8 is given as follows:79 A$%>(Bd^nr:*K±)

= +0.113 ± 0 . 0 1 ,

(104)

and establishes direct CP violation in the .B-meson system. The non-zero value of this CP asymmetry is generated through the interference between a QCD penguin and a colour-allowed tree amplitude, where the former dominates. In our strategy, we obtain the following prediction: A&(Bd

- ^K±)

= +0.127i°;S°26,

(105)

which agrees nicely with the experimental value. Moreover, assumptions (i) and (ii) listed in Subsection 8.3.1 imply the following relation: Foe

| ^

BR(B d BR(B d -»7rFK±).

A^p(Bd

- 7T+7T-)

(106)

0.38±0.04 0.31±0.11 where we have also indicated the experimental values, which give us further confidence into our working assumptions. Moreover, since we may write H = G3(d,e;1), the Bd —+ n^K^

(107)

data allow us to convert the CP asymmetries A^(Bd

- 7T+7T-) = Grid,6;7) +

A^(Bd-^n TT-)

= G2(d,e;j,d)

(108) (109)

35 into a value of 7. 8 1 ' 1 1 5 The corresponding result is shown as the quadrangle in Fig. 2, which is in excellent agreement with all the other UT constraints. On the other hand, a moderate numerical discrepancy arises for the ratio R of the CP-averaged Bd -> -K^K*, B± -> w^K branching ratios. 116 This feature suggests a sizeable impact of a hadronic parameter pceld*, which enters the most general parametrization of the B+ —* n+K° amplitude. 117 ' 118 It can be constrained through the direct CP asymmetry of the decay B^ —* -K^K and the emerging B± —> K±K signal, and actually shifts the predicted value of R towards the data. 30 Consequently, no discrepancies with the SM arise in this sector of the B —• irK system. 8.3.3. Observables with a Sizeable Impact of EW Penguins Let us now turn to those observables that are significantly affected by EW penguins. The key quantities are the following ratios: 119 Re =2

Rn=

2

BR(B+ -» TT°K+) + BR(B~ -> ifiK~) BR(B+ -> ir+K°) + BR(B~ -> -K'K0) BR(5° -> TT-K+) + BR(B° -» BR(£° -» TT°K°) + BR(B°d -»

-K+K') TT°K°)

_

E p

= 1.00 ±0.08

(110)

E p

= 0.79 ± 0.08, (111)

where the EW penguin contributions enter in colour-allowed form through the decays with 7r°-mesons in the final states. Theoretically, the EW penguin effects are described by the following parameters: gS=0.69,

S=0°.

(112)

Here q, which can be calculated in the SM with the help of the SU(3) flavour symmetry, 120 measures the "strength" of the EW penguins with respect to the tree contributions, and is a CP-violating weak phase with an origin lying beyond the SM. EW penguin topologies offer an interesting avenue for NP to manifest itself, as is already known for several years. 121 ' 122 In Fig. 10, we have shown the current situation in the Rn-Rc plane: the experimental ranges and those predicted in the SM are indicated in grey, and the dashed lines serve as a reminder of the corresponding ranges in Ref. 42; the central values for the SM prediction have hardly moved, while their uncertainties have been reduced a bit. Moreover, we show contours for values of q = 0.69, q = 1.22 and q = 1.75, with € [0°,360°]. We observe that we arrive no longer at a nice agreement between our SM predictions and the experimental values. However, as becomes obvious from the contours in Fig. 10, this discrepancy can be resolved if we allow for NP

36 q = 1.75 exp. region

g = 0.6) 0.6

Figure 10.

0.7

0.8

Kn

The situation in the RB-Rc

plane, as discussed in the text.

in the EW penguin sector, i.e. keep q and (f> as free parameters. Following these lines, the successful picture described above would not be disturbed, and we obtain full agreement between the theoretical values of Rn
« = 1.08±8;?S, 0 = - ( 8 8 . 8 t } ^ ) ° ,

(113)

where in particular the large CP-violating phase would be a striking signal of NP. These parameters allow us then to predict also the CP-violating observables of the B± —> T^K*- and Bd —» ir°Ks decays, 30 which should provide useful tests of this scenario in the future. Particularly promising in this respect are rare K and B decays.

8.4. Step III: Rare K and B

Decays

In order to explore the implications for rare K and B decays, we assume that NP enters the EW penguin sector through enhanced Z° penguins with a new CP-violating phase. This scenario, which belongs to class C introduced in Subsection 5.2, was already considered in the literature, where modelindependent analyses and studies within SUSY were presented. 123 ' 124 In our strategy, we determine the short-distance function C characterizing the Z° penguins through the B —> nK data. Performing a renormalization-group analysis, 109 we obtain C{q) = 2.35 qe** - 0.82

with

q=q

\Vub/Vccb\ 0.086

(114)

37

If we evaluate then the relevant box-diagram contributions within the SM and use (114), we can calculate the short-distance functions X = 2.35 qe^ - 0.09

and

Y = 2.35 qe^ - 0.64,

(115)

which govern the rare K, B decays with vv and £+£~ in the final states, respectively. In the SM, we have C = 0.79, X = 1.53 and Y - 0.98, with vanishing CP-violating phases. Table 1. Comparison of the predicted values of Re and Rn taking the constraints from rare decays into account with the evolution of the data, as discussed in the text. "Old" data

Prediction with RDs

"New" data

Rc

1.17 ± 0 . 1 2

1.00±g;J|

1.00 ± 0 . 0 8

Rn

0.76 ± 0 . 1 0

0

0.79 ± 0 . 0 8

-82iaii

If we impose constraints from the data for rare decays, in particular those on \Y\ following from B —> Xsn+n~, the following picture arises: « = 0.92±g:gi,

=-(85±\\)°.

(116)

In Table 1, we compare the corresponding predictions of Rc and Rn with the "old" data, which were available when these predictions were made, 42 and the "new" data, which emerged at the ICHEP '04 conference.102 We observe that the data have moved accordingly. The values in (116) are compatible with all the current data on rare decays, and are in accordance with the new B —> TTK data. However, we may still encounter significant deviations from the SM expectations for certain rare decays, with a set of predictions that is characteristic for our specific NP scenario, thereby allowing an experimental test of this picture. The most spectacular effects are the following ones: • B R ( X L —> 7r°i/P) is enhanced by a factor of O(10), which brings it close to the Grossman-Nir bound, 125 whereas BR(K+ —• TT+I/&) remains essentially unchanged. Consequently, we would also have a strong violation of the following MFV relation: 126 (sin2/3) m/P = -(0.69tg:g)

(sin2/%Ks

,

+(0.725 ±0.037)

where we have indicated the corresponding numerical values.

(117)

38

• The decay Ki, —* 7r°e+e~ would now be governed by direct CP violation, and its branching ratio would be enhanced by a factor of 0(3). The interesting implicatios for K\, —> 7r°/z+M~ were discussed in a recent paper. 127 • In the case of Bj —> K*fi+fi~, an integrated forward-backward CP asymmetry 124 can be very large, whereas it vanishes in the SM. The corresponding NP effects for the lepton polarization asymmetries of B —> Xsl+l~~ decays were recently studied. 128 • The branching ratios for B —• Xs^vv and Bs^ —> /i + /i~ decays would be enhanced by factors of 2 and 5, respectively, whereas the impact on K\, —»/x+/z~ is rather moderate. If future, more accurate, B —>rnr,TTK data will not significantly modify the currently observed patterns in these decays, the scenario of enhanced Z° penguins with a large CP-violating NP phase <> / will remain an attractive scenario for physics beyond the SM. It will then be very interesting to confront the corresponding predictions for the rare K and B decays listed above with experimental results. 9. Conclusions and Outlook Flavour physics offers interesting strategies to explore the SM and to search for signals of NP. In the 5-meson system, data from the e+e~ B factories agree on the one hand remarkably well with picture of the KobayashiMaskawa mechanism, where the accordance between the measurement of sin 2/3 through Bd —> J/tpKs decays and the CKM fits is the most important example. On the other hand, there are also hints for discrepancies with the SM, and it will be very interesting to monitor these effects in the future. Despite this impressive progress, there are still regions of the B-physics "landscape" left that are unexplored. For instance, 6 —• d penguin processes are now close to enter the stage, since lower bounds for the corresponding branching ratios that can be derived in the SM are found to be close to the current experimental upper limits. 129 In fact, the BaBar collaboration has already reported the first signals for the Bd —> K°K° channel, in accordance with these bounds. 130 The lower SM bounds for other non-leptonic decays of this kind and for B —• fry transitions suggest that these modes should also be observed soon. For the more distant future, decays such as B —> p£+£~ decays are left. Since the various b —> d penguin modes are governed by different operators, they may be affected differently by NP. Moreover, as we have emphasized throughout these lectures, also the £?s-meson system

39

is still essentially unexplored, and offers a very promising physics potential for the search of NP, which should be fully exploited - after first steps at run II of the Tevatron - at the LHC, in particular by LHCb. These studies can nicely be complemented through the kaon system, which governed the stage of CP violation for more than 35 years. The future lies now on rare decays, in particular on the K —> TTUU modes, and any effort should be made to measure these very challenging - but also very rewarding - decays; this is the goal of the NA48 (CERN), E391(a) (KEK/J-PARC) and KOPIO (BNL) experiments. In addition to these electrifying aspects, flavour physics offers many more exciting topics, which we could unfortunately not cover here. Important examples are the D-meson system, electric dipole moments, and the search for flavour-violating charged lepton decays. For the search of NP and the exploration of its nature, it is important to keep an eye on all of these processes and to aim for the whole picture. In particular correlations between various K and B decays play an outstanding role in this context, as we have illustrated through the discussion of the B —> ITK puzzle. A fruitful interplay between flavour physics and the direct NP searches by ATLAS and CMS at the LHC is also expected, and will soon be explored in much more detail. 131 I have no doubt that an exciting future is ahead of us! Acknowledgments I would like to thank the organizers for inviting me to this wonderful Winter Institute in such a spectacular environment, and would also like to thank the participants for their stimulating interest in my lectures. References 1. J.H. Christenson et al., Phys. Rev. Lett. 13, 138 (1964). 2. V. Fanti et al. [NA48 Collaboration], Phys. Lett. B465, 335 (1999); A. Alavi-Harati et al. [KTeV Collaboration], Phys. Rev. Lett. 83, 22 (1999). 3. L. Wolfenstein, Phys. Rev. Lett. 13, 562 (1964). 4. J.R. Batley et al. [NA48 Collaboration], Phys. Lett. B544, 97 (2002); A. Alavi-Harati et al. [KTeV Collaboration], Phys. Rev. D67, 012005 (2003). 5. For a recent review, see A.J. Buras and M. Jamin, JEEP 0401, 048 (2004). 6. B. Aubert et al. [BaBar Collaboration], Phys. Rev. Lett. 87, 091801 (2001); K. Abe et al. [Belle Collaboration], Phys. Rev. Lett. 87, 091802 (2001). 7. A.B. Carter and A.I. Sanda, Phys. Rev. Lett. 45, 952 (1980); Phys. Rev. D23, 1567 (1981); I.I. Bigi and A.I. Sanda, Nucl. Phys. B193, 85 (1981).

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103. 104. 105. 106.

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P H Y S I C S AT T H E LARGE H A D R O N COLLIDER

MICHEL LEFEBVRE University of Victoria, Department of Physics and Astronomy, PO Box 3055 STN CSC, Victoria, British Columbia, V8W 3P6 E-mail: [email protected]

Canada

The Large Hadron Collider (LHC) at CERN is scheduled for first collisions in 2007. In these lectures the motivations for the LHC, its physics programme and its experimental challenges are reviewed. Emphasis is given to the multi-purpose proton-proton detectors ATLAS and CMS and their physics goals. Some of the important foreseen measurements and searches are discussed, including precise measurements of the mass of the W and of the top quark, the search for the Higgs boson(s) and for supersymmetric particles.

1. Introduction Most of our knowledge of the fundamental structure of matter comes from wave scattering experiments. Historically, optical microscopes were first used to study the structure of matter. They can only resolve structures to about the size of the wavelength of the light used. To further increase the resolution power, particles can be utilized. The Einstein - de Broglie relations p = h/X and E = hv provide the key to small scale investigations; the larger is the momentum of a particle, the smaller is its matter wavelength and hence the larger its resolution power. For fixed target experiments, the energy available to probe nature, or to create new states, grows as y/E\>eam. For colliding beams of equal energy, it grows as i^beam- Colliding beams are therefore more effective for research at the energy frontier. Let a be the cross section (expressed in fraction of a barn = 10~ 28 m 2 ) for a given scattering process (e.g. pp —> H + X) and L the collider's luminosity (usually expressed in c m _ 2 s _ 1 ) , then the event rate is simply given by R = La. Defining the integrated luminosity L = J Ldt, the number N of events is then N = lia. Therefore discovering a rare process with some significance requires a large integrated luminosity. To achieve this in a reasonable amount of time, a large luminosity is needed. 44

45 The Large Hadron Collider (LHC) is currently under construction at CERN. It is scheduled to start operation in 2007. With proton-proton collisions of centre of mass energy y/s = 14 TeV, it will be the first accelerator to directly explore the TeV scale. Its design luminosity of 10 34 c m ~ 2 s - 1 will allow searches for new particles up to masses of ~ 5 TeV a . The LHC will also operate as a heavy-ion collider; for example, 2 0 8 p b 8 2 + on 2 0 8 p b 8 2 + collisions at 1148 TeV centre of mass energy will allow the investigation of the so-called quark-gluon plasma. The LHC is being installed in the 27 km long circular tunnel originally built for the Large Electron Positron (LEP) collider. Its beam energy is limited by the bending power of the magnets needed to keep the beams in a circular orbit. In the LHC, the proton beams will be accelerated from a momentum of 450 GeV to 7 TeV with the help of superconducting dipole magnets operating from 0.535 T to 8.33 T. Building the LHC is a very challenging project 1 , on track for first collisions by summer 2007. Table 1 lists a few LHC parameters foreseen for commissioning, the first year of operation and for nominal operation. The design luminosity of 10 34 cm~ 2 s _ 1 is usually referred to as high luminosity while 10 33 c m _ 2 s _ 1 is called low luminosity. The bunch crossing time of 25 ns is particularly challenging for the experiments. The stored beam energy of 362 MJ is enormous: it corresponds to a fully loaded Airbus 380 plane (maximum take-off weight of 560 t) moving at 130 km/h! The high luminosity and high collision rate pose serious challenges to the detectors. Table 1. A few LHC parameters foreseen for commissioning, the first year of operation and for nominal high luminosity operation. Number of particles per bunch Number of bunches Bunch harmonic number Bunch spacing DC beam current Stored beam energy Luminosity (ATLAS and CMS) Events per bunch crossing

commiss 1.15 44 44 2021 0.009 5.65 0.015 21.2

1 s t year 0.4 2808 3564 25 0.20 127 0.12 2.7

nominal 1.15 2808 3564 25 0.582 362 1.0 22.2

units 10 1 1

ns A MJ 10 3 4 c m " 2 ! - 1 for 70 mb

Four large-scale collaborations will operate detectors in different points around the LHC. ATLAS 2 and CMS 3 are multi-purpose detectors with a a

"Natural units" with h= c = 1 are used throughout, unless otherwise specified.

46

broad physics programme, ranging from the search for the Higgs boson(s) to supersymmetric particles, as well as precision measurements. The LHCb 4 experiment is dedicated to the physics of B-hadrons and their CP-violating mixing and decays. The ALICE 5 experiment will study heavy ion collisions to explore the behaviour of nuclear matter at very high energies and densities, and in particular the formation of quark-gluon plasma 6 .

2. Physics Motivations for the LHC The Standard Model of the strong, electromagnetic and weak interactions (SM) is a well established theory, with predictions verified to high precisions - often better than 0.1% - by current and previous experiments. But many important questions remain. Is the Higgs mechanism really the electroweak symmetry hiding mechanism? Where does the gauge symmetry group SU(3) C x SU(2) L x U(1) Y realized in the SM come from? Why is the weak interaction chiral? Why are there three generations of fundamental fermions? What sets the measured ratios of particle masses? What is the size of an electron? of the Z boson? of the top quark? Is supersymmetry realized in nature? Are there extra spatial dimensions? Can all forces be unified? What is the origin of the asymmetry between matter and antimatter? What is the origin of QCD confinement? Can quarks and gluons be deconfined in a plasma? What is dark matter? The high luminosity colliding beams of the LHC will provide the highest centre of mass energy ever achieved in the laboratory. It is an unprecedented project also in terms of the cost, complexity and size of the experiments, and in terms of the effort from the scientific community: the four large-scale experiments involve in total over 4000 physicists from all over the world. The experimental programme of the LHC is supported by the strong physics cases behind these important questions.

3. Basics of Proton-Proton Collisions The inelastic proton-proton cross section at y/s = 14 TeV is expected to be about 70 mb. The corresponding event rate is then R = La = 7.0 x 108 Hz at high luminosity. These events are usually classified as either soft (or large distance) interactions where the invariant masses of all particles involved are small, or hard (or short distance) interactions where a few partons form large invariant masses.

47

3.1. Minimum

bias

events

Inelastic proton-proton collisions are dominated by soft interactions. Experimentally, inelastic events are selected with a minimum bias trigger. Minimum bias events are usually associated with inelastic non-singlediffractive events. Similarly to Rutherford scattering of electrons being scattered off atoms, these events can be described as collisions at large distance between the protons which interact as a whole. Such events are characterized by small momentum transfer and final state particles with large longitudinal (along the colliding beam direction) momentum p\, and small transverse momentum px (about (px) ~ 500 MeV), hence with small scattering angle; most energy escapes in the beam pipe. 3.2. Hard scatter

events

Occasionally, a proton-proton collision will result in a hard scattering process. For such short distance interactions, the momentum transfered between the two interacting protons is large enough to resolve the proton; the beams should then be described as a compound object of partons, quarks and gluons, with a wide band of energies. These events are characterized by a large momentum transfer and typically produce final state particles with large mass and/or large scattering angles. To probe nature innermost secrets, these are the interesting events. But they are rare; for example the cross section for the production of top-antitop pairs from gluon fusion is about 830 pb, which is about 8 orders of magnitude smaller than the inelastic proton-proton cross section. The partons of the colliding protons that do not participate in a hard scatter will produce the underlying event. These partons will scatter with small angles; therefore understanding minimum bias events helps understanding the underlying event. Unlike in electron-positron collisions, the hard scattering particles (partons a and b) carry only a fraction (xi and X2) of the incoming protons (1 and 2). The center of mass energy of the hard scattering \ / | is then smaller than the nominal centre of mass of the collider (T/S = 14 TeV for the LHC) and is given by s « X1X2S. The probability density of parton a to carry a fraction x of the proton momentum is described by the parton distribution function (pdf) of the proton fa(x,Q2), where Q is the 4-momentum exchanged in the interaction. For example, if both partons carry the same fraction of energy, that is if xi « x2, then producing a particle of mass 100 GeV at the LHC requires x « 0.007, but producing a particle of mass 3 TeV needs two partons at 1 w 0.21. Parton distribution functions are

48

needed to translate a given parton interaction of cross section a (ab —• X; s) to the corresponding cross section in a proton-proton collision: I dx1dx2fi1)(x1,

a (pp - X; s) = Y,

3.3. Useful

Q 2 )/ fc (2) (z 2 , Q2) a (ab - X; s)

kinematics

For most events, the longitudinal momentum of the center of mass of the hard scattering system will be different for different events, while its transverse momentum will be of the order of 500 MeV (Fermi motion inside the proton). Consequently, it is often useful to consider kinematic variables that have a well defined behaviour under longitudinal boost. Consider a beam along the z axis. For a given particle of velocity /3, momentum p and energy E, we can define the transverse mass mx, the transverse (with respect to the beam axis) momentum px and the rapidity y: m

T = \JPI +Pl+m2

y

fl + pcosO cosS

\-i {1-P

\E-pJ

2

where 6 and are the polar and azimuthal angle of p respectively. Note that tanhy = P cos 6. We also have the inverse relations E = m x cosh y

p x = PT sin <j>

Py = PT COS <j>

p z = m x sinh y

We obtain that mx, px and remain invariant under a longitudinal boost Po, while the rapidity y only changes by the addition of a constant: m T = mx

PT

=

PT

y = y + oln

2

4>' — 4>

\l-po

Therefore, the difference between the rapidities of two particles is also invariant under a longitudinal boost. The pseudorapidity r\ is defined as the rapidity in the limit of a massless particle 6 X] = lim y = — ln t a n m—>0

2

Note that sinh77 = l / t a n # , cosh77 = l / s i n # and tanh?7 = cos#.

49

4. The Experimental Challenges The LHC experiments will face many experimental challenges. Two of them are particularly important.

4.1. Event

pileup

At high luminosity, the minimum bias event rate is about R = La = 7.0 x 108 Hz. Using Table 1, the corresponding number of events per bunch crossing is 7.0 x 108Hz x | | | | x 25ns = 22. If one of them is a hard scattering event of interest, then the others (with (p T ) « 500 MeV) will overlap with it creating an event pileup. At hight luminosity, on average about 800 charged particles are produced over the pseudorapidity range |T/| < 2.5 at each bunch crossing, most of them with low px- The interesting events can therefore be extracted by requiring particles to have a pr above some low threshold. The importance of such a requirement is shown in Figure 1 for a simulated event with a Higgs decaying into four muons with a pileup of 30 minimum bias events: with no cut applied, this event has many particle tracks; but a pr > 2 GeV cut reveals the four high px tracks in a rather clean environment. Remarkably, the number of charged particles produced per unit of pseudorapidity is approximately constant:

^ * « 7 for M < 5 dr]

Experimentally, the detector channel occupancy (the fraction of events for which a channel has a signal) can therefore be controlled through a segmentation in constant rj intervals. High rate of event pileup is a serious experimental difficulty at the LHC and it has a large impact on detector design. Typical detector response time is 20 to 50 ns which, at high luminosity, corresponds to an integration over one to two bunch crossings. Detector channel occupancy needs to be kept low through a fine readout granularity; this implies a large number of electronic channels, and therefore challenges in cost and detector operation. Additionally, the high flux of particles from the proton-proton collisions produces a high radiation environment, especially in the forward regions, of up to 10 17 n/cm 2 and 107 Gy (or J/kg) in ten years of LHC operation. This will affect all detector components and on-detector electronics.

50 30 m i n i m u m b i a s e v e n t s

+

I!

//

In

all c h a r g e d particles w i t h In I •= 2.5

r e c o n s t r u c t e d t r a c k s w i t h p t > 2.0 G e V

Figure 1. Simulation of a H —• 4fi event in the CMS inner detector overlapped with 30 minimum bias events. Top: no cut is applied, and particle tracks are shown. Bottom: after a p x > 2 GeV is applied.

4.2. QCD

background

At the LHC, the high px event rate is dominated by quantum chromodynamics (QCD) jet production: final state quarks and gluons fragments into collimated jets of (colour singlet) particles, mainly pions. Figure 2 shows various Feynman diagrams for QCD jet production. But the most interesting events at the LHC are usually rare processes involving heavy particles (e.g. Higgs boson, top quarks) or weak processes (e.g. W production). Figure 3 shows the LHC cross section for various processes of interest. The production of QCD jets with px > 200 GeV is expected to be about five orders of magnitude larger than the production of the SM Higgs boson. Hence it is difficult at the LHC to detect a Higgs boson decaying into jets, unless it is produced in association with other particles that allow to tag the event. 5. The ATLAS and CMS Detectors The LHC will open a new window into nature's fundamental laws. It is not yet known how the new physics will manifest itself. Therefore, LHC detectors must be able to detect as many new and hypothetical particles and sig-

51

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y

-J^ (b)

VlSULs

(c) \JUUSL*JUUL/

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(d) Figure 2. Feynman diagrams for various QCD jet production processes, a) qq' —> qq'. b) qq -+ qq- c) qq -+ gg. d) gg - » g g .

natures as possible. ATLAS (A Toroidal Lhc Apparatus, see Figure 4) and CMS (Compact Muon Solenoid, see Figure 5) are both multi-purpose detectors designed to detect efficiently and measure precisely electrons, muons, taus, photons, jets from quarks and gluons, as well as tagging b-jets and measuring the missing transverse energy of events. From the interaction point outwards, both detectors consist of the following sub-detectors: an inner detector immersed in a solenoidal magnetic field used to detect and to measure the momentum and charge of charged particles, and to measure the position of secondary vertices; an electromagnetic (EM) calorimeter, optimized for the measurement of energy, position and direction of electrons and photons, and for their identification; a hadron (HAD) calorimeter, optimized to measure the energy and position of hadrons and jets, and to estimate, with the help of the electromagnetic calorimeter, the missing transverse energy; a muon spectrometer, used to detect muons and to measure their momentum and charge in conjunction with the inner detector. Neutrinos (and possibly other new particles) traverse the detector without interacting. Since most of the proton-proton collision energy is lost along the beam pipe, the missing total energy of the event due to noninteracting particles cannot be measured. But, since the transverse momentum of the colliding partons is negligible and since the transverse mo-

52

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Figure 3. Proton-proton cross sections at the LHC, showing the corresponding number of events for an integrated luminosity of 10 f b - 1 , which corresponds to one year (10 7 s) at low luminosity (10 3 3 c m _ 2 s - 1 ) . Note that the production of a Higgs boson is 10 1 0 to 10 1 1 times less likely than a minimum bias event.

mentum of all particles escaping down the beam pipe is small and to a large extent balanced, the missing transverse energy can be a good measure of the transverse energy associated to non-interacting particles. Good estimate of the missing transverse energy is an important requirement for the LHC detectors. It requires the calorimetry to be as hermetic as possible and to cover the full azimuthal angle and the pseudorapidity region \r\\ < 5, corresponding to down to 0.77° from the beam axis. The main features of the ATLAS and CMS detectors are summarized in Table 2. With current technology, it is not possible for ATLAS and CMS to record all events at the interaction rate of 7.0 x 108 Hz. Their event acquisition capacity is about 100 events/s, with typical event sizes of about 1 MByte. Therefore an event rejection of about 107 is required. To secure a reasonable decision time of about 1 /xs (^> 25 ns), the readout electronics need to store a large amount of data in pipelines while the trigger performs

53 Muon Detectors A.

Electromagnetic Calorimeters Forward Calorimeters /

Inner Detector

End Cap Toroid

Hadronic Calorimeters

Shielding

Figure 4. Overall layout of the ATLAS detector. It has a length of 40 m, a radius of 10 m, a weight of 7 kt and has more than 10 8 electronics channels.

Table 2. Magnet (s)

Inner detector

Main features of the ATLAS and CMS detectors.

ATLAS air-core toroids + solenoid calorimeters outside the field 4 magnets Si layers (pixel and strips) transition radiation detector: particle identification B = 2T

CMS solenoid calorimeters inside the field 1 magnet Si layers (pixel and strips)

I 1 | 1

no particle identification B = 4T cr/p T « CT/P T « 1.5 x ! 0 - 4 p T ( G e V ) © 0.005 5 x 10-4pT(GeV)©0.01 EM Pr>LAr P b W 0 4 crystals calorimeter a/E « W%/y/E(GeV) a IE w 2 to 5 % / v ^ ( G e V ) no longitudinal segmentation | longitudinal segmentation HAD Cu-scintillator Fe-scintillator + Cu-LAr calorimeter > 5.8A and tail catcher > 10A a/E « 6 5 % / i / E ( G e V ) © 0.05 a/E « bQ%/y/E(GeV) © 0.03 Muon Fe air spectroCT/PT « 7% at 1 TeV I &/PT » 5% at 1 TeV 1 meter achieved with inner detector i achieved by spectrometer alone

54 TRACKER

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calculations. Both ATLAS and CMS organize their triggers in three levels. 6. Precision M e a s u r e m e n t s Although proton-proton collisions at the LHC form a complex environment, the large cross sections for various processes will allow important precision measurements. In particular, the precise measurement of the W mass and of the top quark mass will provide further, indirect, constraints on the Higgs mass. If the Higgs is found and its mass measured, it will allow important consistency tests of the SM. By LHC startup in 2007, it is expected that the W mass will be known to about 25 MeV (combination of measurements at LEP and at the Tevatron) and the top mass to about 3.0 GeV (direct measurements at the Tevatron). The large W and top statistics of events expected at the LHC will allow a significant reduction of these uncertainties. 6.1. Measurement

of the W mass

At the LHC, the W boson will be mainly produced via the quark-antiquark annihilation Drell-Yan process with a cross section of about 150 nb. At high luminosity, this corresponds to a production rate of 1.5 kHz: the LHC

55 will be a W factory. The W mass Mw measurement is performed using the W —+ ev and W —+ fiu channels since the W —> jj channel cannot be extracted above the QCD background and the W —• TV channel suffers from the presence of at least two neutrinos in the final state. At low luminosity, the rate of selected useful W decays should be about 60 millions events per year: this corresponds to about 50 times the sample size recorded at the Tevatron and about 6000 times the statistics of events recorded at LEP-II. The statistical error on Mw is therefore expected to be negligible, less than 2 MeV. Consider the decay W —> tv + X. We have M w = (pe + P»? = (Ee + Evf

- (pe + pvf

At LHC, the W mass is obtained from the distribution of the W transverse mass M™ defined from ( M ^ ) 2 = (EET + E^f

- (pip +p^)2

» 2E{EZ (1 - cos A ^ )

Note that M™ is invariant under a longitudinal boost. Furthermore, M™ depends only weakly on the W transverse momentum p™; if the W momentum is all transverse, the dependence is of order (p™/Ew) . It is this property that makes M™ so useful. The W transverse mass distribution itself is sensitive to Mw; comparison of data with simulation yields an estimate of Mw (see Figure 6). The dominant error is expected to be the knowledge of the lepton energy scale of the detector. ATLAS and CMS aim to reach an error on Mw of about 25 MeV per channel. Combining both channels and both experiments could yield an error as small as 15 MeV. Reaching this precision will be a very difficult task. 6.2. Measurement

of the top

mass

The top quark has various unique features. Its mass of about 174 GeV is about equal to the mass of a nucleus of 760s; studying the top may reveal important hints about the origin of mass. Its expected large width of about 1.8 GeV makes it decay before hadronizing, allowing for the first time to study interactions of a bare quark. The large mass of the top renders it essential in calculating many radiative corrections. At the LHC, top quark production is dominated by the strong production of tt pairs, with an expected cross section of about 830 pb. At high luminosity, this corresponds to a tt production rate of 8.3 Hz: the LHC will also be a top factory. At low luminosity, this corresponds to 8 million tt

56 400 350 300

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40

80

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100

120

140

w

mT (GeV) Figure 6. W transverse mass distribution as expected in ATLAS for M\v = 80.3 GeV (light line) and JWw = 79.8 GeV (dark line).

pairs produced per year. Such a large event sample will allow not only the precise measurement of its mass and production cross section, but also the measurement of branching ratios, couplings and, eventually, rare decays. In the SM, the top decays almost exclusively to Wb. For the reconstruction of the mass of the top, many decay channels of the W are considered. The preferred channel is the lepton + jet channel with a branching ratio of about 30%: tt —> WbWb —> fi/bjjb, where £ = e,/i. Common to all channels are two b-jets which can be tagged using displaced vertices in the inner detector: the lifetime of B-hadrons of about 1.5 ps yields a decay vertex displaced by a few millimeters from the primary vertex which can be detected using the high granularity inner detector. For the reconstruction of the mass of the top, many different and complementary analyses are considered. In general, an analytic fit to an event-by-event reconstructed invariant top mass is performed. In most cases precision is limited by systematics, in particular due to physics uncertainties (background, final state radiation, initial state radiation, b-fragmentation, etc.) and jet energy scale (b-jet, light quark jet). An expected uncertainty of 1% on the jet energy scale corresponds to an uncertainty of less than 1 GeV on the top mass. The statistical error is expected to be negligible, less than 100 MeV. AT-

57

LAS and CMS each aim for a top mass precision of about 1 GeV for an integrated luminosity of 10 fb _ 1 .

7. The Search for the Standard Model Higgs Boson In the SM, the strong and electroweak forces are described by a gauge field theory based on the SU(3)c x S U ( 2 ) L X U ( 1 ) Y symmetry group. Fundamental masses can be introduced without violating this symmetry through the Higgs Mechanism7. The SM uses the simplest form of this mechanism: fundamental Higgs fields interact with each other and acquire non-zero vacuum expectation values which spontaneously hides the electroweak part of the gauge symmetry down to the strong and electromagnetic SU(3)c x U(1)EM symmetry - ensuring massless photons and gluons. All fermions and all other bosons acquire mass by interacting with the vacuum Higgs fields. A consequence of this mechanism is the existence of massive scalar Higgs bosons, only one in the minimal SM. All the particle content of the SM has been experimentally verified, except for the massive scalar Higgs boson(s). The search for the Higgs boson(s) and the understanding of electroweak symmetry breaking is one of the major thrusts of particle physics research at the energy frontier. The mass of the minimal SM Higgs boson, M H , is not specified by the theory. Other constraints limit the mass region. For example, for the SM to be self-consistent up to a Grand Unification Theory (GUT) scale of about 10 16 GeV, the theoretical bounds 130 GeV < M H < 190 GeV 8 are required. LEP2 data provides a 95% CL lower bound of 114.4 GeV 9 . The efforts at the Tevatron could possibly improve this limit slightly (or produce a discovery!). Figure 7 shows the predicted SM Higgs boson cross sections for various production processes. Gluon fusion is the dominant production process for the whole M H < 1 TeV range. Vector boson (WW, ZZ) fusion becomes as important as gluon fusion for M H ~ 1 TeV; this process has the distinctive signature of two jets emitted in the forward direction, at small angle to the beam axis. The associated Higgs production with a tt pair or a W or Z boson has a much smaller cross section, but the decay of the associated particle^) produces additional signatures that render the final state relatively easy to extract. The detection of the Higgs through all these production processes is the key to the measurement of the SM Higgs parameters. The Higgs decay branching ratios depend on the Higgs mass itself, see Figure 8. Hence the Higgs search strategy will also vary for different test

58

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masses M H . For search purposes, we distinguish two Higgs mass ranges: the low MH region of M H < 2M Z and the high MH region of 2M Z < M H < 1 TeV. The Higgs width grows from about 1.5 MeV for M H = 100 GeV to nearly the Higgs mass for M H = 1 TeV (see Figure 9). 7.1. Low MH

region

The search for the SM Higgs boson is challenging in the low mass region. It is not possible to trigger on or extract fully hadronic final states, so final states with electrons, muons or photons are sought. Figure 10 shows the overall ATLAS sensitivity for the discovery of a SM Higgs boson over the mass range 100 GeV< M H < 200 GeV for 30 fb _ 1 , or three years at low luminosity. Combining ATLAS and CMS will increase the significance by about \/2-

59

114-GeVAj* (LEP2Umitn

2MZ 1

Figure 8. Standard Model Higgs boson decay branching ratios as a function of its mass. The left region is excluded by direct searches at LEP-II. The remaining mass range is divided into two regions: the low mass region in the middle, and the the high mass region to the right.

The H —> 77 channel has a small branching ratio, but offers the best reconstructed mass resolution; it requires a high performance of the EM calorimetry for photon energy resolution, photon direction reconstruction and 7/jet separation. The dominant decay channel H —» bb leads to a poor mass resolution and must be used in conjunction with Higgs associated production: b-jet tagging through the measurement of tracks with significant impact parameter in the inner detector is crucial for a discovery in this mode. The H —> TIL* —> A£ channel requires excellent identification, reconstruction and measurement of isolated leptons with px > 7 GeV. The significance in this channel is reduced when the WW channel opens up. In the case of the H —> WW* —> ivlv channel, it is not possible to reconstruct a mass peak, therefore discovery relies on measuring an excess of events which requires a very good knowledge of backgrounds. The Standard Model light Higgs boson can be discovered with an integrated luminosity of 30 fb~l, and in most cases, more than one channel is available.

60

id

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400

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Standard Model Higgs boson width as a function of its mass.

7.2. High MH

region

The search for the SM Higgs boson is easier in the high mass region. Figure 11 shows the overall ATLAS sensitivity for the discovery of a SM Higgs boson over the mass range 80 GeV< M H < 1 TeV for 100 fb _ 1 , or one year at high luminosity. Combining ATLAS and CMS will increase the significance by about \/2. The most reliable channel for a discovery in the mass range 2Mz < M H <~600 GeV is H —> ZZ —> 4£; the background is dominated by the total production of Z pairs and is smaller than the signal. In the mass range between 600 GeV and about 1 TeV, the SM Higgs boson could be discovered in the H —> WW —> £v]j channel. Note that this channel extends down to lower masses, which complements the previous channel. For a very heavy Higgs in the mass range 400 GeV< M H < 900 GeV, the channels H -> ZZ -> Uji and H -* ZZ -> iivv complement the WW -> ^i/jj channel. If the Standard Model Higgs boson exists, it will be discovered at the

61 LHC.

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mR (G«V/c ) Figure 10. ATLAS sensitivity for the discovery of a SM Higgs boson as a function of its mass for the low mass region, assuming an integrated luminosity of 30 f b - 1 . The statistical significance is plotted for individual channels as well as for all channels combined. Combining ATLAS and CMS will increase the significance by about V2-

7.3. Higgs mass and

width

Once discovered, the mass and width of the Higgs boson can be measured with good precision. Figure 12 shows the expected experimental precision on the SM Higgs boson mass and width as a function of its mass, now for an integrated luminosity of 300 f b - 1 , i.e. three years of data taking at high luminosity: the Higgs boson mass is expected to be measured with a precision of 0.1% over the mass range 100 GeV< M H < 400 GeV, while the Higgs boson width will be measured with a precision of 6% in the mass range 300 GeV< M H < 700 GeV. Other Higgs sector parameters can be measured by comparing the rates from various Higgs channels.

62

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m„ (GeV) Figure 11. ATLAS sensitivity for the discovery of a SM Higgs boson as a function of its mass, assuming an integrated luminosity of 100 f b - 1 . The statistical significance is plotted for individual channels as well as for all channels combined. Combining ATLAS and CMS will increase the significance by about V2.

8. T h e Search for Supersymmetry Supersymmetry (SUSY) is perhaps the best motivated theoretical scenario for physics beyond the Standard Model. It provides the maximal extension of the Poincare group, the group of space-time symmetries in quantum field theories. SUSY actions are invariant under this extended symmetry group and are composed of an equal number of bosonic and fermionic degrees of freedom: SUSY transforms fermions into bosons. Local SUSY is supergravity; SUSY offers a framework for the unification of gravity and the other forces. In particular, it is possible that SUSY can one day resolve the hierarchy problem, namely the stability of the hierarchy of scales from the electroweak to the Planck scale in the presence of radiative corrections. If SUSY were an exact symmetry of nature, then each particle would have a superpartner (differing in spin by 5) of the same mass. Clearly this is not observed in data, so SUSY must be broken. The hierarchy of scales

63 experimental precision on the SM Hggs mass

110

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10

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10 10 m„(GeV)

200

400

600

800

Higgs mass (GeV)

Figure 12. Expected experimental precision on the SM Higgs boson mass (left) and width (right) as a function of its mass for an integrated luminosity of 300 f b - 1 , or three years at high luminosity.

can nevertheless remain stable if the SUSY breaking mass terms are below a few TeV. In R-parity conserving models, SUSY particles are produced in pairs and the lightest supersymmetric particle (LSP) is stable and weakly interacting. The motivation for the latter property is to provide a good candidate for dark Matter. So far, SUSY does not contradict any "low" energy predictions of the SM. Since there is as yet no evidence for the use of SUSY in nature, SUSY either does not exist or it is beyond the reach of current experiments. It is expected that LHC will discover supersymmetric particles if they exist at the TeV level or less, and above the current reach. The Minimal Supersymmetric Standard Model (MSSM) predicts the existence of five Higgs bosons and the SUSY partners of ordinary particles, as shown in Figure 13. The theory does not predict the mass of these particles, but charginos x ± and neutralinos x° a r e expected to be lighter than squarks q and gluinos g. If kinematically accessible at the LHC, squarks and gluinos will be produced in large quantities via strong processes (see Figure 14). For a squark or gluino mass of 1 TeV, the pair production cross section is about 1 pb, corresponding to 104 events per year at low luminosity. Charginos, neutralinos and sleptons production proceeds via electroweak processes (see for example Figure 14) and therefore is expected at a much smaller rate. The decay of SUSY particles depends on their masses and on other

64

model dependent parameters. Figure 15 shows a few examples: charginos can decay into a W and an LSP; neutralinos can decay into a Z and an LSP; sleptons can decay into a lepton, a Z and an LSP. The weakly interacting LSPs, as for the neutrinos, can only be detected indirectly through the measurement of missing transverse energy. The squarks and gluinos, which are expected to be heavy, undergo more complicated cascade decays which produce final states with many leptons, jets, W, Z, and missing transverse energy. Many decay products are expected to have large pr because they come from heavy particles. Such signatures should be easy to extract from SM backgrounds in ATLAS and CMS.

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9. Other Searches ATLAS and CMS will undergo many searches beyond the SM. Many signatures are predicted by various models: technicolour, leptoquarks, extra gauge bosons, heavy leptons, excited quarks and leptons, quark substructure, more complicated Higgs sector, monopoles, mini black holes... Models with extra spatial dimensions have recently enjoyed much attention. Indeed, string theory requires ten dimensions! Many models attempt to solve the hierarchy problem by postulating the existence of extra dimensions. The possibility of large compact extra dimensions has been explored, in particular in the model of Arkani-Hamed, Dimopoulos and Dvali 10 . In

65

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w± ,

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this model, gravitons are free to propagate in 3 + 1 + n dimensions (the bulk), while other particle are confined to the SM 3 + 1 dimensions (the wall). The n dimensions are compactified, with a common size R. Gravity with fundamental scale M D would then follow Gauss' Law in 3 + n spatial dimensions: V(r\

\

=

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for r < R for r > R

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66

Figure 16. Example of a cascade decay of a gluino, assuming that x? is the lightest supersymmetric particle.

Hence JU[n+2 _ D

M2 •'"Planck (2TTR)H

The weakness of gravity is then only apparent in 3 + 1 dimensions. For compactification in circles, the graviton field is periodic in the extra dimensions. This gives rise to Kaluza-Klein states of graviton with mass proportional to i ? _ 1 . The hierarchy problem can then be reformulated through large extra dimensions by demanding that Mu ~ 1 TeV. If M D = 1 TeV, then n = 1 implies R = 9.4 x 1026 G e V - 1 = 1.9 x 10 13 cm which is of the order of the size of the solar system; hence this is excluded. But n = 2 implies R = 3.9 x 10 11 G e V - 1 = 0.078 mm; n = 3 implies i J = 2 . 9 x 106 GeV- 1 = 57 nm; n = 4 implies R = 7.9 x 103 G e V - 1 = 1.6 pm. Kaluza-Klein states separation is very small: for n = 2, i ? _ 1 = 2.5 meV. The high density of states compensates for their low ~ Mp^anck coupling, yielding chances to observe graviton effects at the LHC. Figure 17 illustrates the production of a graviton is association with a quark. In this case, the signature is a jet with missing transverse energy. Studies 11 have shown that, in this channel, ATLAS will be sensitive to 4 TeV < M D < 7.5 TeV if n = 2, and 5 TeV < M D < 5.3 TeV if n = 4. 10. Conclusions and Outlook The CERN Large Hadron Collider and its experiments are the most ambitious high energy physics project ever attempted. ATLAS and CMS will

67

Figure 17. Example of a graviton production through radiation off a quark. The graviton escapes into the bulk. The event signature is a jet and missing transverse energy.

make a thorough exploration of the laws of nature up to the TeV scale. There are good reasons to believe that the origin of fundamental particle masses will reveal itself in this mass range, perhaps through the discovery of a Standard Model Higgs boson. Searches for physics beyond the SM will include the search for supersymmetry, the search for extra dimensions, and many other exciting searches. LHCb will study CP violation and ALICE will study the formation of quark-gluon plasma. I believe our field is poised for remarkable advances. The LHC programme offers great promises. The next few years will be very exciting indeed. Acknowledgments I would like thank F. Gianotti, K. Jakobs and G. Polesello for very useful material, G. Azuelos for material and enlightening discussions, and R. Seuster for very useful comments. Many thanks also to A. Astbury, B. Campbell, L. Grimard, F. Khanna, and M. Vincter for a superb organization and their kind hospitality at the Lake Louise Winter Institute. Support from the Natural Science and Research Council of Canada is acknowledged. References 1. The Large Hadron Collider Conceptual Design, CERN/AC/95-05 (1995). 2. ATLAS Collaboration, ATLAS Technical proposal, CERN/LHCC/94-43 (1994).

3. CMS Collaboration, CMS Technical proposal, CERN/LHCC/94-38 (1994). 4. LHCb Collaboration, LHCb Technical proposal, CERN/LHCC/98-4 (1998). 5. ALICE Collaboration, ALICE Technical proposal, CERN/LHCC/95-71 (1995). 6. See K. Rajagopal's lectures, these proceedings. 7. P.W. Higgs, Phys.Rev.Lett.13, 508 (1964). 8. See the article from P. Igo-Kemenes, Searches for Higgs Bosons, in the Review of Particle Physics, S. Eidelman et al., Phys.Lett.B592, 1 (2004) and references therein. 9. LEP Working Group for Higgs boson searches, Search for the Standard Model Higgs Boson at LEP, CERN-EP-2003-011, Mar 2003. 23pp. Published in Phys.Lett.B565, 61-75 (2003). e-Print Archive: hep-ex/0306033. 10. Phys.Lett.B429, 263 (1998). See also Scientific American, August 2000. 11. Vacavant and HinchlifFe, Extra-dimension signatures with ATLAS, ATLAS note ATL-PHYS-2000-016.

APPLICATIONS OF T R A P P E D ATOMS FOR F U N D A M E N T A L S Y M M E T R Y STUDIES

GENE SPROUSE* Department of Physics and Astronomy State University of New York at Stony Brook Stony Brook NY 11794-3800, USA

Atoms in traps can be observed for long times, and this increases the sensitivity to small effects resulting from symmetry violations. The physics motivation for these types of studies is presented. The operation of two of the most common atomic traps, the magneto-optical trap, and the dipole force trap are discussed in simple terms, and then several example measurements are presented that are either in progress or planned.

1. Introduction The study of the fundamental interactions of nature is the realm of high energy physics. However, other fields of physics can also contribute to this study. The experiment by Wu, Ambler, et al. 1 , that showed parity violation in weak interactions, used low temperature physics methods to polarize the nuclei. In recent times, there have been great advances in atomic physics methods 2 , and these open up new possibilities for fundamental interaction measurements. A radioactive atom, cooled in a trap, is so cold that the momentum of a neutrino can be inferred by detecting the momentum of the recoiling daughter atom. In order to fully appreciate the possibilities and limitations of measurements like this, some basic understanding of these methods is required. These lectures are meant as an introduction to some of these methods, emphasizing the physics involved with sufficient detail to be able to understand several examples of current efforts to study fundamental interactions with trapped atoms.

*Work partially supported by National Science Foundation. 69

70

2. Laser traps for neutral atoms The techniques for transferring radioactive atoms into atom and ion traps have made great progress in recent years, and it is now possible to consider precision experiments with particular isotopes that optimize the sensitivity for the effect of interest. For example, the alkali element francium offers an 18 times increase in the size of parity violating effects relative to cesium, but could not be considered during the development of the Cs experiment 3 because it has no stable isotopes. That is not to say that precision experiments with radioactive atoms are easy, but they now can be considered for some special cases. One of the great advantages of doing experiments in traps is that not only are the atoms confined in space, and therefore require a much smaller laser beam for excitation, but they are also confined in momentum space, and this means that every atom can be on resonance with the laser beam. These two effects combined greatly reduce the laser power needed to efficiently excite the atoms and therefore the background of scattered light is greatly reduced. In the following, we will first describe the principle of a magneto-optical trap and then a dipole force trap in order to give some basic understanding of their operation and their limitations. We will then describe some of the methods for loading radioactive atoms into traps and their efficiencies. With this basic knowledge, we can then turn to the physics problems that can be addressed in a trap, and their motivation. Lastly we will describe several experimental programs with traps to measure beta-neutrino angular correlations, electric dipole and anapole moments. 2.1. How do laser traps work? transition?

What is a

"cycling"

Almost all laser cooling and trapping that has been done so far has required an atom with a closed two level system, such that after excitation and decay, the atom is returned to the same initial state, ready to be "cycled" again 4 . With such a system, the time for one cycle can be of the order of 2r (r is the lifetime of the excited state), and if the atom is maintained in resonance, could make > 107 cycles/second. Although the momentum hv/c of each absorbed photon is small, it is always in the same direction, while the decay photons are emitted with equal probability for any two opposite directions, so that their momenta average to zero. Some order of magnitude estimates can help to clarify the processes that take place. The first is the lifetime of an alkali p3/2 state is typically 20 nsec, giving

71

Figure 1. Schematic of Zeeman slower. An atomic beam, represented by the dark arrows, originates in the oven to the left, and a slowing laser beam comes from the right. The atoms are maintained on resonance as they slow by the Zeeman shift of the levels in the tapered magnetic field.

rise to a natural line width of about 10MHz. For atoms in a gas at room temperature, the width of the Maxwell Boltzmann distribution is of the order of 300 m/s. The natural line width of the atom then corresponds to a velocity spread of about lOm/sec. We see that the laser will interact only with a very small fraction of atoms that have velocities along the laser beam direction within about 10 m/s of the resonant velocity. If we are interested in cooling atoms to low temperature by tuning the laser to atoms that are already very slow, only about 1% of the atoms can be "captured" as they pass through the laser beams. For stable atoms where it is easy to get large numbers of atoms, this is not a problem, but for dealing with small numbers of radioactive atoms, the efficiency of the capture process is of crucial importance. 2.2. Loading a trap

efficiently

The trapping potentials are rather weak, and can trap only very slow atoms (usually < 10m/ s). Two different strategies have been developed to successfully capture a significant fraction of the radioactive atoms into the trap. (1) An atomic beam is directed from the source toward the trap as shown in Figure 1, and the atoms are decelerated with a laser beam directed against their motion. There are two problems with this: (a) Only a small range of velocities are actually slowed by the beam.

72

(b) Even if an atom is initially on resonance with the laser beam, after absorption of momentum from the laser beam, it is slowed and quickly becomes out of resonance and can not be slowed more. With such a system, one could slow the fastest atoms down only by about 10 m/s. The solution, first demonstrated by Philips and Metcalf5, is to have the atoms move in a magnetic field gradient so that as the atoms slow down, the Zeeman effect compensates for the changed Doppler shift in such a way that the atoms stay in resonance with the laser beam, and continue to be slowed. This "Zeeman slower" is used routinely to load traps, and was successfully used by the Berkeley group to load 21Na into a magneto-optical trap 6 . (2) If atoms are injected into a cell in an atomic beam, then only those with velocity < lOm/s will be captured before they hit a wall and stick. However, the walls can be coated with a "non-stick" substance 7 , allowing the atoms to be physi-sorbed on the wall for a short time and become thermalized, without chemi-sorption where they become tightly bound and lost to the vapor. The thermalization gives the atoms another chance to be captured in the laser trap if they come out with a velocity below the capture velocity of the trap. With this system, the fraction of atoms trapped is increased from the one pass fraction by the number of "bounces" before the atom is lost to an aperture in the system or is chemi-sorbed on the wall. This increase in efficiency can be ~100 for a well designed system 8 .

2.3. The Magneto-Optical

Trap(MOT)

Any trap requires two forces. There must be a restoring force that pushes atoms toward the center. This force is usually conservative, so that energy gained when the atom is pushed from the edge of the trap to the center is given to the atoms as kinetic energy. If the trap is not completely symmetric, an atom will eventually find the lowest point in the wall of the trap, and leak out. A damping force is also necessary to continuously remove kinetic energy from the atoms, and they will eventually settle in the lowest part of the trap. Two counter-propagating laser beams, both tuned just below the resonance for atoms at rest, can provide this damping force. Because the laser is tuned below the resonance, atoms will be Doppler shifted closer to resonance if they are moving toward a laser beam than if they are mov-

73

ing away from the beam, resulting in preferential absorption of momentum against their velocity. The atoms re-radiate symmetrically with respect to the laser beam, so the net effect is a slowing force, opposed to the motion of the atoms. This arrangement has been called "optical molasses" because the atoms behave as if they are moving in a viscous liquid. If 6 orthogonal laser beams cross in the same region, the atoms will be stopped, but a restoring force will be necessary to confine them. The Zeeman tuning discussed above in conjunction with the atom slower provides the key idea to the Magneto-Optical Trap(MOT), the workhorse of atom trapping. If a magnetic field gradient is applied along an axis, then the lowest magnetic sublevels on either side of the zero will be different, i.e. +m will be lowest on one side, and -m will be lowest on the other as shown in Figure 2. Counter-propagating circularly polarized laser beams with opposite hand-

le

'

Figure 2. Experimental arrangement for applying a restoring force to atoms. A magnetic field gradient, and two counter propagating laser beams with opposite circular polarization are needed in each dimension.

edness and tuned below the resonance, can therefore preferentially excite atoms on one side of the center than the other. This provides a true restoring force that will confine the atoms along this axis. Helmholz coils with opposite currents in each coil provide an axial gradient, and a radial gradient that is half as large. The same laser beams provide both the restoring force and the damping force, and can all be derived from one laser beam with appropriate polarizing beam splitters and quarter wave plates. Because it is robust and relatively easy to set up, the MOT has been the real "workhorse" of the atomic physics community. However, we often want to

74

apply a uniform magnetic field to atoms, or define a quantization axis. The central region of the MOT has a zero of the magnetic field, and atoms in the trap have fields in all directions. If we want to have atoms in a well defined state, we must transfer them to a second trap in which the atoms can be polarized, or make modifications to the MOT to get around this problem(Time Orbiting Potential, or TOP trap). 2.4. Dipole Force trap An electric dipole oscillator that is driven by an external field far below resonance(red-detuned) will produce an induced electric dipole moment that is in phase with the driving field. If it is driven far above resonance(blue-detuned) the induced moment will be in anti-phase with the driving field. A tightly focused laser beam will have a strong intensity gradient, and if it is red-detuned, the induced moments will be attracted to the region of highest intensity. This is the principle of the dipole force trap 9 . The light must be far-detuned so that optical excitation is kept extremely low, but this means that the trap depths are weak, and always require loading from another trap where the atoms have already been cooled and confined. Blue-detuned laser beams and special holographic filters have been used to make a "hollow beam" of light in which atoms are repelled from the walls and kept inside the bottle for several milliseconds10. The great advantage of these all-optical traps is that the trapping mechanism is independent of the particular sub-level of the electronic ground state and, for example, the atoms can be placed in a uniform magnetic field and polarized without affecting the trapping process. 3. Applications of atom traps to fundamental interaction studies After these discussions of the basic physical principles involved in trapping, cooling and loading traps, we will now discuss some of the experiments that have been completed or are underway in traps. We focus on experiments that bear on fundamental interactions, and most of these experiments are involved with radioactive nuclei. 3.1. (3 decay angular distributions: momentum.

sensitivity

to

neutrino

In a nuclear beta decay, the angular correlation between the electron and the neutrino is determined by the fundamental nature of the interaction.

75

Since neutrinos are detected with very low efficiency, measurement of this correlation must be done indirectly. The momentum of the recoiling atom is normally too small to detect in a solid or liquid, but because the atoms have very little initial momentum in the trap, it becomes possible. If the initial atom is at rest in an atom trap, the momentum carried away by the neutrino can be inferred by observation of the momentum of the recoiling atom and the electron. There are experiments to measure the /? — v angular correlation at Berkeley11 with 21Na, and at TRIUMF 12 with 3SK. We will discuss the TRIUMF result since it has completed an experiment. At TRIUMF, a beam of radioactive 3SmK atoms is obtained from IS AC, and implanted into a Zr foil. The foil is heated, and the atoms are driven out of the foil, and into a glass container coated with a non-stick material. A MOT captures a large fraction of these atoms, which are then pushed into a second trap that is optimized to measure the recoil Ar momentum distribution, as shown in Figure 3.

iuii

Ix-aiti

Collection chamber

H

15 c m —

Detection chamber

Figure 3. Experimental apparatus for neutralizing radioactive ions, capturing them in a MOT(on left), and pushing them into a second trap(on right) optimized to measure the /? — v angular correlations 1 3 .

An applied electric field functions to collect all charged Ar ions into the micro-channel plate(MCP) atom detector. The time of flight of the atom to the detector is then strongly correlated with the emission angle and energy of the recoiling atom, and careful analysis of this correlation

76

yields a measurement of the /3 — v angular correlation parameters as a = 0.9978 ± 0.0030 ± 0.0037, where a is essentially the same as the angular correlation parameter a, shown in Figure 4, and the errors are statistical

W[6Pu] = 1 + b | + a f c o s B0V a= + 1

•

,uCP

P"

38m K leptons hav<» Ar , * opposite he icity for W (vector) boson exch<mge

v^-^

—> v

\

m=+1/2 m=-1/2

m=+1/2

For scalar exchange, lepton helicities are same: a = -1 Figure 4. Graphic to show the sensitivity of the momentum of the recoil Ar atom to the scalar or vector boson exchange in beta decay 1 4 .

and systematic respectively. This result is currently the best limit on the exchange of scalar bosons in beta decay, and illustrates the usefulness of atom traps for this type of measurement. 3.2. Electric Dipole Moments reversal

of atoms-search

for

time

As was mentioned in the introduction, the increased sensitivity for precision experiments in a trap allows choosing specific atoms that may enhance a particular effect. The search for an atomic Electric Dipole Moment (EDM) is an excellent example of this and we will treat it next. An EDM violates both time reversal(T) and parity(P) transformations, but the product PT is conserved. One can see this graphically in Figure 5 if we imagine the rotating earth with excess + charge on the north pole, and - charge on the South pole, with the angular momentum pointing North. If you reverse time, the angular momentum vector will point to the South. Since the charge is unchanged, the EDM will not reverse with the angular momentum,

77

^ S / '

mirror

I timq

UJILLOL

t time

Figure 5. A rotating earth with excess +charge at the north pole will have an electric dipole moment that does not change with reversal of time, while the angular momentum does. Mirror inversion inverts the dipole moment but not the angular momentum.(from Ref. 15)

and the EDM will violate time reversal symmetry. Likewise, observation of the rotation in a mirror(equivalent to a parity transformation and a 180 deg rotation) also reverses the angular momentum, but not the EDM, so it also violates parity. However, the product generates two reversals of the angular momentum, so that PT symmetry is preserved. It is not easy to measure an EDM for a charged particle, as it will accelerate away unless held by other forces, so EDM experiments are usually done with neutral systems. The most readily accessible fundamental particle is the electron. An atom with an unpaired electron provides the most direct connection to the electron dipole moment, which is predicted in the Standard Model to have |d e | ~ 10~ 41 e • cm. The current limit for the electron EDM of \de\ < 1.6 x 10~ 27 e • cm comes from the Tl measurement of DeMille, et al 16 . Other theories that allow exchange of exotic particles other than the W, are shown in Table 1, and can have much larger EDM. It is clear that improvement of current experiments can have significant impact on theoretical directions. A complimentary way to search for an EDM is in a diamagnetic atom, such as Hg. The proposed EDM measurements in traps will use diamagnetic atoms of either Rn or Ra. How does one interpret searches for EDM in

78 Table 1. Predicted EDM for the Standard Model and several extensions to the Standard Model.(from Ref 17) Physics model Standard Model Left-right symmetric Lepton

flavor-changing

\de\

10~ 4 1 e • cm 10-26 _ 1 0 - 2 8 e . cm 10-26 _ l 0 - 2 9 e . cm

Multi-Higgs

10-27 - l 0 - 2 8 e . cm

Technicolor

10-27 _ l Q - 2 9 e . cm

Supersymmetry

1 0 _ 2 5 e • cm

diamagnetic atoms? The nucleus could have an EDM induced by nucleonnucleon CP violating interactions 18 . To measure this nuclear EDM, we need to apply an electric field to the nucleus and measure the interaction strength. However, it was first realized by Schiff19 that if there are only electric forces in the atom, that the atom distorts in such a way to shield the external electric field from the nucleus. Even if the nucleus has an EDM, there will not be an electric field to interact with it, and it will not be measurable. However, Schiff also realized that there are other forces in the atoms, such as the spin-orbit interaction. We can define the Schiff moment, S, as the difference between the mean square radius of the charge distribution, and the electric dipole moment distribution. The Schiff moment then induces parity mixing of atomic states, giving an EDM to the atom. The current limit from the Hg data is \dng | < 2.1 x 10 _ 2 8 e • cm with 95% C.L. 20 . This result puts a less stringent limit on the electron EDM of \de\ < 1.5 x 10 _ 2 6 e • cm, but it also puts limits on different terms in the CP violating interactions in the nucleus. Proposed measurements in atom traps for Ra and Rn, as well as proposed measurements in Xe and in molecules, can further push these limits and possibly discover an EDM. In each case the proposed experiment will try to take advantage of particular circumstances that allow greatly increased sensitivity to an EDM.

3.2.1. How does one measure an Electric Dipole Moment in an atom? If an atom with a magnetic moment is placed in a magnetic field, it will precess around the field at the Larmor frequency. If in addition, the atom

79

has a permanent EDM, an electric field applied along the same magnetic field direction will cause a slight change in the frequency that reverses when the relative direction of the electric and magnetic fields is changed. This is the basic method to search for an EDM. The sensitivity to an EDM is increased with larger electric fields, longer measurement times, and with larger signal to noise for the detection of the resonance frequency.

I

" T ~ ~ ~ ^ = (1+) + l-»/V2

"1" ¥* = ((1+«))+) +(I-a)i-))/^2 V = ((l~a)+) +(l+a)|-»/\ ; 2 a = -1—i

1

&E

L

- "

AE

Figure 6. Intrinsic nuclear states with octupole deformations can be mixed to produce states with good parity (above). If there are P T violating interactions, then states with EDM are produced.

Flambaum et al 21 have shown that nuclei with low lying octupole deformations can have a large sensitivity to P and T violating interactions that will develop a nuclear EDM. An intrinsic nuclear state with octupole deformation has an electric dipole moment, but since the nuclear eigenstates usually have good parity, the actual states consist of a superposition of two intrinsic states with opposite octupole deformations. This is shown schematically in Figure 6. Since there are two different linear combinations of the intrinsic states, the two states will occur as closely spaced doublets. If there are parity and time reversal violating interactions in the nucleus, then there is mixing of these opposite parity states, and the nucleus can develop a Schiff moment, S = eZA2/3/32(p3)2/AE , where /32 and /33 are the quadrupole and octupole deformation parameters, and AE is the energy splitting of the doublet. Because of the small splitting, AE, there can be enhancement of the Schiff moment by factors of 2000 or more. The large enhancement factors available in octupole deformed nuclei have motivated

80

experiments in Ra and in Rn, both radioactive species that are only available from radioactive sources or from production with accelerators. Since only small quantities of these atoms are available, trapping methods are proposed to utilize the atoms efficiently. 3.2.2. Proposed EDM measurement in

225

Ra

An EDM experiment is under development at Argonne National Laboratory that utilizes 225Ra atoms available from a radioactive source 22 . In 225 Ra the EDM effect is enhanced by two orders of magnitude due to nuclear quadrupole and octupole deformation. The ANL group has extensive experience in dealing with strong radioactive sources, in atom trapping, and in performing precision measurements. The proposed apparatus is shown in Figure 7. The proposed experiment will utilize many of the techniques Magneto-Optical Trap

10 mCi *R» sample

\ * •

'

Atomic B u m

mmm,mmmmmm,mmmm,m,,m^mmmmp.

<* Transverse Cooling

EDM-prohinf rwte

COj-Laser Optical Dlpal* Trap

Figure 7. Experimental arrangement for EDM search in 225Ra.

that we have discussed above. An oven contains a 225Ra source that forms an atomic beam. The beam is collimated with laser beams that cool some of the transverse motion, and then enters a Zeeman slower(not shown) that transfers a large fraction of the beam into the MOT. The Ra atom is not as favorable as an alkali, because the "cycling" pathway is not tightly closed, but has "leaks" to other states. Several other lasers may be needed to return atoms that have leaked to other levels back into the cycle. After

81 accumulation for some period, the atoms are transferred to a dipole trap made by a tightly focused infrared beam from a CO2 laser. The small sample in a very high vacuum should allow application of electric fields in excess of 100 kV/cm. Another key point is that 225Ra has spin 1/2, and therefore does not have a quadrupole moment. This greatly reduces the possibility that atomic collisions can de-phase the nuclei in the trap, and the expected coherence time should be ~ 300 s. This should make the system very sensitive to small EDM.

3.2.3. Proposed EDM measurement in

211

Rn

Another experiment to take advantage of the EDM enhancement in heavy nuclei with octupole deformations is under development at TRIUMF 23 . The particular isotope of interest, 2URn, has spin 1/2. Because it has no quadupole moment, when polarized, it can remain polarized for long times, even in an inert gas atmosphere. This allows for long coherence times and will enhance sensitivity for an EDM measurement. Direct polarization by laser optical pumping is not easy in the rare gases, because the tight binding of the ground state would require UV lasers that are not yet available. The rare gases can be polarized with visible lasers if the atoms are first excited to the metastable states by a gas discharge, but metastable excitation typically has efficiency of 10~ 3 , that is not acceptable for the small numbers of atoms available in this case. There is much experience in using laser polarized Rb to polarize rare gas atoms by spin exchange, and the planned experiment will utilize this method. Because the atoms are not accessible by laser methods, detection of an EDM signal will be done by looking for changes in the nuclear decay anisotropy that are correlated with the external electric field direction. This requires that the radioactive nuclei be confined to a fairly small volume at the center of the TIGRESS detector array at TRIUMF. The challenge is then to polarize the Rn nuclei and concentrate them into a cell where the external fields are applied. Parts of this process have been tested with radioactive Xe isotopes at TRIUMF with the apparatus shown in Figure 8. Further development of the experiment is awaiting the availability of Rn at ISAC in the near future. The planned sensitivity of the experiment should detect an EDM of the order of |dfl„| ~ 6 x 10~ 29 e • cm.

82

Differential pumping apertufCwm Law ^•f-EnergyBeatii

Collimator Figure 8. Apparatus for testing the transfer of radioactive nuclei into a cell for spin exchange optical pumping. After accumulation, the atoms are transferred to the transfer chamber and nitrogen gas is then used as a "piston" to compress them into the cell.

3.3. Parity violation in atoms: Test of the Standard in Cs and prospects for Fr

Model

The strength of the weak interaction between the electrons in an atom and the quarks in a nucleus is predicted by the Standard Model. Because the weak interaction violates parity, it can be separated experimentally from the much stronger electromagnetic interaction. An experiment to measure the atomic weak interaction must be coupled with precision ab-initio calculations of the electronic wave functions in order to compare the strength of the weak interaction with the Standard Model predictions. After including all of the corrections to the atomic theory 24 there is currently good agreement between the predictions of the Standard Model for the experimental

83

measurement in Cs 3 . Further refinement of these experiments would be possible with a measurement in Fr, where the weak interaction effects are 18 times larger. However, the atomic theory would have to also be improved by including still higher order diagrams, but this should be feasible as more computing power becomes available 25 . Measurement of a chain of isotopes with high precision could also lessen the dependence on the theory, but would also require accurate knowledge of the neutron distribution in the Fr nuclei. These types of experiments will become feasible with more intense production of radioactive beams. 3.3.1. Anapole moments, what are they, and how do you measure them?

Figure 9. Current distribution that creates an anapole moment. Note that the magnetic field is completely confined inside the current distribution, and can only be sensed by a penetrating probe(from Ref. 26).

The normal multipole expansion of a charge and current distribution consists of electric and magnetic monopoles, dipoles and quadrupoles. These distributions are assumed to have inversion symmetry and therefore good parity. The lowest non-zero moment with odd parity is called the anapole moment, and can be visualized as a toroidal magnetic field that is generated by a solenoidal current in the shape of a doughnut as shown in Figure 9. This type of current distribution can be generated by the weak interactions between hadrons in the nucleus. The weak interaction between hadrons is normally very difficult to measure, and it is not well characterized experimentally. Anapole measurements can help immensely in determining the properties of this interaction. The Cs experiment to

84 10-JI

H

in

12

14

4-0.12 h/-0.18 h j Figure 10. Constraints on the PNC meson couplings (107) that follow from the results in Table 4 of Ref 27. The error bands are one standard deviation. The illustrated region contains all of the DDH "reasonable ranges" for the indicated parameters (From Ref 27).

test the Standard Model3 also provided the first good measurement of an anapole moment, but it is difficult to interpret because there are several parameters that can be adjusted to fit the result. Figure 10 shows the current experimental situation for determining the parameters of the hadronic weak interaction. 3.3.2. Proposed anapole moment measurement in Fr Anapole moment measurements are needed in many different nuclei to disentangle the nuclear structure and the nature of the weak interaction in nuclei. Francium is a particularly important case to study since the anapole moments should be an order of magnitude larger than in Cs, the atomic calculations are reliable, and there are a large range of isotopes that could be studied. In the Cs experiment, the anapole moment was extracted from the spin dependent parity violating interaction, by subtracting the transition rates from two different hyperfine levels. Orozco 28 has proposed that the anapole moment determines the rate of an E l microwave transition between the two different hyperfine levels in the ground state. An experiment to measure anapole moments in Fr is under development 29 , and measurements of two adjacent isotopes would be able to separate the neutron and proton contributions to the anapole moments. The planned method is to place the

85

atoms in a microwave cavity tuned to the ground state hyperfine frequency (~ 45GHz), and drive the E l transition that is proportional to the anapole moment. A schematic of the proposed experiment is shown in Figure 11. The difficult part of the experiment is to suppress the strong Ml transition

Figure 11. Schematic of the apparatus. The microwave cavity axis is along the yaxis. The microwave electric field inside the cavity oscillates along the x-axis. The two Raman laser beams are polarized along the x-axis and z-axis, respectively. The microwave magnetic field and the static magnetic field are both directed along the zaxis. A dipole trap (not shown) holds the atoms at the origin that coincides with an anti-node of the microwave electric field.

that is 109 times larger. This will be done by suppressing the magnetic transition with several different mechanisms. The proposed strategy is to initially capture Fr atoms in a MOT, and then transfer them to a dipole force trap that confines the atoms to a 10/wn diameter volume centered on a node of the oscillating magnetic field. The polarization direction of the oscillating field will be chosen to suppress the Ml transition. In addition, an applied static magnetic field will move the Am = 0 Ml transition off of resonance to suppress the Ml transition further. The oscillations of the atoms in the trap about the zero point will average the amplitude of the Ml transition still further, so that the expected Ml transition will be at least 2 orders of magnitude less than the expected signal. 4. Conclusions The new atomic physics techniques for laser trapping and cooling have been applied to radioactive atoms, with the goal to study particular nuclei

86

where there is sensitivity to the fundamental interactions. These methods have put limits on the existence of scaler boson exchange in beta decay, and show promise for sensitivity to Electric Dipole moments, and nuclear anapole moments. This field has just begun, and there will certainly be advances in techniques that hold promise in advancing our understanding of the fundamental forces in nature. Acknowledgments This work was supported by the National Science Foundation. References 1. C.S. Wu, E. Ambler, R.W. Hayward, D.D. Hoppes and R.P. Hudson, Phys. Rev. 105, 1413 (1957). 2. G. D. Sprouse and L. A. Orozco, Annu. Rev. Part. Sci. 47, 429 (1997). 3. C.S. Wood, S.C. Bennett, D. Cho, B.P. Masterson, J.L. Robers, C.E. Tanner, C.E. Wieman. Science 275, 1759 (1997). 4. H.J. Metcalf, P. van der Straten, Laser Cooling and Trapping. Springer, New York, (1999). 5. W.D. Phillips, and H. Metcalf Phys. Rev. Lett. 48,596 (1982). 6. Z-T. Lu, C.J. Bowers, S.J. Preedman, B.K. Fujikawa, J.L. Morata, S-Q. Shang, K.P. Coulter, and L. Young. Phys. Rev. Lett. 72, 3791 (1994). 7. D.R. Swenson L.W. Anderson. Nucl. Jnstr. Meth. B29, 627 (1988). 8. S. Aubin, E. Gomez, L.A. Orozco, and G.D. Sprouse, Rev. Sci. Instr. 74, 4342 (2003). 9. S. Chu, J.E. Bjorkholm, A. Ashkin, and A. Cable, Phys. Rev. Lett. 57, 3147 (1986). 10. S. Kulin, S. Aubin, S. Christe, B. Peker, S.L. Rolston and L.A. Orozco, J. Opt. B: Quantum Semiclass. Opt. 3, 353 (2001). 11. N.D. Scielzo et al., Phys. Rev. Lett. 93 102501 (2004) . 12. A. Gorelov, et al., Phys.Rev.Lett. 94 142501 (2005). 13. D.G. Melconian, PhD. thesis, Simon Eraser University, (2004). 14. J.Behr, private communication. 15. H. Wilschut, private communication. 16. B. Regan, E. Commins, C. Schmidt, D. DeMille, Phys. Rev. Lett. 88, 071805 (2002). 17. http : 11 vms streamer!. fnal.gov/VMSSiteJd2/lectures/Colloquium/pre — sentations /DeMille. ppt 18. O. Lebedev, K. A. Olive, M. Pospelov, and A. Ritz Phys. Rev. D 70, 016003 (2004). 19. L.I. Schiff, Phys. Rev. 132, 2194 (1963). 20. M.V. Romalis, W.C. Griffith, J. P. Jacobs, E.N. Fortson, Phys. Rev. Lett. 86, 2505 (2001).

87 21. 22. 23. 24. 25. 26. 27. 28. 29.

N. Auerbach, V. Flambaum, and V. Spevak, Phys. Rev. Lett. 76, 4316 (1996). http : 11 www — mep.phy.anl.gov/atta/research/radiumedm.html http : 1/www.phys.uvic.ca/wrnppc — 2004/svensson.pdf A. Derevianko, Phys. Rev. A 65, 012106 (2002). http : //physics.unr.edu/ ~ tap/Talks/ITAMP2001/PNCITAMP01.htm http : //www.unif r.ch/physics/frap/3cycle/Lecture3.pdf W.E. Haxton and C.E. Wieman, Ann.Rev.Nucl.Part.Sci. 5 1 , 261-293(2001). L.A. Orozco, private communication. E. Gomez, S. Aubin, and G.D. Sprouse, L.A. Orozco, D.P. DeMille, arXiv:physics/0412124 vl( to be published in Phys. Rev. A.)

EXCLUSIVE D SEMILEPTONIC DECAYS AT CLEO-C

N. E. ADAM, CLEO COLLABORATION Wilson Synchrotron Laboratory, Cornell University, Ithaca, NY, 14853

We show preliminary results for the branching fraction measurements of exclusive D semileptonic decays at CLEO-c. Two different methods are used and preliminary numbers shown for some modes.

1.

Exclusive D Semileptonic Decays

In the standard model of particle physics mixing of the quark mass eigenstates in their charged current interactions is described by the Cabbibo Kobayashi Maskawa (CKM) matrix 1 . This 3 x 3 quark mixing matrix, Vij, with i 6 (u,c, t) and j G (d,s,b), is predicted to be unitary, containing only four independent parameters. If the standard model is correct experimental determination of the CKM matrix should verify its unitarity, whilst deviations would indicate the presence of new physics. Measurement of the CKM matrix is difficult, however, as it is close to unity, leaving the small off-diagonal elements to be determined via decays with small branching fractions. It thus remains a continuing experimental challenge to fully test unitarity via precision measurement of the CKM matrix. One of the best experimental frameworks for CKM measurements is the semileptonic decays of B and D mesons. Prom a theoretical viewpoint semileptonic decays are relatively simple when compared to mesons decaying via fully hadronic final states. This simplicity is due to the fact that the semileptonic decays may be factored into the product of the well understood leptonic current and the more complicated hadronic current, allowing the complexity of the strong interactions to be isolated. In addition the strong final state interactions present in hadronic decays are removed. Experimentally semileptonic decays are also tractable and are preferred over purely leptonic decays because of their much larger branching fractions. CLEO-c will obtain a very large, clean sample of D semileptonic decays 88

89 at the ^(3770) charm resonance. For such decays, where the D meson decays to some pseudoscalar meson, X, the partial decay width in the limit of a massless electron is given by, dTjD^Xeu) d?

_ G%\VCX\> 3 + ~ 2 4 7 r 3 Px\fx(Q

2

2

)\ >

(1)

where form factor f^ parametrizes the hadronic matrix element, px is the momentum of X, q2 is the square of the momentum given to the electronneutrino system and Vcx is the appropriate CKM matrix element. Accurate semileptonic branching fraction measurements therefore allow access to the CKM elements Vcd and Vcs. With the improvements in form factor calculations expected from lattice QCD, CLEO-c will afford very precise determinations of these elements. The form factors themselves are also of experimental interest. In recent times lattice QCD techniques have improved to a degree which will enable theoretical form factor predictions for both B and D semileptonic decays at the several percent level2. Experimental measurements of the form factors at a similar level will thus give a measure of lattice QCD accuracy. For B semileptonic decays the CKM elements are not well measured and one of the largest contributing errors is the error on the form factor. Confidence in form factor predictions via theoretical methods for these measurements then becomes highly important. Precision measurements of exclusive D semileptonic branching fractions are thus essential study both for their own sake, and also for the information they provide which then feeds back into the B meson system. 2.

CLEO-c Detector and Datasets

The analyses discussed below use either 55.8p6 _1 (tagging) or 103p&-1 (nontagging) of data taken at the VK3770) resonance with the CLEO-c detector. The detector contains a 6-layer inner stereo drift chamber surrounded by another 47-layer cylindrical drift chamber. The combined drift chambers make up the tracking system and cover about 93% of 47i\ Outside the large drift chamber there is a ring imaging Cherenkov detector (RICH), which covers about 80% of the solid angle, and an electromagnetic crystal calorimeter with 7800 cesium iodide crystals covering 95% of 47r. Charged particle identification is performed using specific ionization (dE/dx) measurements from the outer drift chamber as well as information from the RICH detector. Neutral pions and electrons rely on information from the calorimeter.

90 3.

Methods of Reconstruction and Results

At CLEO-c the exclusive semileptonic branching fractions and associated numbers are being calculated using two different methods. In the first method the semileptonic decay is reconstructed only for events that are known to contain a fully reconstructed, hadronically decaying D, the tagging D. As this method provides limited statistics for the initially small data sets, it is also useful to reconstruct the decays using the whole event, i.e. without requiring the presence of a hadronic tagging mode. There is then the disadvantage that background levels will be higher. The method of reconstruction utilizing a D tag was first used by the Mark III Collaboration 3 at SPEAR. Candidate events are selected by requiring the presence of one of the hadronic D tag modes (conjugates implied): D° -> K-n+, D° -* K-n+ir0, D° -> K-TT+TT0*0, D° -> K°STV+TT~, D°

-> i^Tr+TT-Tr0, D°

D+

->• K°TT+,

D+

-> K°ST:0,

->• X-7T+7T+, D+

D°

->• n'lr+it0,

-*• K°n+TT°,

D+

D°

-»•

-)•

K~K+, K°IV-W-T:+

or D+ —> K~K+-K~ . Prom this sample of events exclusive semileptonic decays are reconstructed using the known 4-momentum of the tagged D. The quality of both tag candidate D's and signal candidate D's are assessed using the kinematic variables AE = ED — Eteam and Mbc = \/E'leam — p'zD. Tag yields are found by fitting the tag candidate Mj c distributions 4 . Signal yields are obtained by fitting U = i?miss— Pmiss distributions for each signal mode. The quantity U is zero for missing particles of zero mass and will thus peak at zero for true signal events containing a neutrino. Table 1. Preliminary branching fractions for the D° exclusive semileptonic decays modes using tag reconstruction. Decay Mode D° ->

K-e+ve

Branching Fraction

PDG (fit)

(3.52 ± 0.1 ± 0.25)%

(3.58 ± 0 . 1 8 ) %

D° - > 7 r - e + f e

(0.25 ± 0.03 ± 0.02)%

(0.36 ± 0.06)%

D° -> K—e+ve

(2.07 ± 0 . 2 3 ± 0 . 1 8 ) %

(2.15 ± 0 . 3 5 ) %

D° ->

(0.19 ± 0 . 0 4 ± 0 . 0 2 ) %

-

p'e+Ve

For the neutral D meson there are four reconstructed signal modes: D° ->• 7i-e+i/ e , D° -> K'e+Ve, D° -> K*-{K--K°)e+ve and D° -> p~e+ue. Fits to the U = Emiss — pmiss distributions are shown in Figure 1, and preliminary branching fraction results are given in Table 1. We have the first observation of the p decay mode. For the charged D meson there are five reconstructed signal modes:

91

U-E^-B^l^V)

0) Figure 1. Fits to D semileptonic U = En Pmiss distributions. Points show data (55.8p6 _ 1 ), lines represent fits. Leftmost plots, (i), show modes: (a) D° —» K~e+ve, (b) D° -> ix-e+Ve, (c) D° -> K*-{K-^)e+ve, (d) D° -> p~e+ve. Rightmost plots, (ii), show modes: (a) D+ -> Ks(n+n-)e+ve, (b) D+ -> K*a{K--K+)e+ue, (c) D+ -> •n°e+ve, (d) D+ -> p°e+i/e, (e) D + - • w e + v e .

£>+ -» 7r°e+i/ e , D+ K s ( 7 r + 7 r - ) e + i / e , £>+ ->• P°e+z/e, D+ -»• + - + Jsr*°(iC 7r )e t/ e and £>+ ->• ue + (/ e . Fits to the U = S m i s s — Pmiss distributions are shown in Figure 1. We have the first observation of the u) decay mode. Without the use of the tagging D, the neutrino can be reconstructed using the whole event, as in previous B semileptonic analyses at CLEO 5 . In this method the neutrino, or missing, 4-momentum is given by, -* miss — -* event

/ ^ -'charged

/

J

-* neutral ~ (.-C'miss) PmissJ)

\^)

where, Pevent = (2£^beam, — 2i?beam sina, 0,0) is the event 4-momentum (a = crossing angle) and Yl -^charged and J2 -^neutral are the charged and neutral energy sums respectively. Four semileptonic modes (and charge conjugates) are reconstructed: D° -»• K~e+ue, D° -» 7r~e+i/e, D+ -> Ks{n+ir~)e+ve and D+ —> -K°e+ue. Signal decays are reconstructed by combining a signal 7T or K and signal electron with the missing 4-momentum to form a D candidate. Candidate quality is assessed using the variables AE and Mtc as defined above. In addition, zero neutrino mass supplies the selection criterion, MM2/2pmiss w 0, where MM2 = E^iss - j 4 i s s . Signal yields are obtained by fitting the four modes simultaneously using the method of Barlow and Beeston 6 . This is a binned maximum likelihood fit of the Mtc distributions wherein the monte carlo shape is fit to the data. Preliminary fit results for this method are shown in Figure 2.

92 lDJ^i.'ev I

n^^n

i •

T

• y • - • 4

-' -

-•

- - * * •

11111 - 1 ,

•

1.6 1.81 1.821.83 1.84 1.85 1.861.87 1.88 1.89

(b)

1°*-* M " I 1400

1200

>

-+n

1000

$"" > 600

400

200

1.8 1.81 1.821.83 1.64 1.85 1.86 1 87 1.88 1.8 M ^ (GeV)

(c)

:

'

° 1.8

. ...J- L

1.81 1.821.83 1.84 1.85 1.66 1.87 1.68 1. H.(GeV)

(d)

Figure 2. Fits to non-tagging D semileptonic modes. Points represent data (103p6 -1 ) and stacked histograms are: Clear - Signal MC, Gray - Summed Background MC, Black Fakes from Data. Modes are: (a) D° -> w~e+i/e, (b) D° K-e+ve, (c) D+ -> 7r°eTi/e and (d) D+ -» Ks(ir+ir-)e+ve. 4.

Conclusions

T h e first CLEO-c measurements of exclusive D semileptonic branching fractions, the most accurate t o date, will soon be published. In addition two new modes have already been observed for the first time, D° —> p~e+ve and D+ ->• uje+ue. For the full CLEO-c dataset branching fraction errors are expected t o be down t o the several percent level or better for all D semileptonic decay modes.

References 1. 2. 3. 4.

M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973). C. Aubin et al, Phys. Rev. Lett 94, 001601 (2005). Mark III Collaboration, J. Adler et al, Phys. Rev. Lett. 62, 1821 (1989). CLEO Collaboration, Q. He et al, arXiv:hep-ex/0504003, submitted to Phys. Rev. Lett.. 5. CLEO Collaboration, S. B. Athar et al, Phys. Rev. D 6 8 072003 (2003). 6. R. Barlow and C. Beeston, Comput. Phys. Coram. 77, 219 (1993).

D I R E C T CP VIOLATION RESULTS FROM BABAR

T. ALLMENDINGER E-mail:

Ohio State University, [email protected]

Direct CP violation results from BABAR are presented in this note. This includes the recent observation of direct CP violation in the B°-meson system at the level of 4.2 standard deviations in the B° —> K+-K~ decay mode, using 227 million BB decays collected with the BABAR detector at the PEP-II asymmetric-energy e+e~ collider at SLAC. In addition results from the decay modes B° -> K+n°, B° -> K*+ir°, B° -> -K+TT- and B° - • (pn)° are discussed.

1. Introduction Mixing induced CP violation in the B-sector has been established in b —> ccs transitions 1 ' 2 . The experimental evidence for direct CP violation in Bmesons presented by Belle3 for the decay mode B° -»• TT+TT~, which suggests large interference between penguin and tree diagrams, is not confirmed by Babar 4 . Theoretical predictions with different approaches suggest a sizable CP asymmetry Acp(K+n~). Babar has recently reported the observation of direct CP violation in the decay B° -> K+ir~ a at the level of 4.2a. Direct CP violation can be observed in two different ways. One is the observation as an asymmetry in yields between a decay and its CP conjugate when at least two contributing amplitudes carry different weak and strong phases. For example in the standard model, the decay B° —> K+-K~ occurs through two different mechanisms ("penguin" and "tree"), which carry different weak phases and, in general, different strong phases. Second is mixing-induced CP violation and direct CP violation are both observable in the time evolution of the asymmetry between B° and B° decays (e.g 7r+7r~), where mixing-induced CP violation leads to a sine oscillation with amplitude S„n and direct CP violation leads to a cosine oscillation with amplitude Crv. a

Unless otherwise stated, charge conjugate modes are included implicitly

93

94 "3 S0.84 - (b) 0 82

HgH

08

- M

"

1" "

1"

"

11

"

1 ' '

" fcJB,
^ifjcffl!

-

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-

0.78 1.5

2

2.5

3

3.5

4 4.5 5 p(GeV/c)

3

3.5

4

4.5

p(GeV/c)

Figure 1. (b) The measured Cerenkov angle for pions (upper band) and kaons (lower band) from £>*+ —> D°TT+, D° —> /C~7r+ decays reconstructed in data. The curves show the expected angle 0C as a function of laboratory momentum, for the K and w mass hypothesis, (c) The average difference between the expected value of 6C for kaons and pions, divided by the uncertainty, as a function of momentum.

2. Data Sample and Experimental Methods The results presented here are based on a sample of 227 million BB pairs collected with the BABAR detector at the SLAC PEP-II e + e~ asymmetricenergy storage ring located at the Stanford Linear Accelerator Center. A fJ-meson candidate is characterized kinematically by the energysubstituted mass mEs = y ( | s + Po • P B ) 2 / ^ O _ P B a n d e n e r g y difference AE = Eg — \yfs, where the subscripts 0 and B refer to the initial T(45) and to the B candidate, respectively, and the asterisk denotes the T(45) frame. Background for charmless B-meson decays arises primarily from random combinations in continuum e + e~ —> qq events (q = u,d,s,c). This background is rejected with requirements on kinematic variables of resonance daughters and on event-shape variables. An important input for most charmless analysis is the excellent kaon particle identification based on a detector of internally reflected Cerenkov light (DIRC), providing K-ir separation over the range of laboratory momentum relevant for most analysis (Fig. 1). 3. Charge Asymmetry Measurements 3.1. B° ->

K+n-

Two-body neutral B decays are constructed from pairs of oppositelycharged tracks located within the geometric acceptance of the DIRC and

95 originating from a common decay point near the interaction region. Each track must have an associated Cerenkov-angle (6C) measured with at least five signal photons detected in the DIRC. The 6C measurement is used to separate kaons and pions in a maximum-likelihood fit that determines signal and background yields corresponding to the four distinguishable final states (TT+TT-, K+n~, K~TT+, K+K~). The selected sample contains 68030 events and is composed of two-body B decays (signal) and combinations of real kaons and pions produced in qq events (background). An unbinned, extended maximum-likelihood fit is used to extract yields, the signal asymmetry (AKTT), and the background asymmetry {AhKn). The fit uses TUES, AE, 6C, and the Fisher discriminant F described in Ref. 5 to distinguish signal and background components for each of the four 7r+7r~, K+TT~, K~TT+, and K+K~ combinations. The fitted signal yields are UK-K = 1606 ± 51, n^ — 467 ± 33, and UKK = 3 ± 12. The direct CP-violating asymmetry is AKlt

= -0.133 ± 0.030 (stat) ± 0.009 (syst),

(1)

and the background asymmetry is A\v = 0.001 ± 0.008. The dominant source of systematic error is the potential difference between kaons and pions in the dependence of track reconstruction and particle identification on the charge of the particle. To estimate this systematic uncertainty the statistical uncertainty (0.008) on the measurement of AhKn is used as a conservative systematic error on AK^3.2.

B+

->•

K+TT°

B meson candidates are reconstructed by combining a ir° with a charged pion or kaon (h+). B+ —> h+w° candidates are selected in the region with m E S > 5.22 GeV/c2and -0.11 < AE < 0.15 GeV. The number of signal B candidates is determined with an unbinned, extended maximum-likelihood fit based on mEs> A S , 9C, and event-shape Fisher discriminant. For B+ ->• h+ir° the likelihood fit results are •/VB+_+7r+7ro = 379 ± 41 and NB+^K+K0 = 682 ± 39. The dominant systematic uncertainties for B+ -t + 0 h Tr arise from the Fisher discriminant signal PDF parameters, selection efficiencies, and the AE resolution. The branching fractions B(B+ -> TT+TT0) = (5.8 ± 0.6 ± 0.4) x 10~ 6 and B(B+

-> K+n°) = (12.0 ± 0.7 ±

0.6) x 10~ 6 are extracted. The charge asymmetries are A^+Va = —0.01 ± 0.10 ±0.02 and AK+no = 0.06 ±0.06 ±0.01. No evidence for CP violation is found in contrast to the measurement of charge asymmetry in B° —> K+TT~ decays 7 ' 9 .

96

3.3. B+ -»• K*+ir° The decay B+ —> if *+it° is particularly interesting in the light of recent measurements of direct CP-violation in the B° —> K+n~ and B+ -> K+n° channels 7>9>8. An unbinned maximum likelihood fit to the variables TTIES, AJ5, mjf„ and a event-shape neural net variable N is used to extract the total number of signal B+ -»• K*+ir° and continuum background events and their respective charge asymmetries. A total of 23,465 events were fitted, of which 11,960 had positively charged candidates. The central value of the signal yield from the maximum likelihood fit is 89 ± 26 events, over an expected background of 634 ± 40 events from other B decays. A branching fraction of B(B+ -»• K*+TT°) = [6.9 ± 2.0 ± 1.3] x 10~ 6 and charge asymmetry of

ACp(B+ -»• K*+ir°) = 0.04±0.29±0.05 is obtained. The significance of the branching fraction result is calculated to be 3.6 standard deviations, showing evidence for this decay. The systematic error of the branching fraction and asymmetry is dominated by the contribution of K** resonances. 4. Time-dependent Measurements 4 . 1 . B° ->• 7T+7T-

A time-dependent CP asymmetry measurement can be performed in the decay mode B° —> TT+TT~. After selection of events with two charged tracks, a maximum-likelihood fit is performed using TUES, A.E, a Fisher discriminant F and 9c, the Cerenkov angle. Signal and background yields of the four related h+h~ modes (h = TT,K) are determined in a first fit and fixed in the final fit where information about B-flavor and decay-time is added. The CP parameters in the decay B° —> ir+ir~ are measured to be Cn+7t- = -0.09 ± 0.15 ± 0.04 and Sn+7V- = -0.30 ± 0.17 ± 0.03, which does not indicate presence of significant CP violation. This result is not compatible with Belle's measurement with 275 million BB pairs 10 . 4.2.

B°

-> (PTT) 0

A measurement of CP-violating asymmetries in B° —> (/97r)° —>• 7r+7r~7r° decays is made using a time-dependent Dalitz plot analysis. The results are obtained from a data sample of 213 million T(45) —> BB decays. This analysis extends the narrow-p quasi-two-body approximation used in the previous analysis 11 , by taking into account the interference between the p resonances of the three charges. Sixteen coefficients of the bilinear form

97 factor terms occurring in the time-dependent decay rate of the B° meson are measured with the use of a maximum-likelihood fit. Physically relevant quantities are derived from these coefficients. The direct CP-violation parameters ACP = -0.088 ± 0.049 ± 0.013 and C = 0.34 ± 0.11 ± 0.05 are found, where the first errors are statistical and the second systematic. The significance for direct CP violation of this measurement is 2.9a. For the mixing-induced CP-violation parameter S = —0.10 ± 0.14 ± 0.04 is found, and for the dilution and strong phase shift parameters respectively, one obtains AC = 0.15 ± 0.11 ± 0.03 and AS = 0.22 ± 0.15 ± 0.03. For the angle a of the Unitarity Triangle a value of (113 t i ? ± 6)° is derived. 5. Conclusion Direct CP violation in the B-system is established with more than 4a significance based on the charge asymmetry of AKIX = —0.133 ± 0.030 (stat) ± 0.009 (syst), seen in the decay mode B° -4 K+n~. In addition charge asymmetry results from the decay modes B° -> K+n° and B° —> K*+pn° are reviewed with no clear evidence of CP violation. The time-dependent analysis of B° —» 7T+7T- leads to ambiguous results between BABAR and Belle, while the analysis of B° -> (pn)° shows evidence for direct CP violation on a 2.9a level. Further improvements are expected by doubling the existing dataset until the summer of 2006, as all analysis are still statistically limited. References 1. BaBar Collaboration, B. Aubert et al., Phys. Rev. Lett. 89, 201802 (2002). 2. Belle Collaboration, K. Abe et al., Phys. Rev. D 66, 071102(R) (2002). 3. Belle Collaboration, K. Abe et al., Phys. Rev. Lett. 93, 021601 (2004). 4. BaBar Collaboration, B. Aubert et al. hep-ex/0501071 (2005). 5. BABAR Collaboration, B. Aubert et al., Phys. Rev. Lett. 89, 281802 (2002). 6. M. Pivk and F.R. Le Diberder, physics/0402083 (2004). 7. BaBar Collaboration, B. Aubert et al. Phys. Rev. Lett. 93, 131801 (2004). 8. BaBar Collaboration, B. Aubert et al. hep-ex/0412037 (2004). 9. Belle Collaboration, B. Aubert et al. Phys. Rev. Lett. 93, 191802 (2004). 10. Belle Collaboration, Abe, K. et al. hep-ex/0502035 11. BaBar Collaboration, B. Aubert et al. Phys. Rev. Lett. 91, 201802 (2003).

COSMIC RAY VELOCITY A N D ELECTRIC C H A R G E M E A S U R E M E N T S IN T H E A M S E X P E R I M E N T

L U I S A A R R U D A , O N B E H A L F O F T H E AMS-02 C O L L A B O R A T I O N LIP/IST Av. Elias Garcia, 14, 1° andar 1000-149 Lisboa, Portugal e-mail: [email protected]

The Alpha Magnetic Spectrometer (AMS) is a particle physics detector designed to measure charged cosmic ray spectra with energies up to the TeV region and with high energy photon detection capability up to few hundred GeV. It will be installed on the International Space Station (ISS) in 2008 and will operate for more than three years. Due to its large acceptance, the flight duration and the stateof-art of particle identification techniques, AMS will have a remarkable sensitivity on antimatter and dark matter searches. The addition of different detector systems provide AMS with complementary and redundant electric charge and velocity measurements. The velocity of singly charged particles is expected to be measured with a precision of 0.1% and charge separation up to iron is attainable. The AMS capability of measuring a large range of electric charges and accurate velocities, will largely contribute to a better understanding of cosmic ray production, acceleration and propagation mechanisms in the galaxy.

1. The AMS02 detector AMS I1] (Alpha Magnetic Spectrometer) is a precision spectrometer designed to search for cosmic antimatter, dark matter and to study the relative abundance of elements and isotopic composition of the primary cosmic rays with an energy up to ~ 1 TeV. It will be installed in the International Space Station (ISS), in 2008, where it will operate for more than three years. The spectrometer will be able to measure the rigidity (R = pc/\Z\e), the charge (Z), the velocity (ft) and the energy (E) of cosmic rays within a geometrical acceptance of ~0.5m 2 sr. Figure 1 shows a schematic view of the AMS spectrometer. At both ends of the AMS spectrometer exist the Transition Radiation Detector (TRD) (top) and the Electromagnetic Calorimeter (ECAL) (bottom). Both will provide AMS with capability to discriminate between leptons and hadrons. Additionally the calorimeter will trigger and detect photons. The TRD will be followed by the first of 98

99 the four Time-of-Flight (TOF) system scintillator planes. The TOF system [2] is composed of four roughly circular planes of 12 cm wide scintillator paddles, one pair of planes above the magnet, the upper TOF, and one pair bellow, the lower TOF. There will be a total of 34 paddles. The TOF will provide a fast trigger within 200 ns, charge and velocity measurements for charged particles, as well as information on their direction of incidence. The TOF operation at regions with very intense magnetic fields forces the use of shielded fine mesh phototubes and the optimization of the light guides geometry, with some of them twisted and bent. Moreover the system guarantees redundancy, with two photomultipliers on each end of the paddles and double redundant electronics. A time resolution of 130 ps for protons is expected [3]. The tracking system will be surrounded by veto counters and embedded in a magnetic field of about 0.9Tesla produced by a superconducting magnet. It will consist on a Silicon Tracker [4] made of 8 layers of double sided silicon sensors with a total area of ~6.7m 2 . There will be a total of ~2500 silicon sensors arranged on 192 ladders. The position of the charged particles crossing the tracker layers is measured with a precision of ~10/im along the bending plane and ~30/mi on the transverse direction. With a bending power (BL2) of around 0.9 T.m 2 , particles rigidity is measured with an accuracy better than 2% up to 20 GeV and the maximal detectable rigidity is around 1-2 TeV. Electric charge is also measured from energy deposition up to Z~26. The Ring Imaging Cerenkov Detector (RICH) [5] will be located right after the last TOF plane and before the electromagnetic calorimeter. It is a proximity focusing device with a dual radiator configuration on the top made of a low refractive index aerogel 1.050, 2.7 cm thick and a central square of sodium fluoride (NaF), 0.5 cm thick. Its detection matrix is composed of 680 photomultipliers and light guides and a high reflectivity conical mirror surrounds the whole set. RICH was designed to measure the velocity of singly charged particles with a resolution A/3//? of 0.1%, to extend the charge separation up to iron, to contribute to e/p separation and to albedo rejection. Particle identification on AMS-02 relies on a very precise determination of the magnetic rigidity, energy, velocity and electric charge. Velocity of low energy particles (up to ~ 1.5 GeV) is measured by TOF detector while for

100

kinetic energies above the radiator thresholds (0.5 GeV for sodium fluoride and 2 GeV for aerogel) the RICH will provide very accurate measurements; a target resolution of ^ 1 % and ~ 0 . 1 % for singly charged particles is expected, respectively for sodium fluoride and aerogel radiators. The electric charge is measured by the silicon tracker and TOF detectors through dE/dx samplings and on the RICH through the Cerenkov ring signal integration. Charge identification, at least, up to the iron element is expected.

Figure 1. A whole view of the AMS Spectrometer.

2, Velocity m e a s u r e m e n t TOF measures the crossing time between two scintillator planes and extracts the velocity through /3=AL/At. The time of flight resolution for two scintillators, tested in a test beam at CERN in October 2003 with fragments of an indium beam of 158 GeV/c/nuc, is shown in figure 2 as function of the particle charge. One of the tested scintillators had bent and twisted light guides (C2) while the other one had bent light guides (03). A time resolution of 180 ps was estimated for this conservative configuration. However, as the measurement in AMS-02 will be done with four independent measurements, the time resolution which can be inferred is of the order of 130 ps for a minimum ionizing particle. In the RICH detector the velocity of the particle, /?, is simply derived from the Cerenkov angle reconstruction (cos# c = Wn)- Two reconstruction methods were developed: a geometrical method based on a hit-by-hit reconstruction and a method based on a likelihood fit to the pattern of the detected photons. The best value of 0C will result in the former case from

101

the average of the hit velocities after hit clusterization and in the latter from the maximization of a likelihood function L{6C) given by, nhits

We) = n p? WW

(i)

i=l

where the probability of a hit belonging to a Cerenkov ring of angle 6C (pi) is function of the closest distance of the hit to the Cerenkov pattern (rj). In both methods the hits position is weighted by the detected signal rij. For a more complete description of the method see [6]. The resolution expected for /? ~ 1 singly charged particles crossing the aerogel radiator is around 4mrad while for those crossing the NaF radiator is around 8mrad. The accuracy of the velocity determination improves with the charge. Figure 2 (right plot) shows the evolution of the velocity resolution for indium beam fragments of 158 GeV/c/nuc detected with a RICH prototype corresponding to 1/6 of the final RICH detector. The radiator plane was placed perpendicular to the beam direction. The photon expansion length between the radiator and the detection matrix was adjusted to 42.3 cm, allowing fully contained Cerenkov rings.. ; 1

1

0.4

:1

0.35

1 1

0.3

\

0.25 0.2

:

J(P + & A = (7.77 ± 0.05) x 10"4 B = (7.3 ± 0.2) x 10"5

\

x2 = 55.2/20

:V

0.15

M^i

0.1 0.05

;

^~~^*-m , {j jj 7.5

10 12.5 15 17.5 20 22.5 25 Zselected with scintillator

Figure 2. Time of flight resolution for a set of two scintillators and different charged nuclei (left), and evolution of the /3 resolution with the charge obtained for a RICH prototype with an aerogel 1.03 radiator, 3 cm thick. Both results are from nuclei fragments of an indium beam of 158 GeV/c/nuc taken at CERN in October 2003.

3. Charge measurements As it was said previously, TOF and tracker measure the charge (Z) through dE/dx samplings. Figure 3 a) shows the charge measurement from the

102

anode signal of one of the TOF counters (C2) tested in ion beam at CERN in 2003, in principle the most unfavourable one. Charge separation up to the aluminium is visible. Figure 3 b) shows the combined measurements for 4 or more ladders on the tracker K side. The ion species can be distinguished up to Z=26.

Figure 3. Charge measurements with T O F , Tracker and RICH prototypes tested at CERN in October 2003, with fragments of an indium beam of 158 GeV/c/nuc. (a) The square root of the integrated charge measured with T O F scintillator's anode show different peaks corresponding to charges up to aluminium, (b) Combined Z measurements for 4 or more ladders on the tracker K side, (c) Charge peaks distribution measured with the RICH prototype having an n=1.05 aerogel radiator, 2.5 cm thick, (d) Comparison of the charge measurements made by the tracker and by the RICH.

RICH charge measurement is based on the fact that the number of Cerenkov photons produced in the radiator depends on the particle charge through N7 oc Z2L sin2 8C where L is the radiator thickness. Once the total number of photoelectrons (Np,e) associated to a Cerenkov ring is computed one has to correct it by the photon ring overall efficiency in order to derive the charge. The uncertainty on charge determination results from two distinct contributions. One of statistical nature independent of the nuclei charge and depending essentially on the amount of Cerenkov signal detected for singly charged particles (Np,e ~ 10). Another one of systematic nature

103 scaling with the charge and coming essentially from non-uniformities on the radiator plane and photon detection efficiency. The RICH goal of a good charge separation in a wide range of nuclei charges implies a good mapping and monitoring of the potential non-uniformities present on the detector. Charge peaks reconstructed with the RICH prototype for data taken at CERN during October 2003, are shown in figure 3 c). The RICH configuration included an aerogel radiator of n=1.05 and 2.5 cm thick. A charge resolution for helium events slightly better than AZ ~ 0.2 was observed together with a systematic uncertainty of 1%. A clear charge separation up to Z=28 was achieved. For a more complete description of the charge reconstruction method see [6]. Finally figure 3 d) presents the comparison of charge measured by tracker and RICH. Ions can be distinguished and identified up to Z=26, an excellent correlation is obtained. 4. Acknowledgements I would like to express my acknowledgements to the AMS collaboration for giving me the opportunity to attend the Lake Louise Winter Institute 2005. I also express my gratitude to the Fundagao da Ciencia e Tecnologia for the financial support to participate in the meeting. 5. Conclusions AMS is a spectrometer designed for antimatter and dark matter searches and for measuring relative abundances of nuclei and isotopes.The velocity of singly charged particles is expected to be measured with a precision of 0.1% and charge separation up to iron is attainable. Real data analysis was done with data collected with prototypes of TOF, tracker and RICH in test beams at CERN, in October 2002 and 2003 References 1. S. P. Ahlen et al, Nucl. Instrum. Methods A 350,34 (1994). V. M. Balebanov et al., AMS proposal to DOE, approved April 1995. 2. D. Casadei et al., Nuclear Physics B (Proc. Suppl.) 113,133 (2002). 3. The AMS collaboration, AMS on ISS, http://ams.cern.ch/AMS/AMS.pdf. 4. W. J.Burger, Nuclear Physics B (Proc. Suppl.) 113,139 (2002). 5. M. Buenerd, Proceedings of the Fourth Workshop on Rich Detectors (RICH02) June 5-10, 2002, Pylos, Greece. 6. F. Barao, L. Arruda et al., Nucl. Instrum. Methods A 502,310 (2003).

ELECTROWEAK PHYSICS AT LEP2

P. A Z Z U R R I Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy E-mail: [email protected]

The measurements resulting from the analysis of the LEP2 data have brought more strong evidence in support of the standard electroweak model. In particular the LEP2 data has revealed (i) the first determination of the SU(2) gauge bosons selfcouplings, (ii) the first direct measurements of the W decay-couplings, and (iii) the current best direct measurement of the W mass.

1. Introduction During the LEP2 program a total of about 3 fb _1 of e + e~ data at centreof-mass energies •v/s=161-209 GeV, have been collected. A selection of Standard Model (SM) electroweak measurements established with this data is given in the following. 2. Single Photons and Photon Pairs Single photon final states arise at LEP2 from the e + e~ —• Z7 —» i>Vj process. The missing mass distribution in single photon events selected at LEP2 energies is shown in Fig. 1, and clearly shows the Z mass peak decaying into neutrino pairs. The analysis of these events provides a direct measurement of the Z decay rate to neutrinos, and from this the number of light neutrino families is derived to be N„ — 2.84 ± 0.08, in good agreement with the more precise indirect determination from the LEPl Z width measurements, Nv = 2.984 ± 0.0081. Photon pair productions provide a test of the purely QED process e + e~ —• 77. As can be seen in Fig. 1, the measured LEP2 cross-sections agree nicely with the QED predictions at the percent level. Both results on single photon and photon-pair productions at LEP2 can be used to extract limits on the scale of many new physics models beyond the Standard Model, up to the TeV level2. 104

105 130 s f e 208 GeV ALEPH DELHI L3 OPAL

• ALEPH Va + 0.4 GeV • DELPHI Vs + 0.2 GeV

, • L3 Vs - 0.4 GsV )|<J-EP preliminary • OPAL Vs,- 0.2 GeV

f H J ft % 0

25

50

75

100

125 150 175 200 Recoil mass (GeV/c2)

205

210 Vs [GeV]

Figure 1. Distribution of the recoil mass in single photon events from all LEP2 data (left). Ratios of measured cross-section over QED predictions for photon-pair production at different LEP2 energies. The shaded area represents the theoretical uncertainty (right).

3. Fermion Pairs Fermion pairs with qq, / i + / i _ and T+T~ final states are produced in e + e~ collisions with a 7/Z s-channel exchange. The total cross-sections and forward-backward asymmetries measured at LEP2 energies are in agreement with the electroweak predictions for 7/Z interference at the percent level. Bhabha e + e~ —> e + e~ final states get additional large contributions from the ^-channel 7 exchange, for forward angle scattering. Also in the Bhabha channel the LEP2 measured total and differential cross-sections are in nice agreement with electroweak predictions at the 1-10% precision level, according to the scattering angle 2 . Just like for photons, also fermion pair final states have been analyzed to extract limits on the scale of different physics models beyond the Standard Model, up to the TeV level2. 4. Single W and Z Single electroweak boson productions e + e~ —> Wei/ and e + e~ —> Zee represent four-fermion final states. The luminosity weighted cross-section averages for these processes, at the LEP2 average centre-of-mass energy of •v/s ~198 GeV, are a(e+e~ —> Wei/) = 0.77 ± 0.05 pb for single W production, and qqee) = 0.55 ± 0.03 pb for single Z production. Both measurements are in agreement with the SM expectations at 7% and 5% precision level2.

106

5. W and Z Pairs W-pair production is one of the most interesting processes of the electroweak model, where the non-abelian structure of the SU(2) group leads to the presence of gauge boson self couplings that play a crucial role establishing the gauge cancellations that guarantee the W-pair process unitarity and the renormalizability of the theory. Results for the W-pair cross-sections as a function of the LEP2 energy2 are shown in Fig. 2, and are in agreement with the SM expectations at the 1% level. The measured W-pair production rates represent the first clear proof of the presence of both the WW7 and WWZ couplings dictated by the SU(2)®U(1) gauge structure. Results for LEP2 Z-pair cross-sections are also shown in Fig. 2 where the agreement with the SM expectations is at the level of 5%. In this case the Z-pair data rules out the presence of purely neutral gauge self couplings, such as ZZ7 and ZZZ vertices, that are not predicted by the electroweak theory.

I

30-

17/02/200J

' LEP

' /'

PRELIMINARY

/

>•-"" .,.-*"*'

S

3

' •

6s

'

1

ZZTOandYFSZZ

—

20-

itB2t = 1 -

_^~*~---.f-t-"-r*"™'

10-

1

L E P PRELIMINARY

Q.

f,i22fl = 1 f6CEM = 1 f,(ZZZ> = 1

1f' /' j

160

isYFSWW/RacoonWW ...no ZWW vertex (Gentle) ....only v0 exchange (Gentle)

180

200

Vs (GeV)

180

190

200

Vs (GeV)

Figure 2. Combined LEP results for production cross-sections for W-pairs (left) and Z-pairs (right), as a function of the centre-of-mass energy. The lower shaded curves represent the Standard Model predictions and uncertainties. The upper curves on the W-pair production plot show the predictions in the absence of the 7 W W and ZWW couplings. The upper curves on the Z-pair production plot show the predictions in the presence of different possible ZZ7 and ZZZ couplings.

107 6. Gauge bosons self-couplings The structure and magnitude of the 7WW and ZWW couplings are extracted from the W-pair event rates and angular distributions 2 . A fit with the ALEPH data 3 to the 28 parameters of the most general Lorentz-invariant vertex structures leads to results in agreement with the SU(2) ev) = 10.69 ±0.17%, B(W -> iiu) = 10.57 ±0.16%, B(W -* rv) = 11.39 ±0.23%, and B(W —> qq) = 67.51 ± 0.29%. These results insure the lepton-quark universality of charged currents at the 0.6% level (gq/g£ = 1.000 ± 0.006), and of the lepton family universality of charged currents at the 1% level. However, the tau coupling to the W appears to be 2.6 standard deviations larger than the combined electron and muon couplings as 2gT/(ge + g^) = 1.036 ±0.014. The W hadronic decay fraction can also be interpreted as a test of the unitarity of the CKM quark mixing matrix in the first two families, as S I ^ ' K * — u > c ; J = d,s,b) = 2.000 ± 0.026, and from this extract the Wcs coupling amplitude \VCS\ = 0.976 ± 0.014, without CKM unitarity assumptions. 8. W boson mass and width The first LEP2 W mass determination has been extracted from the W-pair production threshold cross-section2 yielding m\y = 80.40 ± 0.20 GeV/c 2 . For the direct measurement, the W invariant mass is reconstructed eventby-event in all qqqq and qq£i^ decays of W-pairs, from the kinematics of the visible decay particles, and the resolution of the W mass peak is improved by applying a kinematic fit imposing energy-momentum conservation constraints from the LEP2 energy. The W mass and width values can be extracted from the W mass data distributions using different fit methods, and

108

yielding m w = 80.412 ± 0.042 GeV/c 2 , and Tw = 2.150 ± 0.091 GeV/c 2 , where the weight of the fully hadronic (qqqq) channel is only 10% because of large uncertainties coming from possible final state interactions effects between the two W hadronic decay products. The inclusion of the current W mass determinations in the electroweak fit yields a constraint on the SM higgs mass 114 < rrih < 260GeV/c 2 at 95% confidence level2. W-Boson Mass [GeV]

W-Boson Width [GeV]

TEVATRON

80.452 ±0.059

TEVATRON -

2,102 ±0.106

LEP2

80.412 ±0.042

LEP2

2.150 ±0,091

Average

80.425 ± 0.034

Average

2.133 ±0.069

pp indirect

2.141 ±0,057

X*/DoF:

X2/DoF: 0.1/1

0.3/1

NuTeV

80.13610.084

LEP1/SLD

80.363 ±0.032

LEP1/SLD

2.091 + 0.003

LEP1/SLD/m,

80.373 ±0.023

LEP1/SLD/m,

2.092 ± 0.002

80

80.2

80.4

m w [GeV]

2.4

r w [GeV]

Figure 3. Summary of W mass and width measurements. Direct measurements from LEP2 and the TEVATRON are shown on the top, indirect constraints from other electroweak determinations on the bottom.

Acknowledgments I would like to thank Roberto Chierici for providing the most recent combined results for four-fermion productions. I also have to thank Stefania who fortunately could not come to the conference, and Aafke Kraan for nicely reviewing this paper. References 1. Particle Data Group, S. Eidelman et al, Phys. Lett. B 592, 1 (2004); (http://pdg.lbl.gov). 2. LEP Collaborations ALEPH, DELPHI, L3, OPAL and Electroweak Working Group, A Combination of Preliminary Electroweak Measurements and Constraints on the Standard Model, hep-ex 0412015, and references therein. (http://lepewwg.web.cern.ch) 3. ALEPH Collaboration, Improved Measurement of the Triple Gauge-Boson Couplings 7 WW and ZWW in e+e~ collisions, CERN-PH-EP/2004-065 , submitted to Phys. Lett. B.

W H A T C A N W E L E A R N A B O U T N E U T R I N O S AT SNOLAB?

ALAIN BELLERIVE Department of Physics, Carleton University, Ottawa ON K1S 5B6 Canada Review of the scientific program of the new Canadian International Facility for Underground Science: SNOLAB.

1. Introduction The Sudbury Neutrino Observatory Laboratory (SNOLAB) was funded by the Canadian Foundation for Innovation in June 2002. When completed, SNOLAB will be an expansion of the existing underground facility for the Sudbury Neutrino Observatory (SNO) located on the 6800 ft level of INCO's Creighton Mine near Sudbury in Ontario. The observations in recent years that neutrinos change from one type to another, implying that they have mass, has led to great interest in the scientific community. These new findings require a modification of the most basic theories for elementary particles and have provided a strong confirmation that our theories of energy generation in the Sun are very accurate. New experiments to provide further information on neutrino properties and the origin of the dark matter in the Universe are being developed. These include projects that could be sited in the new SNOLAB being developed near the SNO underground site. Such future measurements will provide insight into fundamental questions such as why our world is composed of matter rather than anti-matter. The answers to such questions require a further understanding of the evolution of the Universe and the laws that govern the interactions between elementary particles.

2. The Infrastructure The SNOLAB facility will provide infrastructure for exciting new measurements in particle astrophysics which can only be carried out in a deep ultra-low radioactivity conditions. The 2 km of over burden at the site pro109

110

vides 6010 m of water equivalent of shielding from cosmic rays and offers a uniquely low background environment for the next generation of experiments exploring the frontiers of particle physics in the study of low energy solar neutrinos, neutrinoless double beta decay, dark matter, and neutrinos from Supernova explosions. The new facilities will consist of a modern surface building, new experimental halls, ultra-low background materials testing laboratory, chemistry laboratory, and other supporting infrastructure. Construction of the surface facility and the design of the underground excavations are completed. The underground layout of SNOLAB is depicted in Figure 1. Excavation has begin and is expected to be completed in 2006. Space for experiments will become available in early 2007.

3. The Science 3.1. Low Energy Solar

Neutrinos

Low energy neutrinos produced in the core of the Sun are the perfect probes to investigate matter induced neutrino oscillations. The SNO+ proposal 1 describes a plan to fill the SNO detector with liquid scintillator. With a lower energy threshold, it will allow precision measurements of the pep, CNO, and 7 Be fluxes. Because of the much greater depth of the Sudbury site, the background due to cosmic-ray produced radioactivity in the detector would be reduced by several orders of magnitude (especially the n C induced background) and this will enable the first direct measurement of the fundamental pep solar nuclear reaction. Unlike the higher energy 7 Be and 8 B neutrinos, there is very little uncertainty in the theoretical predictions for the intense pep flux; so that a precision measurement of this flux will test critically the solar model and allow a low energy measurement of the electron neutrino survival probability. By mapping out the neutrino oscillations over the largest possible energy range, one can get stringent constraints on the underlying physics parameters of neutrino-matter interaction and explore new physics beyond the Standard Solar Model. 3.2. Neutrinoless

Double Beta

Decay

The search for neutrinoless double beta decay is one of the most pressing but challenging tasks facing particle physics today. With the demonstration by Super-K, SNO, and KamLand that neutrino oscillations occur with large mixing amplitudes, it implies that neutrinos must possess mass even

Ill

Figure 1. The medium grey area is the existing SNO cavern. The dark grey area is the first phase of excavation at SNOLAB; the hatched area is the new utility room, while the light grey area is the projected phase II. The first available space underground for assembly area, small prototypes, and low-energy background counting room will be the ladder laboratories.

112

though they are not mass eigenstates. The oscillation measurements determine mass-squared differences among the neutrino mass states but they do not determine an absolute mass scale. The measurement of neutrinoless double beta decay would provide unique information about the absolute mass values for neutrinos, as well as establishing the Majorana nature of the neutrino. There are several efforts world wide into the search for neutrinoless double beta decay. The scale of these experiments is such that only a small number will actually proceed to full scale measurements and these selected experiments will need the combined efforts of the world community if they are to succeed. Rather than initiate another project, the Canadian physicists have opted to join two of the most promising existing teams, Majorana 2 and EXO 3 . Germanium, used by the Majorana project, offers the advantage of a very high energy-resolution together with a largely proven technology. With highly segmented germanium crystals and pulse shape analysis, together with very clean construction techniques, it is expected that substantial improvements in the rejection of backgrounds can be achieved. The EXO group is exploring the use of xenon detectors which offer the prospect of good energy-resolution, very high purity, excellent tracking of the electrons, and the prospect of tagging events with the barium daughter, again leading to very good background rejections. The EXO Canadian group is leading the construction of the WIPP liquid-prototype detector and is developing new concepts for a gaseous xenon TPC. The partnership with the Majorana and EXO collaboration is a natural extension of the research activities at Carleton, Laurentian, and Queen's.

3.3. Dark

Matter

Current models explaining the evolution of the Universe, and measurements of the various components of its constitution, all have in common that an appreciable contribution to its mass is non-luminous and non-baryonic, and that a large fraction is cold dark matter in the form of non-relativistic massive particles. Accelerator experiments have explored only a small range of masses and types of possible candidate particles. Many competing cold dark matter detector experiments have started restricting cross-sections and masses for various candidates. They all leave room for an interpretation in terms of weakly interacting massive particles (WIMPs), one of which, the SUSY neutralino, remains one of the best candidate. The interaction of WIMPs with ordinary matter can be either coherent

113 or spin-dependent. The detection reaction would be elastic scattering off a detector nucleus and the nuclear recoil energy would be the measurable quantity. The PICASSO project 4 uses a technology developed in Canada and exploited by Bubble Technology Industries in Chalk River, Ontario. The PICASSO detection technique is based on the phase transition induced by nuclear recoils in a super-heated CiFw droplet detector. It is a promising alternative to other more conventional detector approaches. Its unique characteristic is the possibility of eliminating or decreasing the sensitivity to major sources of background, such as gamma rays; while keeping an adequate sensitivity to neutralino-induced nuclear recoils because its sensitivity to various types of radiation is temperature or pressure dependent. It has been shown that, depending on the temperature of operation, the detector can be either fully sensitive to cold dark matter or completely insensitive to nuclear recoils produced by neutralinos; while responding in a well understood manner to residual background, such as that produced by alpha-emitting contamination of the detector material. The PICASSO experiment recently reported an improved limit for the existence of cold dark matter WIMPs interacting via spin-dependent interactions with nuclei5. The prototype experiment was installed in the Sudbury Neutrino Observatory at a depth of 2070 m and no evidence for a WIMP signal was found. Improved limits on the spin-dependent crosssection on protons and neutrons have been reported and suggest a very promising R&D program at SNOLAB. 4. Conclusion The SNOLAB facility will enable significant breakthroughs in basic physics by addressing critical questions in particle astrophysics. It will build new partnerships with international researchers and facilities of the highest caliber and enable exciting new measurements in the field of elementary particle physics. References 1. M. Chen, Invited presentation at the Canadian Association of Physicists (CAP), University of British Columbia, Vancouver, BC, June 5-8, 2005. 2. http://majorana.pnl.gov/ 3. http://www-project.slac.stanford.edu/exo/ 4. V. Zacek, II Nuovo Cimento 107A (1994) 1247; PICASSO Collaboration, Nucl.Inst. Meth. A388 (1997) 91. 5. PICASSO Collaboration, hep-ex/0502028, to be published in Phys. Lett. B.

FLAVOR A N D CHIRAL OSCILLATIONS W I T H D I R A C SPINORS *

A. E. BERNARDINI Department of Cosmic Rays and Chronology, State University of Campinas, PO Box 6165, SP 13083-970, Campinas, SP, Brazil, E-mail: [email protected] S. DE LEO Department of Applied Mathematics, State University of Campinas, PO Box 6065, SP 13083-970, Campinas, SP, Brazil, E-mail: [email protected]

We report about recent results on Dirac wave packets in the treatment of neutrino flavor oscillation where the initial localization of a spinor state implies an interference between positive and negative energy components of mass-eigenstate wave packets. In this context, a new flavor conversion formula can be obtained when the effects of chiral oscillation are taken into account.

1. Introduction The Dirac formalism is useful and essential in keeping clear many of the conceptual aspects of quantum oscillation phenomena that naturally arise in a relativistic spin one-half particle theory. Our aim is the investigation of how the inclusion of chiral oscillation effects can modify the flavor conversion probability formula which was previously obtained by using fermionic instead of scalar particles, i. e. in treating the time evolution of the spinorial mass-eigenstate wave packets, we shall take into account the chiral nature of charged weak currents and the time evolution of the chiral operator with Dirac wave packets. To do it, we shall use the Dirac equation as the evolution equation for the mass-eigenstates.

""This work is supported by capes/brazil. 114

115

2. Dirac Wave Packet Formalism The main aspects of oscillation phenomena can be understood by studying the two flavor problem. In addition, substantial mathematical simplifications result from the assumption that the space dependence of wave functions is one-dimensional (z-axis). Moreover, since we know that neutrinos are fermions, the time evolution of a spin one-half particle must be described by the Dirac equation. To introduce the fermionic character in the study of quantum oscillation phenomena, we shall use the Dirac equation as the evolution equation for the mass-eigenstates. In this context, the time evolution of flavor wave packets can be described by 9(z,t) = tp! (z, t) cos 0i>i + ip2(z, t) sin 0i/ 2 = Ui(.M) cos2 0 + ^2(2,*)sin2 #1 va + [V>i (z, t) — ip2 (z, t)] cos 9 sin 9 v$ = i/Ja(z,t;0)va+il>l3(z,t;e)t/p,

(1)

where rpi(z,t) satisfies the Dirac equation for a mass rrii. The natural extension of a scalar prescription reads tpa(z,0,9) = 4>a(z,0,6)w

(2)

where to is a constant spinor which satisfies the normalization condition w^w = 1 and
ipi(z,t) = /

-^-exp[tp*2]

y~]{bs(p„Tni)us(p„mi)exp[-iE(pz,mi)t]

+ ds*(-pz, mi) vs(-p:,mi) exp [+iE(p„mi)t]}.

(3)

At time t = 0 the mass-eigenstate wave functions satisfy ^ ( 2 , 0 ) = ip2(z,0) (this guarantees the instantaneous creation of a pure flavor-eigenstate va as we have appointed in section II). The Fourier transform of ipi(z, 0) is Y^ [bs(pI,mi)us(pz,mi)

+ ds*(-pz,mi)v8(-p,,mi)].

(4)

t=l,2

By observing that the Fourier transform of cj)a(z,0,d) we immediately obtain the Fourier transform of ipa{z, 0,6), ¥>(p*-po)w= ] P [b'{p„mi)ua(p„mi)+ds*(-pz,mi)vs(-p„mi)]. «=1,2

(5)

116

Using the orthogonality properties of Dirac spinors, we find bs{pz,mi) =
5

-pQ)us^(pz,mi)w,

=
(6)

These coefficients carry an important physical information. For any initial state which has the form given in Eq. (2), the negative frequency solution coefficient ds*(-pz,m,) necessarily provides a non-null contribution to the time evolving wave packet. This obliges us to take the complete set of Dirac equation solutions to construct the wave packet. Only if we consider a momentum distribution given by a delta function (plane wave limit) and suppose an initial spinor w being a positive energy mass-eigenstate with momentum p0, the contribution due to the negative frequency solutions ds*(-pz,mi) will be null. Having introduced the Dirac wave packet prescription, we are now in a position to calculate the flavor conversion formula. The following calculations do not depend on the gamma matrix representation. By substituting the coefficients given by Eq. (6) in Eq. (3) and using some spinor properties 5 , we obtain

ipi(z, t) =

-^
f x I cos [E(p.,mt)t]

«7° ( T V + mi) ^

)

' sin [E(pz, m;)t] \ w.

(7)

3. Flavor and Chiral Oscillations In treating the time evolution of the spinorial mass-eigenstate wave packets in the previous section, we have overlooked an important feature. We have completely disregarded the chiral nature of charged weak currents and the time evolution of the chiral operator. In the following, we aim to investigate if (and eventually how) the flavor oscillation formula could be modified by this additional effect. It is well known that from the Heisenberg equation, we can immediately determine whether or not a given observable is a constant of the motion. If neutrinos have mass, the operator 7 5 does not commute with the mass-eigenstate Hamiltonians. This means that for massive neutrinos chirality is not a constant of the motion. Observing that neutrinos with positive chirality are decoupled from charged weak currents, this additional effect cannot be ignored. By assuming that the normalizable mass-eigenstate wave functions %plt2(z,t) are created at time t = 0 as a —1 chiral eigenstate, we can calculate the time evolution of the chiral operator 7 5 and construct an effective oscillation probability which takes

117

into account both flavor and chiral conversion effects, i.e. r+°°

2

P K ^ ^ ^ U 2E

8 = 1 L'

Re

/

dzip'ltL(z,t)ip2,L(z,t)

\

sin 29

y 1 [Dco(t) - DFCo(t)].

(8)

After some algebraic manipulations, by following an UR approximation we explicitly calculate the terms Dco(i) and DFCO(i),

f 2Pn2-m2 V j

Dco(i) « 1 - ~\ + exp

4^?

Po

{ x c o s ^ f j + i i ^ s i n ^ , ] } } \ V2apg

X

) \ Tpl

x l c o . J ^ p i ^ i ^ i ^ i n J ^ p i , ] } } ,

(9)

DFCO^exp^^*)] x { [l - =Sg*] cos [$£,] + ^

{ x cos [ 4 p n + ^ i + ^ *] + 4 " ' ; ^ | - " > g

^

t

.sin [%gt] }

sin [ 4 ^ + 2 ^ + ^ t] }(10)

In the hypothesis of minimal slippage between the mass-eigenstate wave packets (AvL -C a), and for long distance between source and detector (L » a),i.e. o Am2 the standard flavor oscillation probability is reproduced. In fact, ,

r\ ~ sin2 [26] ["-,

PD ( ^ , r ->t I//9,!; L) «

^

sin^ 26 2

[1

m?+ml2 ]

^-r -]

"{'-['-(^^l-f^]} 1 I — [*£*]}

sin [20]Sin2[^L].

(11)

118 4. Conclusions In order to quantify some subtle changes which appear in the standard flavor oscillation probability 1 due to chiral oscillations coupled to the flavor conversion mechanism of free propagating wave packets, we have reported about some recent results on the study of flavor oscillation with Dirac wave packets 4 . By taking into account the spinorial form of neutrino wave functions and imposing an initial constraint where a pure flavor-eigenstate is created at t = 0, for a constant spinor w, it is possible to calculate the contribution of positive and negative frequency solutions of the Dirac equation to the wave packet propagation and, finally, to obtain the oscillation probability. Particularly, we have noticed a term of very high oscillation frequency depending on the sum of energies in the new oscillation probability formula. In addition, the spinorial form of the wave functions and their chiral oscillating character subtly modify the coefficients of the oscillating terms in this flavor conversion formula. Once we have assumed the interactions at the source and detector are chiral only the component with negative chirality contributes to the propagation. In this case, we are obliged to consider chiral coupled to flavor oscillations in order to compute the modifications to the standard flavor conversion formula. In fact, when chiral oscillations are taken into account, these modifications introduce correction factors proportional to vn\Jp% which are, however, practically un-detectable by the current experimental analysis. It leads to the conclusion that, in spite of often being criticized, the standard flavor oscillation formula resorting to the plane wave derivation can be reconsidered when properly interpreted, but a satisfactory description of fermionic (spin one-half) particles requires the use of the Dirac equation as evolution equation for the mass-eigenstates. References 1. B. Kayser, Phys. Lett.B592, 145 (2004), in [PDG Collaboration] Review of Particle Physics in Neutrino mass, mixing and flavor change by B. Kayser. 2. B. Kayser, On the quantum mechanics of neutrino oscillation, Phys. Rev.T>24, 110 (1981). 3. A. E. Bernardini and S. De Leo, Analytic approach to the wave packet formalism in oscillation phenomena, Phys. Rev.T>70, 053010 (2004). 4. A. E. Bernardini and S. De Leo, Dirac Spinors and Flavor Oscillation, Eur. Phys. J.C37, 471 (2004). 5. C. Itzykinson and J. B. Zuber, Quantum Field Theory (Mc Graw-Hill Inc., New York, 1980). 6. S. De Leo and P. Rotelli, Neutrino Chiral Oscillations, Int. J. Mod. Phys.37, 2193 (1998).

D E T E C T I O N A N D M E A S U R E M E N T OF G A M M A RAYS IN T H E AMS-02 D E T E C T O R

J. BOLMONT, ON BEHALF OF THE AMS COLLABORATION Laboratoire de Physique Theorique et Astroparticules Universite Montpellier II - Place Eugene Bataillon 34095 MONTPELLIER Cedex 5 - FRANCE E-mail: [email protected] In addition to its main physics goals such as direct search for anti matter or accurate cosmic ray spectra measurements, AMS-02 will also have great gamma ray detection capabilities in the range 1-300 GeV. In this note, we review the two different methods that will be used to detect and measure gamma rays. Different physics goals are also presented such as the study of standard gamma sources and the search for photons produced by neutralino annihilations in the Galactic Centre.

1. Introduction The main physics goals of the AMS experiment are the search for antimatter and dark matter, as well as the precise measurement of the charged cosmic-ray spectra. Several years ago, it was proposed as well to use the AMS-02 detector for the measurement of cosmic-ray photons *. With two different detection modes based on the use of the Silicon Tracker (SiTracker) and the Electromagnetic Calorimeter (ECAL), AMS will be able to study different kinds of gamma sources such as pulsars, blazars or gamma ray bursts. In the following we briefly describe the ECAL and Si-Tracker subdetectors, present their performances and explain the two corresponding detection modes. We will show predictions for some standard gamma sources. Finally we will study the sensitivity of AMS to photons produced by neutralino annihilations in the Galactic Centre. 2. Detecting photons with AMS-02 AMS-02 is a particle detector which will operate on the International Space Station (ISS) for a more than 3 year mission starting from 2008. It is composed of different sub-detectors as shown in Fig. 1. Two complementary 119

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modes will be used to detect photons with AMS : the conversion mode with the Silicon Tracker and the single photon mode with the Electromagnetic Calorimeter. 2.1. The Si-Tracker

and the Conversion

Mode

The five planes of the Si-tracker are located inside the supraconducting magnet. The planes are covered with double sided silicon sensors, the three inner ones having sensors mounted on both sides, resulting into 8 layers with a total area of 6.7 m 2 . The tracker measures the trajectory of charged particles with an accuracy of 10 /im in the bending direction and 30 ^m in the non-bending direction. The event signature for the conversion mode is two reconstructed tracks coming from a common vertex located upstream with respect to the first tracker layer. The main sources of background for this mode are protons and electrons which interact in the AMS material producing secondaries reconstructed as double track events mimicking e+e~ pairs. Preliminary analysis suggests a rejection factor larger than 5 x 10 4 .

2.2. The ECAL and the Single Photon

Mode

The Electromagnetic Calorimeter is a three-dimensional electromagnetic sampling calorimeter with a thickness of ~ 16 Xo- It consists of 1 mm scintillating fibers sandwiched between grooved lead planes. The event signature for the single photon mode is the presence of a single electromagnetic shower in the ECAL with no hit in the other subdetectors. The main source of background comes from protons that are not

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interacting in other sub-detectors. The rejection factor for protons is about 103 using the latest analysis. 2.3.

Performances

The AMS performance for gamma-ray detection has been studied using dedicated simulation and reconstruction packages. The results of the simulation have been checked against test flight results a and test beam data obtained with proton and ion beams in Si-Tracker and electron and proton beams in ECAL, for the energy range of 2-250 GeV. A good agreement has been found. The acceptance and effective area from simulations after all cuts and selections for the two detection modes are shown in Fig. 2. At high energy, ECAL has a larger acceptance than Si-Tracker. The opposite behaviour is observed at energies below 10 GeV. Fig. 3 shows the relative energy and angular resolutions for the two detection modes. An excellent angular resolution in the Si-Tracker and the complementarity of the two detectors in the energy measurement will enhance the quality of the gamma detection in AMS-02. 3. Sensitivity studies for sources Using the ROOT 2 framework, we developped a fast simulation tool 3 to evaluate the sensitivity of AMS-7 for different kinds of sources. This tool computes the number of detected photons using parametrizaa

AMS-01 flew on board the Space Shuttle in 1998.

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tions of the detector acceptances, exposure b and the differential flux of the sources measured by EGRET 4 . Table 1 shows predictions obtained with a few sources from the third EGRET Catalog 5 , for one year of operation in orbit. One notices that most of the statistics at low energy will be collected in the conversion mode. Table 1. Number of photons predicted for different sources of the 3 E G R E T Catalog for one year of operation. For Vela, we use a spectral index of 2. 3EG Name J0534+2200 J0834-4511 J1255-0549 J1635+3813

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4. Dark Matter sensitivity studies The gamma emission of the Galactic Centre due to the neutralino annihilations in the dark matter halo has been studied with different models, using DarkSUSY 6 and SUSPECT 7 Monte Carlo programs. The neutralino, predicted to be the Lighest Supersymmetric Particle (LSP) in several supersymmetric theories, is a Weakly Interacting Massive Particle (WIMP) and therefore excellent dark matter candidate. In the assumption of a Navarro Frank & White (NFW) halo density profile 8 , Fig. 4 shows the expected fluxes with conventional models such as Minimal SuperGravity Grand Unified Model 9 (mSUGRA), with non thermal scenario as Anomly Mediated Supersymmetry Breaking 10 (AMSB) and with the Kaluza-Klein (LKP) model 11 . The AMS sensitivity at the 95% Confidence Level (CL) is shown. b

Obtained with a simulation of the orbit.

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Neutralino or B f n Mass (GeV/c2) Figure 4. The integrated 7 flux from the Galactic Centre as a function of mx for the NFW halo profile parametrizations with standard set of parameters. Prom these studies, one concludes t h a t AMS will be able t o set interesting exclusion limits for various models and W I M P hypotheses. 5.

Summary

During its more t h a n 3 year mission on b o a r d of t h e ISS, AMS-02 will provide new g a m m a measurements in t h e range of 1-300 GeV. Several galactic and extragalactic sources such as pulsars, nebulas or blazars will be studied. In addition, AMS-02 will have a non-negligible discovery potential in various Cold Dark M a t t e r scenarios. References 1. R. Battiston et al., Astropart. Phys. 13 (2000) 51-74. 2. http://root.cern.ch.

3. J. Bolmont et al., AMS Note 2004-02-01. 4. G. Kanbach et al, Space Sci. Rev. 49 (1988) 69-84. 5. R.C. Hartman et al., Astrophys. J., Suppl. Ser. 123 (1999) 79-202. 6. http://www.physto.se/~edsjo/darksusy/ 7. http://www.1pm.univ-montp2.fr:7082/~kneur/suspect.html 8. J.F. Navarro, C.S. Prank, S.D.M. White, Astrophys. J. 462 (1996) 563-575. 9. R. Barbieri et al, Phys. Lett. B 119 (1982) 343. 10. D. Hooper and L. Wang, Phys. Rev. D69 (2004) 035001. 11. E.W. Kolb and R. Slansky, Phys. Lett. B 135 (1984) 378.

HIGGS B O S O N DISCOVERY P O T E N T I A L AT CMS

J. BROOKE ON BEHALF OF THE CMS COLLABORATION University of Bristol, H H Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom E-mail: [email protected] The potential for discovering a Higgs boson with the CMS detector at the LHC is presented, in the context of the Standard Model and its minimal supersymmetric extension. The special case of a Higgs decaying to invisible particles is discussed, and the discovery potential presented.

1. Introduction The Compact Muon Solenoid (CMS) is one of two general purpose detectors that will operate at the Large Hadron Collider (LHC). The LHC will collide protons with a centre of mass energy of 14 TeV, initially with a luminosity of 1032 c n r " 2 s - 1 . After three years of running, the luminosity will be increased to 10 34 c m - 2 s - 1 . The CMS detector will be used to search for new physics at previously unattainable energies. In particular, identification of the mechanism responsible for electroweak symmetry is one of the major goals. The potential for discovering a Higgs boson at CMS has been discussed in detail 1 ; only the major points are highlighted here. 2. Searches for a SM Higgs The mass of the Higgs is a free parameter of the Standard Model (SM), but direct searches have excluded a SM Higgs with mass up to 114 GeV at 95% CL 2 . Precision measurements of electroweak parameters have been used to place an upper limit on the SM Higgs mass, through its appearance in loop diagrams, of 260 GeV at 95% CL 3 . The cross-sections of SM Higgs production processes at the LHC are shown in Figure 1. Gluon-gluon fusion dominates, but the associated modes, particularly vector boson fusion, are also of interest as the production signatures provide a useful tool for background rejection. The 124

125

Figure 1. Standard Model Higgs production cross-sections, calculated using the HIGLU, HQQ, W2H and V2HV programs 4 .

Figure 2. Standard Model Higgs branching fractions, calculated using the HDECAY program 5 .

branching fractions of a SM Higgs are shown in Figure 2. The search for a SM Higgs is conducted over three mass ranges. For mu < 130 GeV, inclusive searches for Higgs decays to 77 provide the single most significant channel; 6<7 discovery can be achieved with only 30 fb _ 1 integrated luminosity in the mass range. This channel demands good efficiency for reconstruction of converted photons, for which special algorithms have been developed. An excellent understanding of calorimeter calibration is also required. Searches for 77 and TT in the qqH production mode will also provide good significance for mjj around 130 GeV. Decays to bb, though dominant, suffer from very large QCD background. Discovery is possible in the tiH and WH production modes, but yield poorer significance. Searches for decays to ZZ* (in A£ final states) and WW* (in 2£ plus missing transverse energy) allow discovery with relatively small numbers of events over the mass range 130 GeV < m # < 500 GeV. Since the gluon fusion production rate decreases with m # , at very high masses exclusive searches in the qqH production mode offer greater significance. The discovery potential for a SM Higgs using these channels is summarised in Figure 3. 3. Searches for S U S Y Higgs In the Minimally Supersymmetric Standard Model (MSSM), a Higgs doublet is required, resulting in 5 physical particles; two neutral scalars, h and

126 qqH, H-*WW-*ivfl qqH, H-iZZ-illv^, H-»WW7WW - d l v ^ , , NLO H^ZZ'/ZZ - » I T I T , NLO qqH, H-*yy,T*r H-+7Y inclusive, NLO ttH,WH,H-»bE Total significance

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H, a pseudo-scalar A and the charged Higgs H+, H~. For JTIA > m™ax (the decoupling region), the lightest scalar, h, has SM-like phenomenology and can be identified in the same way as the SM Higgs. Figure 4 shows 5a discovery contours for h in the (rriA, tan/3) plane for 30 f b - 1 . It is clear that h —> bb in tiH and h —» TT in qqH are important channels in covering low rriA- For JTIA less than about 120 GeV, discovery of h is not possible. Fortunately, the heavy neutral Higgs H is SM-like in this region. Figure 5 shows the ha discovery contours for H/A; decays of H/A to r pairs, and of H in the qqH production mode, allow at least one neutral Higgs to be discovered for all (TRA, tan/3). The charged Higgs can be searched for through it's decays to rv. The H+ may be produced via quark fusion, or in association with t or tt. The discovery potential for these three searches is shown as 5a significance counters in Figure 6. 4. Invisible Higgs Search Various extensions to the Standard Model can result in a significant branching fraction for Higgs to invisible states. In particular the SUSY decay H —> X1X1 m a y have significant cross-section if it is kinematically possible. It is evident that invisible final states of the Higgs can only be found using associated production modes. Of these, vector boson fusion (VBF) is preferred for its higher cross-section. An invisibly decaying Higgs boson may therefore be searched for in final states comprising two jets (with

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Et > 40 GeV) and large missing transverse energy (E^ISS > 100 GeV) . The main backgrounds in this channel are Zjj, where the Z decays invisibly, Wjj, where a charged lepton from the W decay is unidentified, and QCD dijet production with large E™ss • These backgrounds may be reduced by making use of the distinctive shape of VBF events, with the cuts Arjjj > 4.4, rjjx • rjj2 < 0, and Afaj < 1.0 (where subscripts j l and j2 refer to the two jets). In addition, a central-jet veto is applied between 6

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the jets, utilising the absence of colour flow in VBF. The background levels may be measured with good accuracy from the data, using Zjj and Wjj events with reconstructed Z —> 11 and W —• Iv decays. This allows the model independent 95% CL shown in Figure 7 to be achieved with 10 fb _ 1 . 5. Conclusions In conclusion, the prospects for Higgs discovery at CMS are good. After three years of LHC running, 30 f b - 1 integrated luminosity will allow a Standard Model Higgs to be discovered with 5cr certainty. If the MSSM is realised, at least one Higgs can be discovered over most of the {m^, tan/3) plane with 30 f b - 1 , while 100 fb _ 1 will provide full coverage. An invisibly decaying Higgs can be discovered with as little as 10 f b - 1 (assuming SM production rates and an invisible branching fraction of at least 0.15). References 1. S. Abdullin et al, CMS Note 2003/033, (2003). 2. The ALEPH, DELPHI, L3, OPAL collaborations and the LEP Working Group for Higgs Boson searches, Phys. Lett. B 565, 61 (2003). 3. The ALEPH, DELPHI, L3, OPAL collaborations, the LEP Electroweak Working Group, and the SLD Electroweak and Heavy Flavour Groups CERN-PHEP 2004-069, (2004). 4. M. Spira, hep-ph/9510347; M. Spira, Fortsch.Phys. 46, 203-284 (1998). 5. A. Djouadi, Kalinowski, M. Spira Comput.Phys.Commun. bf 108 56-74 (1998). 6. O.J.P. Eboli and D. Zeppenfeld Phys.Lett.B 495, 147 (2000). 7. B. Di Girolamo et al, hep-ph/0203056, (2001).

A M S T R A N S I T I O N RADIATION D E T E C T O R A N D T H E SEARCH FOR D A R K M A T T E R

G. CAROSI* Massachusetts Institute of Technology, Bldg 44-119, 51 Vassar St. Cambridge, MA, 02139, USA E-mail: [email protected]

AMS-02 is a high precision magnetic spectrometer scheduled to be placed on the International Space Station (ISS) in 2008. This proceeding focuses on the Transition Radiation sub-detector (TRD) which allows positron/proton separation up to 300 GeV and how this will affect the search for signatures of neutralino dark matter in cosmic rays. The design, testing, and current status of the T R D will be discussed.

1. Signatures of Dark Matter in Cosmic Rays Since the 1930s evidence has been steadily accumulating that a large fraction of the energy density of the universe consists of gravitating matter which does not interact electromagnetically. This "Dark Matter" has currently only been observed through gravitational effects. Strong theoretical arguments call for the majority of this dark matter to be new Weakly Interacting Massive Particles (WIMPs), left over from the Big Bang. If these relic WIMPs (such as the supersymmetric neutralino) are majorana particles they can co-annihilate to standard model particles in the halo of the galaxy and show up as anomalous features in the spectrum of cosmic rays. The energy of these features would thus be correlated to the mass of the WIMPs. One of the best channels to search for this anomalous spectral feature is in positrons due to their relatively low intrinsic background. A rise in the positron spectrum at around 10 GeV has been observed in the HEAT series of balloon experiments but the statistics have been too low to make any definitive statements about the actual spectrum (figure 4). 1

*on behalf of AMS collaboration

129

130 2. Overview of the AMS-02 Detector The AMS-02 detector consists of a number of sub-detectors stacked on top of one another in order to measure different properties of incoming cosmic rays, the layout of which can been seen in figure 1 and the details of which are quoted elsewhere.2

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There are a number of additional design considerations in building a space experiment which are not usually required in standard particle physics. Design constraints, such as limits on weight, power and data rates, must be considered (14,809 lbs, 2.8 kW and 2 Mb/sec respectively for AMS02). The AMS-02 experiment must also endure vibration loads of up to 9 g acceleration at takeoff and operate for more then 3 years without service on the Space Station where temperatures will vary between —40° — +65°C. As a result the detector elements go through rigorous vibration, thermal vacuum, radiation, and quality control testing. 3. Principles of Transition Radiation Transition radiation (TR) is a collinear soft (~5-30 keV) X-ray emission which occurs when highly relativistic charged particles (7 > 1000) cross the boundary between materials of different dielectric constants. We exploit this process to distinguish between protons (no TR photons) and positrons (lots of TR photons) at energies up to 300 GeV. Without the TRD the positron signal would be swamped by a large flux of miss-measured protons at a few GeV.

131

4. Construction of the A M S T R D System Currently the majority of the TRD system is designed and is being built and integrated. The layout of the TRD gas system is outlined in figure 2.

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The main detection volume consists of a carbon fiber octagon support structure supporting 20 layers of straw proportional tubes interleaved with a fleece radiator material. Production and integration of this structure is currently being carried out at RWTH in Aachen, Germany. The proportional tubes detect both the standard j ^ particle energy deposition as well as the TR X-rays. In between the straw tubes are layers of polypropylene/polyethylene 10 \im fiber fleece radiator material. The fleece maximize the number of points in which a transition radiation X-ray can be generated while minimizing the amount of X-ray absorbing material. The straw tubes consist of 6mm diameter kapton tubes arranged in modules of 16 straws with lengths ranging from 0.8 - 2.0 meters and 100 /xm mechanical tolerance. A 30 /j,m gold-plated tungsten wire strung down the middle of the straw tube serves as the high voltage signal wire. Currently all 328 modules (5248 straw tubes) have been produced and are being integrated. The TRD gas system (designed by MIT) is currently being assembled at MIT and CERN. It consists of a supply system (Box-S) and a circulation system (Box-C). Box-S consists of storage vessels containing the 49.5 kg of Xe and 4.5 kg of CO2 required for the mission as well as a series of

132 buffer volumes and a mixing tank in order to mix the gas to a ratio of Xe:CC>2 80:20 (by volume) to 1% accuracy. Even for a perfectly gas tight system there will be diffusion through the straw tube walls so the system can replenish the detector with up to 7 liters/day. Box-C circulates the gas through the system to ensure uniformity in the gas mixture. It also contains calibration tubes coated with an Fe 55 source and an ultrasonic C 0 2 detector to monitor gas quality in real-time. The Slow Control and Monitor electronics control both the commands sent to the gas system and the readout of the calibration tubes, CO2 sensor, pressure and temperature sensors. It will automatically mix the Xe : CO2 gas to a ratio of 80:20 by volume. It will also close off sections of straw tubes in the TRD if a high leak rate is detected (which could be the result of micrometeor impacts). It is being developed at MIT and INFN in Rome. The DAQ electronics are the responsibility of TH Karlsruhe, Germany. They consist of 5248 readout channels with a maximum power budget of 20 W. The frontend-readout electronics are based on VA analog multiplexers and are equipped with a 12-bit AD-converter covering a range of 40 mips (at gas gain of 3000). Separate crates contain data reduction and low/high voltage supply cards. 3 p+/e~

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5. Physics Reach of AMS-02 Detector with the T R D A 20 layer TRD test detector was setup in a CERN test beam in 2000 in order to measure actual performance. 3 million protons, electrons, muons,

133 and pions with energies from 5 - 250 GeV were recorded. The analysis used single clean tracks and a likelihood method to separate the protons from the positrons while keeping 90% of the electrons (figure 3). From these results studies were made of the expected positron spectrum for AMS-02 (with the TRD and ECAL combined discrimination power) for different dark matter models, an example of which can be seen in figure 4 (compared to HEAT). 4

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6. Conclusions The TRD detector on AMS-02 will be able to discriminate between high energy cosmic protons and positrons at the 102 — 103 level up to 300 GeV. When combined with the ECAL it will be able to give a total proton rejection of 106 with 90% electron efficiency, allowing precision measurements of the positron spectrum to several hundred GeV. References 1. 2. 3. 4.

J.J. Beatty et al., Phys. Rev. Letters 9 3 241102 (2004). M. Aguilar et al. (AMS Collaboration), Physics Reports 366, 331-405 (2002). Th. Kim, Th. Siedenburg, NIM A 535, 165-170 (2004). P. Maestro, Ph.D thesis. INFN University of Siena, Italy (2004).

HIGH SENSITIVITY B-PHYSICS M E A S U R E M E N T S W I T H T H E ATLAS D E T E C T O R

JAMES R. CATMORE* Department

of Physics, University of Lancaster Lancaster, LAI 4YB, UK E-mail: James. [email protected]

The ATLAS detector will fully exploit the large b-quark production rate which is expected from the LHC. Precise measurements of quantities associated with the Bd and Bs systems, and with rare decay channels, form important components of the ATLAS beauty programme. The expected performance of the detector with respect to these measurements will be reviewed.

1. Introduction ATLAS 1 , currently under construction, is scheduled to begin collecting data in 2007. The largest of the LHC experiments, it is a general-purpose 4ir detector and is designed with both 'discovery physics' and high-precision measurements. The Inner Detector (ID) and the muon system will be particular important for B-physics measurements, the former for providing high-granularity tracking data close to the interaction point and the latter for acting as the basis of the B-trigger. 2. B-Physics Trigger Strategies The LHC luminosity will rise in three stages - from 0.5 x 10 3 3 cm~ 2 s _ 1 in 2007, through to the 'low' period in 2008 (2.0 x 10 3 3 cm- 2 s _ 1 ), and up to 'high' luminosity (10 x 1 0 3 4 c m _ 2 s _ 1 beyond 2010. The luminosity of the machine will degrade by a factor of ~ 2 during a run. At low luminosity, bb pairs will be produced at a rate of ~ 106Hz. Only 10Hz can be committed to permanent storage, so in addition to rejecting non-bb events the trigger must also be able to select only those processes of specific interest. It must also be able to deal with the changing luminosity * Funded by the United Kingdom Particle Physics and Astronomy Research Council

134

135 of the machine. With these requirements in mind, a range of B-physics triggering strategies have been developed. The ATLAS trigger is a three-stage mechanism. The first stage (LVLl) is activated by signatures of interesting physics events in the muon and calorimetry systems, and defines a geographical Region of Interest (Rol) around all events upon which it triggers. The second stage (LVL2) performs ID track reconstruction in the Rol, and then searches for specific decay candidates. The third stage (Event Filter) takes all events selected by LVL2 and performs full reconstruction, applying tight topological and kinematic cuts on the events. Data passing this stage will then be stored for offline analysis. A number of trigger strategies have been developed for B-physics events 2 , ranging from a di-muon scheme (which requires two muons with a PT threshold of around 5-6 GeV at LVLl) at high luminosities, to triggers requiring deposits in the electromagnetic or hadronic calorimeters as well as a muon. These triggers will be switched on at lower luminosities, and will significantly widen the scope of the B-physics programme. 3. The current ATLAS B-physics studies The processes which are currently being assessed for potential measurement in ATLAS 3 are summarized in table 1. Table 1. Event Type Decays to Charm

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CPV BR aproduction, bb correlations ^production, bb correlations

136

4. Measuring <j)a and A r a with Ba —• J/ip(p The -Bg-Bg system is subject to mixing due to weak interactions. It is characterized by two eigenstates which differ in mass and width. ATLAS will be able to access the mass difference via the hadronic decay modes Bs ->• DS7T and Bs -> Dsa\. The width difference, and the CP-violating relative phase between mixing and decay s, can be measured with the channel Bs —> J/ip(j>. Ba —> J/ip is a decay of a scalar meson to two vectors, so the final state is an admixture of three helicity configurations. These can be expressed in terms of the decay amplitudes Ao, A± and A\\ (known as transversity amplitudes), which are CP-eigenstates and only two of which are independent. As both the Bs and the Bs decay to the same final state in this channel, measurement of the CP-violating weak phase (f>s requires that the contributions from the amplitudes be separated out. An angular analysis is deployed to achieve this. In the rest frame of the decaying B-meson, the process is characterized with three decay angles, Q\, 62 and , which are defined in [8]. The expression for the proper decay time dependent angular distribution can be derived by combining the equations of 5 —>• VV decays 7 and Bs — Bs mixing 6 :

± w

(eu02A,t) = j^lJ2f(t)tFi(^^A)

(i)

The f(t)f are bilinear combinations of the amplitudes A0, A±, A\\, and the Fi are trigonometric functions of the three angles. The precise forms can be found in [4]. The expression (1) is a function of eight parameters: the difference in mass and width between the physical eigenstates (AM g , A r s ) , the average width ( r s ) , the relative strong phases Si = So — S± and S2 — So — d\\, the weak phase
procedure

and expected

performance

To obtain the eight parameters, the Bs —> J/rpcj) decays will be identified firstly using the di-muon triggering scheme, and then through suitable topological and invariant mass cuts. Using a maximum likelihood estimator, the

137 decay angles and proper decay times of the Bs mesons will be fitted to the theoretical distribution to simultaneously extract the eight parameters. All performance studies to date 5 have involved the fitting of the eight parameters to simulated signal and background events. The estimated performance of the detector with respect to this channel is summarised in table 2. Comparing the physics reach of ATLAS in this channel with the LHCb Table 2. Estimated performance of ATLAS in the channel Bs -t J/i{>(j> Number of events Proper time resolution Background

300 000 0.063ps 15%

Tag efficiency, wrong tag fraction

63%, 38%

<7stat(AF s,Ts)

12%, 0.7%

s • XS = 20, Xs — 40)

0.8%, 3% 0.03,0.05

experiment (figure 1), the performances can be seen to be complimentary. The lower shaded region represents the Standard Model, and the upper region an example of a 'New Physics' model. The 3a discovery lines for both experiments are shown, the LHCb calculations (as given in 2000) being for five years at a luminosity of 5 x 1 0 3 2 c m - 2 s - 1 (240000 events). Whilst neither experiment will be able to access the lower values of <j>s predicted by the Standard Model, both will be sensitive to the larger values predicted by new physics models. 5. Rare Decays In the Standard Model, the flavour changing neutral current processes b ->• s and b —> d occur only at loop level, and should have very small exclusive branching ratios (< 10 - 5 ). New physics processes may increase the branching ratios considerably. ATLAS will collect considerable quantities of these events. In particular the channels £?<* -> // + /x~ and Bs ->• n+n~ are self-triggering under the dimuon scheme and can therefore be collected during high-luminosity runs. Around 100 Bs -¥ n+n~ events and 20 Bd -> M+M~ events can be expected after three years at low luminosity and one year at high luminosity 3 . After one year of high luminosity data-taking, it is estimated 3 that a measurement on the Bs channel branching ratio will be made with a significance of 4.5cr, and that the 95% confidence level upper limit of the branching

138 LRC sensitivity to weak phase ^s HI channel Bs-J/Nf^MM)*

20

30

40

SO xs

Figure 1. Comparison of performances of ATLAS and LHCb for the measurement of 4>a with the channel Bs -* J/ip(j>.

ratio for the Bj. channel will be 3 x 10~ 10 . Given that the Standard Model branching ratio is 1.5 x 10~ 10 , ATLAS has a strong chance of being able to observe new physics processes after one year of high luminosity running. 6. Conclusions A flexible and highly selective trigger strategy will permit ATLAS to identify a wide range of interesting events in a very challenging experimental environment. Among a number of channels which are currently being investigated, the decays Bs -> J/ip, B& -* y+H~ and Bs -> /x+£t~ are particularly promising for their capacity to reveal new physics. These studies are on-going. References 1. The ATLAS Collaboration, ATLAS: Detector and Physics Performance Technical Design Report, volume 2 CERN/LHCC/99-15, 561-618 (1999). 2. J. Baines, Nuclear Physics B (Proc. Suppl.) 120, 139-144 (2003). 3. M. Smizanska, EPJdirect A l , 1-11 (2003). 4. M. Smizanska, Nuclear Instruments and Methods in Physics Research A 446, 138-142 (2000). 5. M. Smizanska ATL-PHYS-99-003 (1999). 6. R. Fleischer, Physics Reports 370, issue 6, 536-680 (2002). 7. S. U. Chung, Spin Formalisms CERN 71-8 (1971). 8. B Decays at the LHC CERN-TH/2000-101, 40-49 (2000).

M E A S U R E M E N T S OF T H E C K M A N G L E Ot F R O M BABAR

CARLOS A. CHAVEZ Department of Physics, University of Liverpool, Oxford Street, Liverpool L69 72E, United Kingdom On behalf of the BABAR

collaboration

The measurements of B -> nn, B ->• pir, B —> pp decays made by the BABAR collaboration are presented. These decays involve 6 —• dull quark transitions which are sensitive to the Unitarity Triangle angle a. Constraints on a are derived, and when the results of the measurements are combined the central value a ~ 100° is obtained, with a precision of 0 ( 1 1 ° ) .

1. Introduction In the Standard Model of particle physics (SM), the Cabibbo-KobayashiMaskawa (CKM) matrix Vqq*1, describes the charged current couplings in the quark sector. The Unitarity Triangle (UT) is a useful representation of relations among CKM matrix elements, and measurements of its sides and angles are important for the understanding of CP violation in the SM. Measurements of the CP parameter sin(2/3) by BABAR and Belle experiments have reached 3% precision, and are consistent with the prediction of the SM. It is of great importance to measure the other angles of the UT. This paper is a summary of the experimental constraints on the CKM angle a — arg[—VtdVt*b/VudV*b] obtained by the BABAR experiment using B —» hh decays, where h = IT, p. Experimental results are quoted with statistical errors preceding systematic errors unless otherwise stated. 2. Extraction of a from B —>• hh {h = iz,p)

decays

The decays of neutral B mesons into the TT TT~, p^ir^ and p+p~ final states involve b —> dull transitions, and the leading-order topologies are a tree level process illustrated in fig. 1(a), and one-loop penguin diagrams such as that shown in fig. 1(b). The presence of penguin contributions introduces additional phases, and the CP parameter A can be expressed in terms of a +

139

140

as 2ial-P/Te-*«

1 - P/Te*

W

'

where T and P are complex amplitudes dominated by tree and penguin topologies respectively. 1

.X: (a)

(b)

Figure 1. An example of a tree (a) and a penguin decays B° -> n*^, B° -»• p±Tr^ and B° -> p±p*.

(b) diagram contributing

to the

Experimentally, one measures the time-dependent decay rate e-|At|/r

f± (At) = —

[1 ± Shh sin(Am d At) =F Chh cos( Am d At)], (2) 4r where At is the proper time difference between the B decaying to the hh final state, denoted Brec, and the other B in the event, denoted Btag', T is the B° lifetime and Am^ is the B°B° oscillation frequency. The signal decay rate distribution is / + ( / _ ) if the Btag is B°(B°). The CP asymmetry parameters Shh and Chh are related to the parameter A by 29mA _ 1 - |Aj2 fc M> 1 , l \ | 2 2' ~ 1 i | \ | 2 2( ) 1 + |A| ' *~l + |A| S

C h h

3

Due to the presence of penguin contributions, experimental access is restricted to the measurable parameter aes, which can be shifted from the value of a by aeff — ot + <5aPenguin- It is possible to disentangle the effects of the tree and penguin contributions. Using strong isospin symmetry 2 , the different amplitudes in B -> hh decays are related by A-hh

=

T/n^hh + A-hh i

(4)

A-hh — ny^hh + Ahh .

(5)

These relations correspond to triangles in the complex plane. The phase difference between Afc^ and A^ is related to |aeff — a\. The triangles

141 have a common base if electroweak penguin contributions are neglected, i.e. \-A£h\ — l^h°l- I n order to extract a, the branching fractions, B, and CP asymmetries must be measured for the decays B° -> h+h~, B+ -> h+h°, B° -> h°h°. In the case of charged B meson decay (and B° -*• 7r°7r° where there is no vertex information), the time-integrated CP asymmetry ACp = (N- N)/(N + N) is studied, where N(N) is the number of B(B) decays to the final state. The isospin relationships among the amplitudes in B -» pir decays are pentagonal 3 , which complicates the extraction of a. The results of the corresponding time-dependent Dalitz plot analysis 4 are presented.

3. Experimental techniques A Signal candidate, Brec, is reconstructed by combining the relevant number of charged tracks and/or neutral clusters. The remaining particles in the event are examined in order to infer whether the second B meson (Btag) decayed as a B° or B° (flavor tag). A multivariate technique 5 is used to identify the flavor of the B meson. The decay time difference At ~ Az/P^c is calculated from the known boost of the e+e~~ system (/?7 = 0.56), and the measured distance, Az, along the collision (z) axis between the Brec and Btag decay vertices. The resolution on Az is typically 180^m. Signal decays are identified using two kinematic variables: (1) the difference, AE, between the reconstructed energy of the B candidate in the e+e~~ center-of-mass (CM) frame and y/s/2, and (2) the beam-energy substituted mass TUBS = \ / ( s / 2 + P i ' PB)2/E? — p2B. Here, -^s is the total CM energy, and the candidate B momentum, p e , and the four-momentum (Ei, pi) of the e+e~ initial state are defined in the laboratory frame. Table 1. The BABAR measurements of the branching fractions (B) and CP asymmetries in B —• 7T7T and pp decay; the last column shows the values of the longitudinal polarisation fractions measured for pp final states.

7T+7T

B

CP Asymmetries

4.7 ± 0 . 6 ± 0 . 2

S = -0.30 ±0.17 ±0.03

0

5.8 ± 0 . 6 ± 0 . 4

ACp

= - 0 . 0 1 ± 0.10 ± 0.02

7T07r°

1.2 ± 0 . 3 ± 0 . 1

ACp

= - 0 . 1 2 ± 0.56 ± 0.06

7r±7r

~p~^rpz

30 ± 5 ± 4

S = -0.19 ±0.33 ±0.11

p±p°

22.btl74 ± 5.8

ACp = -0.19 ±0.23 ±0.03

p°p°

< 1.1 (90% C.L.)

C = -0.09 ±0.15 ±0.04

fL = 0.99 ± 0.03 ± 0.04

C = -0.23 ± 0.24 ± 0.14 fL = 0.97 ± 0.07 ± 0.04

142 4. R e s u l t s The measured values of the branching fractions and CP asymmetries for B meson decay to TTTT and pp final states 6,T are summarised in Table 1. The CP asymmetry measurement for B° —»• 7T+TT~ decay shows no evidence of CP violation. The statistical significance of the branching fraction measurement in B° —> 7r°7r° decay is 5.OCT, and the measurement of the timeintegrated CP asymmetry, Anovo, enables an isospin analysis yielding the constraint \a - aeff\ < 35° (90% C.L.). The small value of B(B° -> 7r°7r°) limits the sensitivity of the isospin analysis to extract a, however is not small enough to establish a strong bound on \a — aefj\. For the vector-vector {pp) final states, both />'s must have the same helicity, h, with possible values h = 0, ± 1 ; the h = 0 helicity state corresponds to longitudinal polarisation, and is CP-even. The longitudinal polarisation fraction, /L, is defined as the fraction of helicity zero state in the decay. The decays B° —• p+p~ and B ± —> p±p° are found to yield p's which are almost 100% longitudinally polarised. The measurement of B(B+ -> p+p°) and the upper limit on B(B° —> p°p°) indicate a small penguin pollution in B —> pp decays. An isospin analysis of the B —» pp decay amplitudes corresponding to longitudinal p polarisation yields the value a = (96±10±5±11)°, where the last error is due to penguin contributions, and is determined using the p^p° and p°p° branching fractions. A complete time-dependent Dalitz plot analysis of B° —> •K+TT~/K° decays has been performed using a data sample corresponding to the production of 213 million BB pairs 8 . A maximum-likelihood fit is used to determine the 16 coefficients of the bilinear form factor terms involved in the time-dependent decay rate of the B° meson. These coefficients yield measurements of the direct CP asymmetries Ap7t = —0.088 ±0.049 ±0.013, C = 0.34 ± 0.11 ± 0.05 and the mixing-induced CP asymmetry S = -0.10 ± 0.14 ± 0.04, the dilution parameter AC = 0.15 ± 0.11 ± 0.03 and the strong phase shift AS = 0.22 ± 0.15 ± 0.03. From these measurements a can be extracted with few theoretical assumptions; it is found that a = (113liY±6)°). The relative strong phase <5+_ between the B° ->• p~ir+ and B° -> p+n- transitions is (67±|f ± 7)°.

5. Conclusion The confidence level dependence on the value of a obtained from the isospin analysis is shown in fig. 2 for 7T7T (dotted curve) and for pp (dash-dotted curve); the behaviour resulting from the time-dependent analysis of pir is

143

shown also (dashed curve). When the results of the measurements are combined the value a = (100 ± 11)° is obtained. The strongest constraints on a come from B —» pp decays, and the first time-dependent CP analysis in B° —> 7r+7r 7T°. In summary the BABAR experiment has made significant progress toward a precision measurement of the angle a. ."'1

'1

I ' M

; ISO

B

-

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> mi

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0

20

40

60

80 100 120 140 160 180

a

(deg)

Figure 2. The Confidence level dependence on the value of a obtained from the isospin analysis of wn (dotted curve), pp (dash-dotted curve), and from the timedependent Dalitz plot analysis of pn (dashed curve), from the CKM fitter group (http://ckmfitter.in2p3.fr).

Acknowledgements I would like to thank my BABAR colleagues for helpful discussions. This work is supported in part by CONACyT, Mexico, and by PPARC, UK. References 1. N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963); M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973). 2. M. Gronau and D. London, Phys. Rev. Lett. 65, 3381 (1990). 3. H. Lipkin et al., Phys. Rev. D 44, 1454 (1991). 4. H.R. Quinn and A.E. Snyder et al, Phys. Rev. D 48, 2139 (1993). 5. BABAR collaboration (B. Aubert et al), Phys. Rev. Lett. 89, 201802 (2002). 6. BABAR collaboration (B. Aubert et al), Phys. Rev. Lett. 89, 281802 (2002); hep-ex/0412037; hep-ex/0501071. 7. BABAR collaboration (B. Aubert et al), Phys. Rev. Lett. 93, 231801 (2004); hep-ex/0412067. 8. BABAR collaboration (B. Aubert et al), hep-ex/0408099.

SYSTEMATICS OF IDENTIFIED H A D R O N S P E C T R A AT P H E N I X

M. CSANAD FOR THE PHENIX COLLABORATION Mid-rapidity transverse momentum distributions for 7r , K^, p and p are measured by the PHENIX experiment at RHIC in Au+Au, d + A u and p + p collisions at ^/SNN' =200GeV up to 2-4GeV. Also particle ratios of iv~/ir+, K~ /K+, p/p, p/n and p/7r are measured, as well as the nuclear modification factor, all as a function of pt and in every of the above collision systems. Finally, the measured p + p and A u + A u spectra are compared to the Buda-Lund hydro model.

1. Introduction The motivation for ultra-relativistic heavy-ion experiments at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory is the study of nuclear matter at extremely high temperature and energy density with the hope of creating and detecting deconfined matter consisting of quarks and gluons - the quark gluon plasma (QGP). The PHENIX experiment at RHIC published spectra measurements in Au+Au collisions1 and in p+p and d+Au collisions2, all at ^ S N N =200GeV. In this paper, we present a comparision of the ^ S N N =200GeV Au+Au, d+Au and p+-p results. 2. M e a s u r e m e n t s The PHENIX experiment 3 has a unique hadron identification capability in a broad momentum range. Pions and kaons are identified up to 3 GeV/c and 2 GeV/c in pt, respectively, and protons and anti-protons can be identified up to 4.5 GeV/c by using a high resolution time-of-flight detector 4 . We compare here identified particle production in d+Au, p + p and peripheral and central Au+Au collisions. First, we calculate the nuclear modification factor by taking the Au+Au and d+Au spectra, scaling them down by the number of binary nucleonnucleon collisions (denoted as A^oii and taken from Glauber calculations 5 for each centrality class separately) and dividing them by spectra measured in p + p collisions (where iVcoii is obviously one). Now, if a Au+Au or a 144

145

d+Au collision would be nothing but a combination of a lot of nucleonnucleon collisions, this ratio would be one. In contrary, if there are effects due to the high Nco\\, eg. some type of medium is produced, this ratio can deviate from one. Furthermore, from hydro, one would expect scaling with the number of participants rather than the number of collisions. Fig. 1 compares the nuclear modification factors for pions, kaons and (anti)protons in Au+Au and d+Au collisions. Pions show a much lower #AuAu at high pt in central than in peripheral Au+Au collisions, as expected from the large energy loss suffered by the quarks in central collisions. The nuclear modification factor is slightly larger in d+Au than in peripheral Au+Au, despite the comparable number of binary collisions, but we can not draw a definite conclusion due to the large systematic error of the peripheral i?AuAu- The proton and antiproton nuclear modification factors show a quite different trend, however. PHENiX PRELIMINARY

" A'AuAu u A u '» " idAu l l l l l l i i i—i

| i

P+P

-X-_J

I i

i

i I i i i i I i i

K++K" A Au+Au 00-5% N ,=1065 • Au+Au 60-92% N^pl 4.5 • d+Au 00-20% N„»=15

• • ! • • • • 3

PrfGeV/c)

p^GeV/c)

0.5

1

1.5

2

MGeV/c)

Figure 1. Nuclear modification factors for different particles and collision species. Solid bars on the left indicate pt-independent normalization uncertainties, error bars indicate statistical errors. Empty boxes indicate systematical errors.

Another important thing is to compare particle over antiparticle ratios. What we see is that all collision species result in a particle over antiparticle ratio of one, independently of transverse momentum or centrality, except in the case of p / p , where the ratio is a bit smaller than one but still independent of collision type and pt as it is seen on Fig. 2. We can interpret the flat and collision species independent ratios of one as a sign of thermalization, and the difference between protons and antiprotons tells us that there is a small but nonzero net baryon density or baryochemical potential. The

146

lack of centrality dependence indicates that the (hadro-chemical) freeze-out parameters are independent of the centrality of the collisions1,6. i, d+Au, Au+Au N C a 200 GeV ~t—i—i—|—i—i—i—r p+p d+Au MlnBlas Au+Au Peripheral Au+Au Central

PHENIX PRELIMINARY

i" i j i T T r - j - r n i-j1 i r i i | i Q P*P |i W A

d+Au MinBlas Au+Au Peripheral Au+Au Central

K7K+

TT/TC*

I I I I I I I I I I I I ! I I I 1 0.5 1 1.5 2

pt (GeV/c)

p, (GeV/c)

3

4

p, (GeV/c)

Figure 2. Proton to pion ratios for different collision species.

Last, but not least, we also calculate proton to pion ratios, which will give us insight into collective dynamics effects, and also tell us something about a possible baryon yield enhancement mechanism. The p/7r ratio in d+Au is very similar to that in peripheral Au+Au collisions, and lies slightly above the p + p ratio. The p/7r ratio in central Au+Au collisions is, however, much larger. All are plotted on Fig. 3. The difference between the ratio in central and peripheral Au+Au clearly indicates that baryon yield enhancement is not simply an effect of sampling a large nucleus in the initial state, but it requires the presence of a substantial volume of nuclear medium with high energy density and pressure that generate a strong radial flow. Now let us pick a model to compare it to our results. We choose the Buda-Lund hydro model 7 which is successful in describing the BRAHMS, PHENIX, PHOBOS and STAR data on identified single particle spectra and the transverse mass dependent Bose-Einstein or HBT radii (and so the -R0ut/-Rside w 1 behavior) as well as the pseudorapidity distribution of charged particles in Au+Au collisions both at ^/SNN = 130 GeV 8 and at V ^ J N = 200 GeV 9 . In Au+Au collisions, we see a clear evidence for a 3-dimensional Hubbleexpansion, as the longitudinal and transverse flow is the same 9 .

147 PHENIX PRELIMINARY 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1' •

MinBias d+Au

»

MinBias p+p

A

Au+Au 0-10%

T

Au+Au 60-92%

Hi * p/7r*

p/ir

a

j&fot

*"|

j0t 1 1

i

Pr(GeV/c)

p T (GeV/c)

Figure 3. The ratio of protons to 7r + and antiprotons to n in minimum bias p + p and d + A u compared to peripheral and A u + A u collisions. Statistical error bars are shown.

Buda-Lund fits to run4 PHENIX Au+Au data PHENIX 0-30% central BudaLund — « t

Preliminary BudaLund fits to PHENIX run3 p+p data PHENIX run3 p+p

?

kt

JT A-

I 10 10

BudaLund hydro -

"

•**.

-•

•-•..- V .

• • • / "

-i

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.

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,

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" • * * . . . •

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,

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.'"":-. . * m,-m (GeV)

Figure 4. This figure shows a Buda-Lund fit to 200GeV Au+Au and p + p data, latter is preliminary. The dashed line in the left panel is a not fitted region, where jets start to dominate particle production.

The result of the Buda-Lund fits to p + p data at V'SNN = 200GeV indicate that there is no radial flow (/?t = 0.0 ± 0.19) in p + p collisions and the flow has a one-dimensional (Bjorken) flow profile. This also means, that the spectra slopes correspond to the temperature of the system. Furthermore the temperature distribution T(x) in the model is char-

148 acterized with a central temperature To and a radius i? s where the temperature drops to the half of the central one. To is found to be greater than the critical value calculated from lattice QCD 10 : Tc = 164 ± 3MeV, and T0 = 196 ± 13MeV in Au+Au 9 and T0 = 239 ± 21MeV in p+p. The Buda-Lund fits thus indicate quark deconfinement at RHIC. i? s is found to be finite and this is an indication for temperature inhomogeneity and for the presence of a cross-over instead of a phase transition, where no hadrons could emerge from a (superheated) region with T > Tc. In fact, the temperature inhomogeneity also explains why Rout « i^ide 11 3. Summary The nuclear modification factor of pions, kaons and also protons observed in d+Au is similar to the one observed in peripheral Au+Au collisions. Pions are suppressed in central Au+Au, and do not scale with Ncou. RAUAU for protons and antiprotons confirms previous observations that the production of high pt baryons in Au+Au scales with the number of binary nucleonnucleon collisions. Particle over antiparticle ratios are near to one for pions and kaons, and slightly below one for protons, independently of pt and collision type. This can be interpreted as a sign of thermalization. The proton to pion ratio in p + p and d+Au is similar to that in peripheral Au+Au. In central Au+Au we see a baryon yield enhancement, which can be caused by the presence of a hot and dense nuclear matter with a strong radial flow. Buda-Lund fits to p t spectra show us an evidence for a 3d Hubble flow in Au+Au and a Id Bjorken flow in p+p collisions, and an indication of deconfinement temperatures reached in both reactions.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

PHENIX Coll., S. S. Adler et al, Phys. Rev. C 69, 034909 (2004). F. Matathias for the PHENIX Collaboration, arXiv:nucl-ex/0504019. PHENIX Coll., K. Adcox et al, Nucl. Instrum. Methods A 499, 469 (2003). PHENIX Coll., M. Aizawa et al., Nucl. Instrum. Methods A 499, 508 (2003). R.J. Glauber and G. Matthiae, Nucl. Phys. B21, 135 (1970). J. Rafelski, J. Letessier and G. Torrieri, arXiv:nucl-th/0412072. T. Csorgo and B. Lorstad, Phys. Rev. C 54, 1390 (1996). M. Csanad, T. Csorgo, B. Lorstad, A. Ster, Acta Phys. Pol. B 35, 191 (2004). M. Csanad, T. Csorgo, B. Lorstad and A. Ster, J. Phys. G 30, S1079 (2004). Z. Fodor and S. D. Katz, JHEP 0203 (2002) 014. M. Csanad, T. Csorgo, B. Lorstad and A. Ster, Nukleonika 49, S45 (2004).

DEEP, D A R K & DIRECTIONAL: T H E D R I F T D A R K M A T T E R E X P E R I M E N T AT B O U L B Y M I N E

J. C. DAVIES ON BEHALF OF THE DRIFT COLLABORATION! Department of Physics and Astronomy, University of Sheffield, S3 IRE, E-mail: j . c.davies ©Sheffield, ac. uk

UK

One of the most intriguing puzzles in physics in recent times is that of dark matter. The DRIFT experiment is the first directionally sensitive dark matter search. The design is based on a gaseous time projection chamber and employs carbon disulphide gas at low pressure. DRIFT-I was installed in the underground laboratory at Boulby mine in 2001 and has acquired more than 1500 hours of data. The first module of the second generation detector, DRIFT-II, was installed in the new underground experimental hall at Boulby mine in February 2005 and has begun performing initial calibration and data runs. Further modules are due to be positioned underground throughout 2005.

1. Introduction The solutions to the many questions surrounding dark matter in our Universe continue to be elusive and to challenge both experimental and theoretical physicists. The favoured particle dark matter candidate at present is the Weakly Interacting Massive Particle (WIMP), or, more specifically, the lightest supersymmetric particle, the neutralino. There are many experiments throughout the world built with the purpose of searching for these exotic particles. One such detector is DRIFT (Directional Recoil Identification From Tracks) 1 ' 2 , which is based around a time projection chamber designed to search for a WIMP signal of galactic origin. DRIFT, which operates in the Boulby Underground Laboratory (North Yorkshire, UK), is the first dark matter detector with the capability to acquire directional information and, therefore, to identify a signal as galactic in origin. Most models suggest that the Earth is travelling through a halo of WIMPs in the Milky Way. A dark matter detector should, therefore, observe a directional 'WIMP wind' signal (Figure 1). *UKDMC (Univ. of Sheffield, Univ. of Edinburgh, R.A.L., Imperial College); Occidental College, L.A.; Temple Univ., Philadelphia; Univ. of New Mexico; Univ. of Boston 149

150

Figure 1. Diagram demonstrating the possibility for a directional dark matter detector to observe a correlation between nuclear recoil tracks from WIMP interactions and the WIMP wind.

Figure 2. Diagram illustrating the DRIFT design concept used in the irst two generations of DRIFT detectors,

2. T h e D e t e c t o r s The DRIFT design concept (Figure 2) employs time projection chambers (TPCs) with multi-wire proportional chambers (MWPCs) for readout. The first generations of detector use carbon disulphide (CS2) gas due to its electronegativity, which allows negative ions to be drifted within the TPCs, rather than electrons, and so avoids large diffusion and greatly improves the spatial resolution.

Figure 3. Photograph showing the DRIFT-II commissioning vessel in the background and the first full DRIFT-II internal detector in the foreground.

Figure 4. Photograph showing the first DRIFT-II module in the Boulby Underground Laboratory,

DRIFT-I is the first full-scale detector from the DRIFT collaboration 1 ' 2 . It was installed underground at Boulby mine during the summer of 2001. It consists of a 1 m 3 fiducial volume within two back-to-back TPCs, with a shared central cathode, and uses two MWPC readouts mounted horizontally. This detector Is placed Inside a stainless steel vacuum vessel, which Is filled with CS2 gas at low pressure (standard running pressure of 40 torr, giving a target mass of 167 g). The DRIFT-I data acquisition system was

151

designed at SLAC. In 2004 new alpha veto hardware was installed, as was ~ 8 tons of CH 2 neutron shielding - 30 g / cm2 thick on all sides - in the form of polypropylene pellets. DRIFT-II is the newest DRIFT detector and began taking data underground in March 2005. The design is basically an improved and expanded version of DRIFT-I. DRIFT-II will be an array of modules, with each module consisting of a stainless steel vacuum vessel with internal dimensions of 1.5 x 1.5 x 1.5 m 3 and with a hinged door (Figure 3). Each vessel contains two back-to-back TPCs and two MWPC readouts mounted vertically (Figure 2), which will reduce the effects of falling debris and allow both MWPCs to operate in identical environments. Each module (Figure 4) is connected to the gas flow system to ensure the CS2 gas remains uncontaminated. Care has been taken in choosing the materials used for detector components to ensure they are at least a specified minimum purity. The spatial resolution is improved, as is the 3-dimensional track reconstruction capability, and the background noise level of the data acquisition system is reduced compared with that of the first detector, DRIFT-I. 3. Background Simulations Simulations investigating neutron backgrounds relevant to DRIFT-type detectors have been performed using SOURCES, GEANT4 and FLUKA 3 ' 4 . The geometry set up is shown in Figure 5. The background investigated was that of neutrons produced via spontaneous fission and (a, n) reactions in and around the detector, along with muon-induced neutrons from deeply penetrating cosmic rays. These simulations were used to estimate the amount of passive neutron shielding required to keep the nuclear recoil rate sufficiently suppressed and to formulate requirements for the purity of materials used in the detector construction. An example energy spectrum of neutrons produced due to uranium and thorium contamination in NaCl is shown in Figure 6. The neutron spectra after different layers of hydrocarbon shielding are shown in Figure 7 and the resulting recoil energy spectrum is shown in Figure 8 4 . The rates of nuclear recoils due to the neutron background sources investigated are shown in Table l 4 . 4. Data Analysis Initial data was taken using a prototype DRIFT detector at Occidental College, L.A., with a fiducial volume of 1 ft3 (Figure 9). DRIFT-I has acquired over 1500 hours of data and its response to neutrons, alphas and gammas

152

Figure 5. GEANT4 image, using VRML, showing a geometry used for simulations of 4 detectors with CH2 shielding surrounding them.

Figure 6. Energy spectrum of neutrons generated in the rock salt surrounding the detector, as calculated using modified SOURCES. Spectra due to 60 ppb uranium, 130 ppb thorium and U and T h combined are shown.

Ensrgy / teV

Figure 7. Energy spectra of neutrons originating in the surrounding rock and travelling through layers of CH2 shielding.

Figure 8. Energy spectrum of nuclear recoils produced by neutrons generated due to uranium and thorium contamination in the rock surrounding the detector.

Table 1. Neutron background rates per year at 10-50 keV recoil energies from different sources in a 167 g, 3.33 kg and 10 kg T P C (40 g cm 2 of CH 2 shielding against rock neutrons and 50% efficiency to detect electromagnetic component of the muon-induced cascades were assumed). Detector mass kg 0.167 3.33 10.0

Rock 0.01 0.2 0.6

Nucl ear recoil rates per year at 10-f )0keV Detector Muons Total 0.19 0.12 0.06 2.4 3.9 1.3 7.2 3.8 11.6

has been seen (Figure 10 1 ' 2 ). The DRIFT-II data acquisition system has been redesigned from the DRTFT-I DAq system and uses a grouping technique and so records signals from 512 wires through only eight channels. The DAq also has wires used as alpha vetoes in both the x and y planes. An example of a possible alpha event is shown in Figure 11. Work on data analysis, including writing algorithms for automated cuts, is still in progress.

153

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I

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r

.

flCff!**^ O

\

\ no ^. jgammasli

20O0 Energy

/

c™»... •

.<£r'

S recalls 4000

Figure 9. Plot showing the discrimination between nuclear recoils and gamma events achieved by the prototype foot-cubed DRIFT detector. R2 is the 2-D projection of the track; Energy: 1000 NIPs ~ 20 keV

0

2000

4OO0

Energy (NIPs} Figure 10. Plot of data from a 2 5 2 Cf calibration run, using an energy threshold that allows gamma events to be rejected. R2 is the 2-D projection of the track; Energy: 1000 NIPs ~ 20 keV.

3860

«fip

Figure 11. Plot showing the raw waveforms from the Grid DAq of an alpha-type event. The multiple dips of the waveforms come from the 8-channel grouping of the readout wires. A large signal can also be seen on one of the veto wires (second from bottom).

Acknowledgments This work was performed in affiliation with the UK Dark Matter and DRIFT Collaborations. This work is funded by PPARC. We also acknowledge the funding from EU FP6 programme ILIAS (contract number RII3-CT-2003-506222). This work is also funded in the US by NSF grant 0300973. References 1. 2. 3. 4.

G. D. M. M.

J. P. J. J.

Alner et al, Nucl. Instrum. & Meth. A 5 3 5 , (2004) 644. Snowden-Ifft et al, Nucl. Instrum. & Meth. A 4 9 8 , (2003) 155. Caxson et al, Astrop. Phys. 2 1 , (2004) 667. C a r s o n et al, Nucl. Instrum. & Meth. A. I n press.

ELECTROWEAK A N D QCD RESULTS F R O M D 0

M. EADS Northern Illinois University, E-mail: [email protected] For the D 0 Collaboration We present some of the results in the areas of QCD and Electroweak physics for Run II of the D 0 experiment at the Fermilab Tevatron. QCD results include dijet angular decorrelations and inclusive jet and dijet cross sections. Electroweak results include the decay of Z bosons to t a u pairs and several results on gauge boson pairs. No deviations from the Standard Model have been observed.

1. Introduction The D 0 experiment is a multi-purpose collider detector located at the Fermilab Tevatron proton-antiproton collider. After undergoing a substantial upgrade, the experiment is now taking data at y^s = 1.96 TeV. There are many new results based on this Run II data in the areas of Quantum Chromodynamics (QCD) and Electroweak physics. 2. QCD Results A study has been performed of the angular correlations in jets produced in the D 0 detector 1. At leading order in QCD, jets are expected to be produced back-to-back in azimuth (0). One would then expect that the difference in azimuthal angle between two jets is A 0 = n. However, higher order effects, such as additional soft radiation in the event, will cause this angular difference to be less than IT. The distribution of A is sensitive to higher order effects. Additionally, this measurement does not rely on measuring the energy of the jet and hence does not suffer from energy scale systematic uncertainties. Figure 1 shows the A
155

Figure 1. T h e A distributions in different p™ax ranges. Results from HERWIG and PYTHIA are overlaid on the data. HERWIG results agree with the data, but PYTHIA results require modifications to the default parameters.

constant and to the parton density functions. Furthermore, many new physics models predict enhancements in the dijet mass cross section at large values of invariant mass. Figure 2 shows both the inclusive jet cross section and the dijet cross section distributions. These distributions are consistent with the next-to-leading order perturbative QCD theoretical predictions.

I

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10 10

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— *

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D 0 Data, L = 143 pb'1 NLO (JETRAD) CTEQ6M

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^ 500

cone R = 0.7, | y M | < 0.5 600 Pr[G«V/c]

1 0

200

| 1200

1400

MJJ, GeV/c

Figure 2. The left plot shows the inclusive jet cross section, measured in different ranges of jet rapidity (with statistical errors only). NLO pQCD calculations are overlaid on the data. The right plot shows the dijet cross section, measured at central rapidities. NLO pQCD calculations are overlaid on the data.

156 3. Electroweak Results D 0 has performed a measurement of the cross section times branching fraction for Z bosons decaying to tau pairs 2 . This measurement is a verification of the tau identification abilities for the experiment as well as a test of lepton universality. Furthermore, some physics models predict final states that would result in an excess of tau pair events over Standard Model predictions. The analysis requires one tau to decay as a muon. The second tau is identified using a neural network that has been trained using the different tau decay topologies. 2008 candidate events are selected in 226 p b - 1 of data. Approximately 55% of these events are estimated to be background events. This results in a measurement of a • Br(Z —> TT) = 237 ± 15stat ± 18sys i 15ium pb. This is consistent with the Standard Model prediction of 242 i 9 p b . D 0 also has a variety of results on diboson production. At the Tevatron, pairs of gauge bosons can be produced through t or u channel quark exchange, or can be produced through an s-channel triple gauge boson vertex. The strength of these triple gauge boson vertices is an important test of the Standard Model. Diboson signatures are also important backgrounds for Higgs and new physics searches. The cross section for the production of pp —> Wj+X has been measured. This analysis requires the W boson to decay to either an electron or a muon and a neutrino. The photon is identified by its signature in the calorimeter and the absence of a matching track in the central tracking system. In the electron channel, 112 events are selected in 162 p b - 1 of data. In the muon channel, 161 events are identified in 134 p b - 1 of data. In both channels, the background is estimated to be approximately half the number of events in data. The combination of both channels results in a cross section measurement for W~fX —> IvX of 1 4 . 8 i l . 6 s t a t i l . 0 s y s i l . 0 j u m pb. This is in agreement with the Standard Model prediction of 16.0 i 0.4 pb. A measurement of the cross section times branching fraction has been performed for events with a photon and a Z boson, with the Z boson decaying to electron or muon pairs 3 . In the ecy channel, 33 data events are present in 177 p b - 1 of data, with an estimated background of 4.7 i 0.7 events. In the mij channel, 68 data events are present in 144 p b - 1 of data, with an estimated background of 10.1 i 1.3 events. Figure 3 shows the three body invariant mass versus two body invariant mass for the candidate events. The combined cross section times branching fraction for both

157 channels is 3.90 ± 0.5lstat+sys ± 0.25;„m pb, which is in good agreement with the expected value of 4.3 pb.

> 0)

(3

r 10 2

N\,(GeV/c2) Figure 3. Invariant mass of the dilepton system vs. invariant mass of dilepton and a photon candidate.

A search for pairs of W bosons has also been performed 4 . This analysis selects events with two opposite sign leptons (electrons or muons) and missing energy. A total of 25 events are selected in between 224 and 252 p b - 1 of data (depending on the channel). The background has been estimated to be 8.1 ± 0.6 s t a t ± 0.6sys ± 0.5;„ m . The data represents a 5.2
158 100

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Figure 4. Dilepton invariant mass vs. missing transverse energy for expected WZ —> \x\x\w events (green or light grey) and for expected Z + jet background events (blue or dark grey). The central box shows the event selection criteria.

0.3

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-0 -0.1 -0.2 -0.3

-

•°4.5:

i

-0.5

,

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Figure 5. Left plot shows the limits on the WWf coupling parameters Are-y and A-y. The point indicates the SM value with the error bars showing the 95% CL intervals in one dimension, the ellipse represents the two-dimensional 95% CL exclusion contour. The right plot shows two-dimensional coupling limits (inner contour) on Xz vs. Ag* at 95% C L . for A = 1.5 TeV. The outer contour is the limit from S-matrix unitarity.

2. V . M . Abazov, et al. ( T h e D 0 C o l l a b o r a t i o n ) , P h y s . R e v . D 7 1 , 072004 (2005). 3. V . M . Abazov, et al. ( T h e D 0 C o l l a b o r a t i o n ) , F E R M I L A B - P U B - 0 5 / 0 2 3 - E , submitted to Phys. Rev. Lett. 4. V . M . Abazov, et al. ( T h e D 0 C o l l a b o r a t i o n ) , P h y s . R e v . L e t t . 9 4 , 151801 (2005). 5. V . M . A b a z o v , et al. ( T h e D 0 C o l l a b o r a t i o n ) , F E R M I L A B - P U B - 0 5 / 0 6 1 - E , s u b m i t t e d t o P h y s . Rev. L e t t .

TIME D E P E N D E N T CP VIOLATION I N B° -* DECAYS

TT+TT-

KOJI HARA High Energy Accelerator 1-1 Oho, Tsukuba, E-mail:

Research Organization, KEK, Ibaraki 305-0801, Japan [email protected]

We present a new measurement of the time-dependent CP-violating parameters in B° —* 7r+7r~ decays with 275 x 10 6 BB pairs collected with the Belle detector at the KEKB asymmetric-energy e + e - collider. We find 666±43 B° —• 7r+7r_ events and obtain the CP-violating parameters S^n = —0.67±0.16(stat)±0.06(syst) and A-KTX = +0.56 ± 0.12(stat) ± 0.06(syst). Large direct CP-violation is observed with a significance greater than 4 standard deviations for any S^n value. Using isospin relations, we obtain 95.4% confidence intervals for the GKM angle <j>2 of 0° < 2 < 19° and 71° < fa < 180°.

1. Introduction In the standard model (SM), CP violation arises from a single irreducible complex phase, the Kobayashi-Maskawa (KM) phase [1] in the weakinteraction quark-mixing matrix. In particular, the SM predicts CP asymmetries in the time-dependent rates for B° and B° decays to a common CP eigenstate [2]. In the decay chain of T(45) -> B°B° -» (7r + 7r-)(/ ta g), where one of the neutral B mesons decays into CP eigenstate TT+TT~ at time £7^ and the other decays at time t t a g to a final state / t a g that distinguishes its flavor, the decay rate has a time dependence given by e-\At\/rBo

P^(At) = —

[1 + q • {Svn sm(AmdAt)

+ A^ cos(Am d At)}], (1)

4TBO

where At = tnir — ttas, TB° is the B° lifetime, Amd is the mass difference between the two neutral B mass eigenstates, and q = + 1 (—1) for / t a g = B° (B°). We measure Snv and .4,™, which are the mixing-induced and direct CP-violating parameters, respectively. If only a b —-> u tree transition contributes to the decay B° —• 7r+7r~,a we would have S^ = sin22 and In this report the inclusion of charge conjugate state is implied.

159

160 = 0. Because of possible gluonic b —> d penguin contributions, Svn may deviate from sin 202, and direct CP violation, Av-„ ^ 0, may occur. We use a data sample of BB pairs collected with the Belle detector [3] at the KEKB energy-asymmetric e + e~ (3.5 on 8.0 GeV) collider [4] operating at the T(45) resonance. Our previous measurement based on a 140 fb _ 1 data sample indicated large <ST7r and A^ values [5], while no significant CP asymmetry was observed by the BaBar Collaboration [6]. In this report, we describe improved measurements incorporating an additional 113 fb _ 1 data sample for a total of 275 x 106 BB pairs. ATTTT

2. B° —* 7T+7T— Reconstruction We use charged tracks positively identified as pions. We select B° —> TT+TT~ candidates using the energy difference AE = EB — E£eam and the beamenergy constrained mass M b c = \/(-^beam)2 _ (PB) 2 > where £ J e a m is the beam-energy at the T(AS) center-of-mass system (cms), and EB and pB are the cms energy and momentum of the B candidate. We define the signal region as 5.271 GeV/c 2 < M b c < 5.287 GeV/c 2 and \AE\ < 0.064 GeV. The flavor q of the accompanying B meson is identified from inclusive properties of particles that are not associated with the reconstructed B decay. We divide events in six tagging categories based on the event-by-event Monte Carlo (MC) determined flavor-tagging dilution factor r [7]. The wrong tag fractions are determined from data [8]. To suppress the continuum background (e + e~ —> qq;q = u,d, s,c), we form a likelihood ratio LR based on event topology variables [5] and impose r-dependent requirements on LR. After the vertex reconstruction [8,9], 2,820 signal candidates remain. Figure 1 shows the AE distributions for the events with (a) LR > 0.86 and (b) LR < 0.86 in the Mb c signal region. We find 415 ± 27 7r+7r- events for LR > 0.86 and 251 ± 16 TT+TT- events for LR < 0.86.

3. Results of CP Asymmetry Measurement We determine Snn and Aw by applying an unbinned maximum likelihood fit to the At distribution of the 2,820 B° —> TT+TT~ candidates containing 666 ± 4 3 7T+7I-- signal events (1,486 B° tags and 1,334 ~B° tags). We obtain S^

= -0.67 ± 0.16(stat) ± 0.06(syst),

A** = +0.56 ± 0.12(stat) ± 0.06(syst).

(2)

Figures 2(a)-(d) show the At distributions and the raw asymmetry with the fit results. We define the raw asymmetry ACP = {N+ - N-)/(N+ + Ar_),

161

^ 2 5 0 (a) O 200

\ ^~

Total V7A n*K KTI

C\]

O CD

150 2100 c LU 0

•

—

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continuum Three-body

„!*, H !

,

,

,

la I

-0.2 0 0.2 0.4 AE (GeV)

$ 3 5 0 JL CM 300

9250 5200 1150

o5100 tfj 50 0

Figure 1. AE distributions in the M^c signal region for B° (a) LR > 0.86 and (b) LR < 0.86.

candidates with

where iV+(-) is the number of observed candidates with q = + 1 (—1).

(a)q

Figure 2. At distributions for the 884 B° —> TT+TV~ candidates with LR > 0.86 in the signal region: (a) 470 candidates with q = + 1 , (b) 414 candidates with q = —1. Raw asymmetry, ACP, in each At bin with (c) 0 < r < 0.5 and (d) 0.5 < r < 1.0. The solid lines show the results of the unbinned maximum likelihood fit results.

162 The CP-conserving case, Snn = Aw = 0, is ruled out with a 5.4 0.86 and 0.5 < r < 1.0 for q = ± 1 subsets. The large direct CP-violation in B° —> 7r+7r_ decays is manifest in the contrast of the yields. The TC+TT~ yields with q = + 1 and q = — 1 are 107 ± 13 and 69 ± 11, respectively, while the K+ir~ and continuum background yields are consistent between q — ± 1 .

>

S

6 0

(b) q = -1

50

—

Total Kit

continuum

0

0.2 0.4 AE (GeV)

0

0.2 0.4 AE (GeV)

Figure 3. AE distributions in the M\,c signal region for the B° with LR > 0.86 and 0.5 < r < 1.0 for (a) g = + 1 and (b) q = - 1 .

7r+ 7r

candidates

We employ isospin relations [10] and the approach of Ref. [11] for the statistical treatment to obtain constraint on fa- Using the measured branching ratios of B —» -K-K decays and the direct CP-asymmetry for B° —> 7r07r° [12], we obtain an allowed range for (j>2 at 95.4% C.L. of 0° < 4>2 < 19° and 71° < cp2 < 180°. Figure 4 shows the obtained C.L. as a function of fa4. Summary We have performed a new measurement of the CP-violating parameters in B° —> 7r+7r~ decays using a 253 fb _ 1 data sample. We obtain S^n = -0.67 ± 0.16(stat) ± 0.06(syst) and > U = +0.56 ± 0.12(stat) ± 0.06(syst). We rule out the CP-conserving case, Swn — Aw — 0, at the 5.4u level. We find compelling evidence for direct CP asymmetry with 4.OCT significance. The results confirm the previous Belle measurement of the CP-violating parameters as well as the earlier evidence for direct CP violation in B° —> 7r+7r~ decays [5].

163

30 60 90 120 150 180 §2 (degrees) Figure 4. Confidence level as a function of the CKM angle <j>2 • The dotted line indicates C.L. = 95.4%.

Acknowledgments We t h a n k t h e K E K B group for the excellent operation of the accelerator, the K E K cryogenics group for the efficient operation of the solenoid, and the K E K computer group and the N i l for valuable computing and Super-SINET network support. We acknowledge support from M E X T and J S P S ( J a p a n ) ; A R C a n d D E S T (Australia); N S F C (contract No. 10175071, China); D S T (India); the BK21 program of M O E H R D and the C H E P SRC program of K O S E F (Korea); K B N (contract No. 2P03B 01324, Poland); M I S T (Russia); MESS (Slovenia); SNSF (Switzerland); NSC and M O E (Taiwan); and D O E (USA). References M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973). A.B. Carter and A.I. Sanda, Phys. Rev. D 23, 1567 (1981); I.I. Bigi and A.I. Sanda, Nucl. Phys. B 193, 85 (1981). Belle Collaboration, A. Abashian et al, Nucl. Instr. and Meth. A 479, 117 (2002). S. Kurokawa and E. Kikutani et al, Nucl. Instr. and Meth. A 499, 1 (2003). Belle Collaboration, K. Abe et al., Phys. Rev. Lett. 93, 021601 (2004). BaBar Collaboration, B. Aubert et al., hep-ex/0501071. H. Kakuno, K. Hara et al., Nucl. Instr. and Meth. A 533, 516 (2004). Belle Collaboration, K.-F. Chen et al., hep-ex/0504023 H. Tajima et al., Nucl. Instr. and Meth. A 533, 370 (2004). M. Gronau and D. London, Phys. Rev. Lett. 65, 3381 (1990). J. Charles et al., hep-ph/0406184.

M O D I F I C A T I O N OF T H E CASIMIR E F F E C T D U E TO A M I N I M A L L E N G T H SCALE

ULRICH HARBACH Institut fur Theoretische Physik Johann Wolfgang Goethe-Universitdt and Frankfurt Institute for Advanced Studies Max-von-Laue-Str. 1 60438 Frankfurt am Main, Germany E-mail: [email protected] SABINE HOSSENFELDER Department of Physics University of Arizona 1118 East 4th Street Tucson, AZ 85721, USA E-mail: [email protected] The existence of a minimal length scale, a fundamental lower limit on spacetime resolution is motivated by various theories of quantum gravity as well as string theory. Classical calculations involving both quantum theory and general relativity yield the same result. This minimal length scale is naturally of the order of the Planck length, but can be as high as ~ T e V - 1 in models with large extra dimensions. We discuss the influence of a minimal scale on the Casimir effect on the basis of an effective model of quantum theory with minimal length.

1. The minimal length scale 1.1.

Motivation

The idea of a minimal length has a long history and was already discussed by W. Heisenberg in the 1930s, who recognised its importance in regularising UV-divergences1. Today, theories beyond the standard model such as string theory or loop quantum gravity - as diverse as they may be - all suggest the existence of a fundamental limit to spacetime resolution of the order of the Planck length. Thus, the motivations for the existence of a minimal length scale are manifold: 164

165 • In perturbative string theory 2 ' 3 , the feature of a fundamental minimal length scale arises from the fact that strings cannot probe distances smaller than the inverse string scale. If the energy of a string reaches this scale Ms = \/o7, excitations of the string can occur and increase its extension 4 . In particular, an examination of the spacetime picture of high-energy string scattering shows, that the extension of the string is proportional to its energy2 in every order of perturbation theory. Due to this, uncertainty in position measurement can never become arbitrarily small. • In loop quantum gravity, spacetime itself is quantised and thus measurements of area and volume at small scales must fall into the spectrum of the respective self-adjoint operators, which is discrete 5 . • Including gravitational effects from general relativity into a classical analysis of the process of position measurement yields a minimal uncertainty 6 , i.e. a minimal length is implicitly contained in the standard model (SM) combined with general relativity. 1.2. Large extra

dimensions

Arkani-Hamed, Dimopoulos and Dvali proposed a solution to the hierarchy problem (the hugeness of the Planck scale compared to the scale of electroweak symmetry breaking) by the introduction of d additional compactified spacelike dimensions in which only the gravitons can propagate 7 ' 8 . The SM particles are bound to our 4-dimensional sub-manifold, often called our 3-brane. Due to its higher dimensional character, the gravitational force at small distances then is much stronger in these models. This results in a lowering of the Planck scale to a new fundamental scale, M{, which can be as low as the TeV-range. Accordingly, in such models the minimal length scale increases to a new fundamental length scale Lf. 2. Quantum theory with minimal length To include effects of the minimal length, we assume that at arbitrarily high momentum p of a particle, its wavelength is bounded by some minimal length L{ or, equivalently, its wave-vector k is bounded by a Mf = 1/Lf9. Thus, the relation between the momentum p and the wave vector k is no longer linear p = k but a function k = k{p)a, which has to fulfil the following properties 10 ' 11 : a

Note, that this is similar to introducing an energy dependence of Planck's constant h.

166

a) For energies much smaller than the new scale it yields the linear relation: for p < Mf we have p fa k. b) It is an an uneven function (because of parity) and k || p. c) The function asymptotically approaches the bound Mf. The quantisation in this scenario is straightforward and follows the usual procedure. Using the well known commutation relations \%ii ™j\ —

(1)

^ij

and inserting the functional relation between the wave vector and the momentum then yields the modified commutator for the momentum and results in the generalized uncertainty principle (GUP) .dpi ,Pj\ = +1

Api&Xj

dkj

dpi

> -

(2)

which reflects the fact that it is not possible to resolve space-time distances arbitrarily well. Because k{p) becomes asymptotically constant, its derivative dkj dp eventually vanishes and the uncertainty (Eq.(2)) increases for high momenta. Thus, the introduction of the minimal length reproduces the limiting high energy behavior found in string theory 2 . In field theory b , one imposes the commutation relations Eq. (1) and (2) on the field <j> and its conjugate momentum II. Its Fourier expansion leads to the annihilation and creation operators which must obey [«fc.afc'J = \ak,al,\

_i

(3)

^k,ti{.

= 5{k - k')

[ap,aj,,] =

dk S(p-p') dp

(4) .

(5)

3. The Casimir energy Zero-point fluctuations of any quantum field give rise to observable Casimir forces if boundaries are present 12 . Here, we consider the case of two conducting parallel plates in a distance o in direction z. Using the framework b

For simplicity, we consider a massless scalar field.

167 developed above, in the presence of a minimal length the vacuum expecation value (VEV) for the field energy density is now given by 13 <0|Jf|0> = < 0 | | ^ d 3 p (alap +

apal)E\0)

« I ^ d » p e x p ( - ^ ) £ ;

,

(6)

where E is the energy of a mode with momentum p. Here, we have used the specific relation from Ref. 11 for k(p)

*/i(p) = e M y expf

|VJ

,

(7)

where eM is the unit vector in p, direction. It is easily verified that this expression fulfills the requirements (a) - (c). To obtain the Casimir energy, the difference of the VEVs of the inside and the outside regions of the plates has to be taken: For Minkowski space in 3 + 1 dimensions without boundaries, the energy density in the present model with minimal length is finite due to the squeezed momentum space at high momenta and given by £Mink = <0|ff|0) = — ^ 7T

.

(8)

JUf

The quantisation of the wavelengths between the plates in the zdirection yields the condition fc; = l/a. Since the wavelengths can no longer get arbitrarily small, the smallest wavelength possible belongs to a finite number of nodes Zmax- As a result, momenta come in steps pi = p{h) which are no longer equidistant Apt = pi — pj_i. Then *max

epiates = 7T £

/»00

Ap, /

9

E p„

,

(9)

Jo

i—i *—

2

dp,, e~epWe-eP'

'max

where p^=p2x+ p2y and E2 = pjj + pf. The result of our calculation is shown in Fig. 1. The slope of the curve changes whenever another mode fits between the plates. Although the slope (and thus the Casimir force) is singular at these points, the plot clearly shows that a finite energy is sufficient to surmount them and thus the result is physical. These singularities result from the assumption of two strictly localised plates and might be cured in a full theory by the minimal length uncertainty on the plate positions.

168 Figure 1. The Casimir energy density between two plates of distance a in units of the minimal length. 2 -3.0

a/L,

4. Conclusion The existence of a minimal length scale is justified on various grounds. The minimal length is considerably increased in models with large extra dimensions. We presented an effective model that incorporates the minimal length into quantum theory. As an application, the Casimir energy for two parallel plates was studied. This example depicts nicely how the minimal length acts as a natural regulator for infinities in quantum field theories. Acknowledgments U.H. thanks the Frankfurt Institute of Advanced Studies for financial support through a PhD scholarship, Marcus Bleicher for fruitful discussions and the provision of funds for the travel, and the organisers of the LLWI for a wonderful conference. S.H. acknowledges support by the DFG and NSF PHY/0301998. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

W. Heisenberg, Ann. Phys. 32 (1938) 20. D.J. Gross and P.F. Mende, Nucl. Phys. B303 (1988) 407. D. Amati, M. Ciafaloni and G. Veneziano, Phys. Lett. B216 (1989) 41. E. Witten, Phys. Today 50N5 (1997) 28. C. Rovelli and L. Smolin, Nucl. Phys. B442 (1995) 593, gr-qc/9411005. C.A. Mead, Phys. Rev. 135 (1964) B849. N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, Phys. Lett. B429 (1998) 263, hep-ph/9803315. I. Antoniadis et al., Phys. Lett. B436 (1998) 257, hep-ph/9804398. D.V. Ahluwalia, Phys. Lett. A275 (2000) 31, gr-qc/0002005. S. Hossenfelder et al., Phys. Lett. B575 (2003) 85, hep-th/0305262. S. Hossenfelder, (2004), hep-ph/0405127. H.B.G. Casimir, Kon. Ned. Akad. Wetensch. Proc. 51 (1948) 793. U. Harbach and S. Hossenfelder, (2005), hep-th/0502142.

EXPLORING THE NEUTRINO UNIVERSE WITH A M A N D A A N D ICECUBE

DAVID H A R D T K E FOR THE ICECUBE COLLABORATION * Department of Physics University of California Berkeley, CA 94720

High-energy neutrino flux measurements allow us to probe the extreme astrophysical environments where hadronic acceleration may occur, and could provide new insights on the origins of very high-energy cosmic-rays. Recent results from the AMANDA telescope are presented. These results include searches for point sources of high energy neutrinos, and searches for diffuse fluxes of extra-terrestrial highenergy neutrinos. The IceCube observatory, currently being constructed at the South Pole, will be the first cubic kilometer scale neutrino detector.

At this conference we saw many examples of how astrophysical observations motivate current experimental research. The baryon-antibaryon asymmetry in the universe motivates us to look for CP violation in the B-meson system. The observational success of the ACDM model motivate us to look for supersymmetric particles at existing accelerators and the LHC. The emerging field of neutrino astronomy, the subject of this contribution, is motivated by the desire to find the origins of the highest energy cosmic rays (E > 1019 eV). Do these ultra-high energy cosmic rays arise from persistent sources (e.g Active Galactic Nuclei), transient sources (e.g. the sources of gamma-ray bursts), or do they come from decays of exotic particles with masses of order the Planck scale? By exploiting the unique properties of the neutrino we hope to answer this question. Extra-terrestrial neutrinos have to date been observed from the Sun and from Supernova 1987A. In both cases, the observed neutrinos were of low energies (few MeV) and were registered in deep underground experiments exploiting the inverse beta decay process or elastic neutrino-electron scat* List of authors papers.shtml

at

http://icecube.wisc.edu/pub.and-doc/conferences/conference-

169

170

tering. The strategies for the observation of high energy neutrinos differ dramatically. In the TeV - EeV range, the favored method is to use natural sources of water as a neutrino target and Cerenkov radiator. The Cerenkov radiation is generated either by long muon tracks created in v^ + N charged current interactions or by relativistic electrons produced during the electromagnetic and hadronic cascades produced at the neutrino interaction vertex. Many experiments (DUMAND, Baikal, Antares, etc.) have used liquid water as a detector. AMANDA (Antarctic Muon and Neutrino Detector Array) and IceCube are the first to use polar ice as the neutrino target and detector. Polar ice is well suited for the construction of large neutrino detectors due to the long absorption lengths for light (RJ 100 m at 400nm). AMANDA consists of 677 optical modules arranged on 19 strings at depths between 1500 m and 2300 m. Each optical module has a large phototube housed in a spherical glass pressure vessel. The vertical spacing between optical modules varies between 10 and 20 meters, and the horizontal spacing between strings averages 50 m. Raw PMT signal are sent to the surface via electrical cables or optical fibers. At the surface, the signals are amplified and fed into a system of ADCs and TDCs. Prompt signals from the phototubes are used to form a multiplicity trigger (typically 24 phototubes in the current detector configuration). Most of the triggers are due to down-going muons. IceCube, currently under construction, will utilize the same basic concepts as AMANDA but with a much larger effective detection volume (~ 0.01 km 3 for AMANDA versus ~ 1 km 3 for IceCube). With such a large volume a different data acquisition and trigger system is required. IceCube will have 4800 digital optical modules (DOMs) on 80 strings at depths between 1500 m and 2500 m. The major technological upgrade that allows IceCube to operate is the use of signal digitization in the ice. Each DOM contains a phototube, on-board high voltage, and waveform digitizers. The DOMs are read out asynchronously via a DSL connection. The surface DAQ will build events with common hit times and trigger the array. The latency of the trigger can be as large as several minutes. Online reconstruction will be done at the South Pole to eliminate most down-going muon events. During the austral summer 2004-2005, the first IceCube string was successfully installed, demonstrating both the performance of the new "Enhanced Hot Water Drill" and allowing in-situ tests of the DOM hardware. In addition, the first few tanks of the IceTop surface air shower array have been installed and tested.

171

Due to the long lengths of the neutrino induced muon tracks, these sparsely instrumented arrays are able to reconstruct neutrino directions with a resolution of order 1-3°. Muon energies (and thus inferred neutrino energies) are measured via dE/dx. The resolution for muon reconstruction is a(AlogioE) » 0.4. Neutrinos detected via their electromagnetic cascades have better energy resolution ( 1 TeV) neutrinos. Due to the good intrinsic pointing resolution of AMANDA/IceCube, potential point sources of neutrinos can be studied. The catalog of possible neutrino point sources includes TeV 7 emitting blazars (e.g. Markarian 421), GeV 7 emitting blazars, microquasars (e.g.Cygnus XI), Pulsar Wind Nebulae (e.g. Crab Nebula), and gamma-ray bursts. Isotropically distributed astrophysical particle accelerators would lead to a diffuse flux of neutrinos. Generic arguments suggest that diffuse extragalactic neutrino fluxes should have a considerably harder energy spectra than atmospheric neutrinos. The atmospheric neutrino background comes primarily from cosmic-ray induced pion production and decay. These neutrino follow a dN/dE oc E~3'7 energy spectrum. The spectral index reflects both the incoming cosmic-ray spectrum (dN/dE oc E~2-7) and the energy losses of pions in the atmosphere before they decay. There is also a small atmospheric neutrino contribution due to prompt decay of kaons and charm with dN/dE oc E'21. Extragalactic neutrinos, however, should have the same energy spectrum as the pre-cursor hadrons accelerated at the neutrino sources. If the acceleration is due to the Fermi shock acceleration mechanism, the neutrino energy spectrum will be dN/dE oc E~2. Analyses of the ultra-high energy cosmic ray spectrum, accounting for propagation effects, are consistent with a spectral index of approximately 2 at the cosmic-ray source. Additionally, measured high energy gamma-ray spectra are consistent with a source spectral index of about 2. Figure 1 shows the up-going high-energy muon neutrino flux measured by the AMANDA detector compared to lower energy FREJUS results. The muon energies are estimated using a neural network energy reconstruction trained on a full detector simulation. The muon neutrino energy spectrum is extracted from the measured muon energy spectrum using regularized unfolding. Also shown in Figure 1 are the parameterized atmospheric muon neutrino fluxes for horizontal (upper solid curved) and vertical (lower solid

172 10

10

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AMANDA-II, unfolded

m

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log(E„/GeV) Figure 1. Preliminary unfolded neutrino spectrum from AMANDA compared to lower energy FREJUS results 1.

curve) neutrinos. As mentioned previously, one expects that extragalactic neutrinos will have a considerably harder spectra than atmospheric neutrinos. For the highest energy bin (100 TeV< Ev <300 TeV), the 90% confidence level upper limit on an E~2 contribution to the neutrino flux is £?*,,„ < 2.6 x 10- 7 GeVcm- 2 s- 1 sr- 1 . AMANDA has used various analysis methods to set upper limits on E~2 diffuse neutrino spectrum, including analyses of neutrino induced cascades 2 and an analysis of horizontal UHE (ultra-high energy) neutrinos 3 . These analyses yield all neutrino flavor limits at the level £2<J>„e+„ +Vr < « 1 0 - 6 G e V c m ~ 2 s - 1 s r - 1 for neutrino energies between a few TeV and a few EeV. These limits are able to exclude certain models of neutrino emission from Active Galactic Nuclei 4 . Current AMANDA measurements are not able to reach the sensitivity needed to be below the Waxman-Bahcall limit 5 on neutrino production (w 1 0 _ 8 G e V c m _ 2 s - 1 s r _ 1 ) . The WB upper limit on diffuse neutrino fluxes is based on extragalactic UHE cosmic ray flux measurements. Several years of IceCube running will enable sensitivity to diffuse neutrino fluxes at or below the WB limit. A second class of high-energy neutrino measurements are point-source searches 6 . For these analyses, we look for neutrino excesses from known objects as well as neutrino hot spots in the AMANDA data. Figure 2 shows the locations of up-going neutrinos from a 4 year (2000-2003) analysis

173 of AMANDA data. The analysis cuts are optimized assuming an E~2 signal neutrino spectrum, and the final sample contains 3329 up-going v^ events. The most significant local excess is 3.35a-. By randomizing the skymap, we find that such an excess is present in more than 90% of the randomized skymaps and deduce that these data shows no evidence for point sources of neutrinos. These data have also been used to test for significant excesses from candidate neutrino emitters and no object shows a statistically significant excess. 90°

Figure 2.

AMANDA neutrino skyplot for a 4-year (2000-2003) analysis.

While AMANDA has found no evidence for extragalactic high-energy neutrinos, the field of neutrino astronomy is rapidly maturing. Gigaton scale neutrino detectors such as IceCube and future underwater arrays will lead to insights into the origins of high energy cosmic rays through the observation of extragalactic neutrinos. References 1. 2. 3. 4.

K. Daum et al, Z. Phys. C66, 417 (1995). M. Ackermann et al., Astroparticle Physics 22, 127 (2004). M. Ackermann et al., Astroparticle Physics 22, 339 (2005). F.W. Stecker et at, Phys. Rev. Lett. 66, 2697 (1991); F.W. Stecker and M.H. Salamon, Space Sci. Rev. 75, 341, 1996; R.J. Protheroe, astro-ph/9607165. 5. E. Waxmann and J. Bahcall, Phys. Rev. D59, 023002 (1998). 6. J. Ahrens et al., Astrophysical Journal 583, 1040 (2003); J. Ahrens et al., Phys. Rev. Lett. 92, 071102 (2004); M. Ackermann et al., Phys. Rev D71, 077102 (2005).

J E T P R O D U C T I O N AT H E R A A N D M E A S U R E M E N T S OF T H E STRONG COUPLING C O N S T A N T as

DORIAN KCIRA ZEUS / DESY,

University of Wisconsin Notkestrasse 85, 22607 Hamburg, Email: [email protected]

Germany

Measurements of HERA that explore the parton dynamics at low Bjorken x are presented together with precise determinations of the strong coupling constant as • Calculations at next to leading order using the DGLAP evolution fail to describe the data at low x and forward jet pseudorapidities. The as(Mz) measurements at HERA are in agreement with the world average and have very competitive errors.

1. Introduction At HERA, forward jet production and jet-jet correlations are expected to be sensitive to the parton dynamics at low Bjorken x (XQJ). In the first section, these type of measurements and comparison to DGLAP, BFKL and other models are presented. For the measurements presented in the second section, jets were selected in kinematic regions where the proton parton distribution functions (PDFs) are well constrained and the DGLAP equations are valid. These measurements allow precise tests of perturbative QCD (pQCD) and the determination of the strong coupling constant, as. 2. QCD d y n a m i c s at low x Inclusive forward jet production was measured by the HI Collaboration x for events in the kinematic region 5 < Q2 < 85 GeV 2 and 10~ 4 < ZBJ < 4 • 10~ 3 , where Q2 is the virtuality of the exchanged photon. Jets were found in the laboratory frame with E^ > 3.5 GeV, 7° < 6& < 20° (corresponding to the 1.74 < rfet < 2.8 a ) , xiet > 0.035, and 0.5 < E | j e t / Q 2 < 5. E^ is the transverse energy of the jet and Xjet is the fractional energy of the proton taken by the jet. a

»7 = — log[tan(0/2)] is the pseudorapidity, where 0 is the polar angle.

174

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250

ous QCD models (right). The DISENT calculations ,.

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Figure 1. Cross section for inclusive forward jet production as a function of XBJ compared to NLO calcul a t i ° n (left) and QCD MC models (right).

The DGLAP model with direct photon interactions alone (RG-DIR, RAPGAP) and the NLO calculation fall below the data, especially at low ZBJ- The description of the data by RAPGAP is significantly improved if contributions from resolved photon interactions are included (RGDIR+RES). The Color Dipole Model (CDM) shows a similar behaviour to RG-DIR+RES. In addition, the CCFM based CASCADE MC predicts a different shape of the distribution that results in a poor description of the data. Jet production in NC DIS has been measured by the ZEUS Collaboration 2 for Q2 > 25 GeV 2 , y > 0.004, E'e > 10 GeV (where E'e is the energy of the scattered positron), and cos(7^) < 0 b . Jets were selected in the laboratory frame with E^ > 6 GeV, 2 < ^ e t < 3, and 0.5 < {E^)2/Q2 < 2. The measurement is presented in Fig. 2 as a function of XBJ and compared to NLO calculations (DISENT, fiR = nF = Q, CTEQ6) and to the CDM (ARIADNE) and MEPS (Matrix Elements + Parton Showers, LEPTO) models. The CDM prediction gives a reasonable description of the data. The NLO and MEPS predictions fail to describe the data in the low XBJ region. The uncertainty induced by the variation of the renormahzation scale is large, indicating that missing higher order or ln(l/a;) terms in the calculation could be important in this region. The HI Collaboration has measured inclusive dijet production in DIS 3 in the kinematic range 5 < Q2 < 100 GeV 2 , 10" 4 < x < 10~ 2 , and 0.1 < y < 0.7. Dijets were reconstructed in the hadronic center-of-mass b

7h is the hadronic angle. It corresponds, in the Quark Parton Model, to the angle of the scattered quark.

176

system (HCM) and selected with the requirements: —1 < r?jet,iab < 2.5 and {Ej?1 ' )* > 7,5 GeV. The azimuthal asymmetry is defined by: S(a)

=

,.isn° d Jo

,, ' X '—TT~*— i where Ad>* is the azimuthal separa-

Wdijet(A0*,x,Q2)dA0'

tion in the HCM frame between the two hardest transverse energy jets. Figure 3 presents the S distribution for a = 120° as a function of x for differ• ZEUS 96-97 ent Q2 compared to predict=-=- -=-l Energy Scale Uncertainty tions of DGLAP NLO cal2
ZEUS

I

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3. Precise tests of QCD and the measurement of as Differential dijet and trijet cross sections have been measured by the ZEUS Collaboration 4 in the kinematic range 10 < Q2 < 5000 GeV 2 and 0.04 < y < 0.6. Jets were found in the Breit frame and dijet (trijet) events were selected with: — 1 < ^jet.iab < 2.5, i?T,jet,Breit > 5 GeV, and invariant mass M 2/3j ets > 25 GeV/c 2 . ' Figure 4 shows the measured dijet and trijet cross sections as a function

177

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178 of Q2 (left) and their measured ratio R3/2 (right). The NLO predictions of NLOJET (nn = pF = (E2T + Q 2 )/4, CTEQ6) corrected for hadronization effects are compared to the data. NLOJET provides a good description of both the shape and the magnitude of the measured cross section. The correlated systematic and the renormalization scale uncertainties largely cancel in the ratio of the cross sections. This cancellation allows the extraction of as(Mz) with a good precision down to Q2 of 10 GeV 2 , using a method similar to that of a previous ZEUS publication 5 . The value of as was measured to be as(Mz) = 0.1179 ± 0.0013 (stat.) ±°;°°*g (exp.) to°046 (th-)4. Conclusions The HERA measurements show that DGLAP NLO calculations at low x and forward jet pseudorapidities fail to describe data but the large theoretical uncertainties prevent a decisive conclusion on parton dynamics at low x. A summary of the as measurements at HERA is shown in Fig. 5. The as measurements at HERA are in agreement with the world average and have very competitive errors. For more accurate measurements of as improved theoretical calculations would be needed.

th. uncert exp. uncert

0.1

0.12

Jet shapes in NCDIS ZEUS (Nucl Phys B 700 (2004) 3) Multi-jets in NC DIS ZEUS (DESY 05-019 - hep-ex/0502007) Inclusive jet cross sections in 7p ZEUS (Phys Lett B 560 (2003)7) Subjet multiplicity in CC DIS ZEUS (Eur Phys Jour C 31 (2003) 149) Subjet multiplicity in NC DIS ZEUS (Phys Lett B 558 (2003) 41) NLO QCD fit HI (Eur Phys J C 21 (2001) 33) NLO QCD fit ZEUS prel. (contributed paper to ICHEP04) NLO QCD fit ZEUS (Phys Rev D 67 (2003) 012007) Inclusive jet cross sections in NC DIS HI (Eur Phys J C 19 (2001) 289) Inclusive jet cross sections in NC DIS ZEUS (Phys Lett B 547 (2002) 164) Dijet cross sections in NC DIS ZEUS (Phys Lett B 507 (2001) 70) 0.14 average World (S. Bethke, hep-ex/0407021) as(M z)

F i g u r e 5. A s u m m a r y of t h e as ments at H E R A .

from m e a s u r e -

References 1. 2. 3. 4. 5. 6.

HI Collab., Contributed Paper N 5-0172 to 32nd ICHEP, Beijing, 2004. ZEUS Collab., DESY-05-017 (2005). HI Collab., A. Aktas et al., Eur. Phys. J. C37 141 (2004). ZEUS Collab., DESY-05-019 (2005). ZEUS Collab., Phys. Lett. B 507, 70 (2001). ZEUS Collab., Nucl. Phys. B 700, 3 (2004).

P A R T O N E N E R G Y LOSS, SATURATION, A N D R E C O M B I N A T I O N AT B R A H M S

EUN-JOO KIM FOR THE BRAHMS COLLABORATION University of Kansas, Lawrence, Kansas 66045, USA E-mail: [email protected] Particle production as observed with the BRAHMS experiment at RHIC is presented. Preliminary baryon/meson ratios and nuclear modification factors at different rapidities will be discussed.

1. I n t r o d u c t i o n Hadrons with high transverse momentum provide a good probe of the high energy density matter created at RHIC, since the production of high pr particles is dominated by the initial hard parton-parton scatterings with large momentum transfer Q2. After hard-scattering, partons traverse a medium with a high density of color charges where they interact strongly, emit gluon radiation, and lose energy before fragmenting into hadrons. The production of hadrons depends on the initial parton distributions in the colliding nuclei, the elementary parton-parton cross section and the hadronization process of partons into hadrons. It is also important to distinguish nuclear effects from initial state effects, such as described by shadowing and/or color glass condensate models, and final state effects. To disentangle all these behaviors requires a very comprehensive data set. The BRAHMS experiment 1 ' 2 has studied p+p, d+Au, and Au+Au collisions over a broad range of rapidity and transverse momentum. We will discuss these data in the context of the above processes. 2. R e s u l t High pr suppressions have been observed in central Au+Au collisions at RHIC 3 ' 4,5 and are attributed to final-state interactions based on the absence of such suppressions in d+Au collisions 6 ' 7 ' 8,9 . The suppression is quantified by use of nuclear modification factors, which are denned as RAA or RCP • 179

180

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fi^>i gives the deviation in yields from AA collisions relative to the scaled yields from nucleon-nucleon collisions. Rcp can provide similar information based on the relative yield in central(C) and peripheral(P) collisions scaled by the mean number of binary collisions, but does not depend on the reference nucleon-nucleon system. Figure 1 shows the rapidity (a) and particle dependence (b) of Rcp in Au+Au collisions at y'Sjvjv = 200 GeV. The observed suppression is similar at forward rapidities (r) ~ 2.2, 3.2) as compared to midrapidity. This result may indicate quenching extends in the longitudinal direction. RCP for protons reaches unity around pr ~ 1.5 GeV/c, but RCP for pions is suppressed at higher pr- The difference between baryon and meson behaviors is discussed later.

(a) O h(0-10%/40-60%)atr|=0 <> h" (0-10%/40-60%) at TI-2.2 • h+ (0-10%/40-60%) at i\~3.2 T h' (0-10%/40-60%) at ii~3.2

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181

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Figure 2. Top row : Nuclear modification factor for charged hadrons at pseudorapidities r] = 0, 1.0, 2.2, 3.2. Systematic errors are shown with shaded boxes with widths set by the bin sizes. Bottom row : Central(field circles) and semi-central(empty circles) Rcp ratios in d + A u collisions at y'sjviv = 200 GeV. Shaded bands indicate the uncertainty in the calculation of (Ncou) in the peripheral collisions (12%).

The rapidity dependence of RJA and Rcp for d+Au collisions 10 is shown in Fig. 2. At midrapidity, RdAipr > 2 GeV/c) shows a Cronin type enhancement compared to the binary scaling limit. At higher rapidity, this enhancement is followed by a suppression which becomes stronger at forward rapidity. Along the bottom row, the RCP for two different centrality ranges is shown as function of pseudorapidity. The more central RCP exhibits greater suppression as the rapidity increases. This is consistent with the picture of parton saturation in the Au-wave function 11 . However, the suppression of Rcp at forward rapidity can also be reproduced in the framework of parton recombination in the final state 12 , without involving multiple scattering and gluon saturation in the initial state. Figure 3 shows the dependence of the high pr behavior on the type of particle in d+Au and Au+Au collisions. Results in Au+Au collisions show ir~ are suppressed at midrapidity and forward rapidity. At forward rapidity, the suppression is stronger for n~, while the p yields are enhanced at both rapidities. In d+Au collisions, the IT" yields are more suppressed at 77 ~ 3.2, while, again, the p yields are enhanced at forward 77. This different behavior between n~ and p is not consistent with standard fragmentation functions, and indicates pions experience high pr suppression while protons do not. This is not yet fully understood. Proton excess might arise

182

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from hydrodynamic expansion, or parton recombination 13 and/or quark coalescence14 processes that enhance the yield of baryons containing three quarks by pulling them from the medium rather than relying on a simple fragmentation origin. The measured p/ir+ and p/ir~ ratios as a function of pr for central Au+Au collisions at different rapidities are shown in Fig. 4. There is a clear increase of the p/ir ratios at intermediate pr (2 < pr < 5 GeV/c) relative to the level seen in nucleon-nucleon collisions 15 ' 16 . There is no significant difference for the ratios at rapidity y = 0 and y ~ 1, and P/TT~ ratio shows a similar tendency up to pr ~ 1.5 GeV/c at T] ~ 2.2. 3. Summary BRAHMS has measured rapidity dependent nuclear modification factors and particle ratios in different colliding systems. The evolution of nuclear modification factors in d+Au collisions may indicate parton saturation in the initial state. The high px suppression in Au+Au collisions at midrapidity also exists at forward rapidity, and depends on particle type. The recombination/coalescence models seem to give a reasonable explanation of the observed baryon-meson production mechanism at intermediate pr-

183

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(a) p/7l + 0-10% central

(b) p/7T

p T [GeV/c]

BRAHMS Preliminary A BRAHMS at y=0 T BRAHMS at y~l B BRAHMS at T)~2.2

p T [GeV/c]

Figure 4. p/7r+ (a) and J)/"' - (b) ratios at rapidity y = 0, 1.0 and r; = 2.2. for 010% central Au+Au collisions at ^/SNN = 200 GeV. Feed-down corrections applied. Comparisons with model calculations13'14 are shown. Acknowledgments This work was supported by the division of Nuclear Physics of the Office of Science of the U.S. D O E , the Danish Natural Science Research Council, the Research Council of Norway, t h e Polish State Committee for Scientific Research and the Romanian Ministry of Education and Research. References 1. BRAHMS Collaboration, Nucl. Instr. and Meth. A499, 437 (2003). 2. BRAHMS Collaboration, Nucl. Phys. A757, 1-27 (2005). 3. PHENIX Collaboration, Phys. Rev. Lett. 88, 022301 (2002). 4. STAR Collaboration, Phys. Rev. Lett. 89, 202301 (2002). 5. PHOBOS Collaboration, Phys. Lett. B578, 297 (2004). 6. BRAHMS Collaboration, Phys. Rev. Lett. 91, 072305 (2003). 7. PHENIX Collaboration, Phys. Rev. Lett. 91, 072303 (2002). 8. STAR Collaboration, Phys. Rev. Lett. 91, 072304 (2002). 9. PHOBOS Collaboration, Phys. Rev. Lett. 91, 072302 (2002). 10. BRAHMS Collaboration, Phys. Rev. Lett. 93, 242303 (2004). 11. D. Kharzeev, Y. Kovchegov, and K. Tuchin, Phys. Lett. B599, 23 (2004). 12. R. C. Hwa and C. B. Yang, and R. J. Fries, Phys. Rev. C71, 024902 (2005). 13. R. C. Hwa and C. B. Yang, Phys. Rev. C70, 024905 (2004). 14. V. Greco, C. M. Ko, Phys. Rev. C68, 034904 (2003). 15. B. Aper et al., Nucl. Phy. B100, 237 (1975). 16. P. Abreu et al., Eur. Phys. J. C17, 207 (2000).

H A D R O N P R O D U C T I O N A N D R A D I A L FLOW I N A U + A U COLLISIONS AT R H I C - P H E N I X

AKIO KIYOMICHI FOR THE PHENIX COLLABORATION 2-1 Hirosawa,

RIKEN Wako, SAITAMA, 351-0198, E-mail: kiyoQbnl.gov

Japan

The centrality dependence of transverse momentum distributions and yields for TT^, K^, p and p in A u + A u collisions at ^ S N N = 200 GeV are measured by the PHENIX experiment at RHIC. The single particle spectra are well fitted with a hydrodynamic-inspired parameterization, termed the "blast-wave" model, to extract freeze-out temperature and radial flow velocity of the particle source. Another motivation is that the suppression of high-pT hadron as a probe of Q G P formation. In central collisions at intermediate transverse momenta ~ 1.5 - 4.5 GeV/c, proton and anti-proton yields constitute a significant fraction of the charged hadron production and show a scaling behavior different from that of pions.

1. Introduction Heavy-ion collisions at high energies offer a unique opportunity to probe highly excited dense nuclear matter in the laboratory. That form of matter is called the quark-gluon plasma (QGP), which is quantum chromodynamics (QCD) analogue of the plasma phase of ordinary atomic matter. Since hadrons contain basic information about collision dynamics, the production of hadrons is one of the important probes of QGP. We present the results of identified hadron spectra and yields in Au+Au collisions l at the energy of ^/SNN = 200 GeV by the PHENIX experiment using the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL). 2. E x p e r i m e n t s The PHENIX 2 is one of the major experiments at RHIC to detect a variety of signals from quark-gluon plasma. It is designed to perform a broad study of A + A, p + A, and p + p collisions to investigate nuclear matter under extreme condition. The detector consists of a large number of subsystems. It comprises two central arms, two forward muon arms, and three global de184

185

Figure 1. a (left): A cutaway drawing of the PHENIX detector. Labeled arrows point to the major detector subsystems, b(right); Mass squared vs. momentum • charge distribution. The lines indicate the PID cut boundaries for pions, kaons, and protons(antiprotons) from left to right, respectively.

tectors (Figure la). The east central arm has a unique hadron identification capability in a broad momentum range, Pions and kaons are identified up to 3 GeV/c and 2 GeV/c in p T , respectively, and protons and anti-protons can be identified up to 4.5 GeV/c by using a high resolution time-of-flight detector. In Figure lb, a plot of m2 versus momentum multiplied by charge is shown together with applied PID cuts as solid curves.

3. R e s u l t s For single particle analysis, we have measured the transverse momentum spectra and yields for TT^, if*, p and p at mid-rapidity in Au+Au collisions at V^NN = 200 GeV over a broad momentum range with various centrality selections. Figure 2 shows the pT distributions for pions, kaons, protons, and anti-protons. The top two plots are for the most central 0-5%' collisions, and the bottom two are for the most peripheral 60-92% collisions. The spectra for positive particles are presented on the left, and those for negative particles on the right. We have observed a clear particle mass dependence of the shapes of transverse momentum spectra in central collisions below ~ 2 GeV/c in pT. On the other hand, in the peripheral events, the mass dependences of the p r spectra are less pronounced and the PT spectra are more nearly parallel to each other. Another notable observation is that at P T above ~ 2.0 GeV/c in central events, the p and p yields become comparable to the pion yields.

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3.1.

Radial

Flow

In order to deduce radial flow velocity and thermal freeze-out temperature, particle spectra were compared to a functional form, which describes a boosted thermal source, based on relativistic hydrodynamics 3 . This is a two-parameter model, termed the "blast-wave" model, in which the surface radial flow velocity (/3x) and freeze-out temperature (TfQ) are extracted from the invariant cross section data according to the equation dN m x d m Tr

x J ' "V ''' Jo V Tf Tfo / \\ T Tio 0 Q J fo / where Jo and K\ represent modified Bessel functions with p being the transverse boost which depends on the radial position according to p(r) = tanh _1 (/3x) • r/R. To study the parameter correlations, a grid of (Tf0,/3T) pairs is generated and then a \ 2 minimization is performed for each particle type. The experimental data include the decay of resonance; we add the decay of mesonic (p,T],oj,K*,,,) and baryonic (A, A, S,,,) resonance effects, the abundance of which is determined by chemical parameters. The two-dimensional grid search results obtained in this analysis for each centrality bin are shown in Figure 3. The expansion velocity parameter is seen

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to decrease moderately toward peripheral collisions and the kinetic freezeout temperature increases significantly, approximately 40%. If one takes these parameters literally, then radial flow is weak in the peripheral collisions and the particles decouple kinetically from each other at temperatures close to the chemical freeze-out temperature. This is a physically reasonable scenario given the small number of participants in the initial expansion phase. For the most central 0-5% collisions, we have obtained freeze-out temperature TfQ = 108 MeV and average flow velocity (/Jp) = 0.57. 3.2. High-px

Hadron

Production

For the high-px region, the scaling behavior of identified charged hadrons has been compared with results for neutral pions. Figure 4 shows the central (0-10%) to peripheral (60-92%) ratio for JVcou (number of collisions) scaled PT spectra of (p + p)/2, kaons, charged pions, and n°. We define Rep as: Yield0" 10% RCP

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The standard picture of hadron production at high momentum is the fragmentation of energetic partons. While the observed suppression of the 7r yield at high px in central collisions may be attributed to the energy loss of partons during their propagation through the hot and dense matter created in the collisions, i.e. jet quenching, it is a theoretical challenge to explain the absence of suppression for baryons up to 4.5 GeV/c for all centralities along with the enhancement of the p/n ratio at px = 2 4 GeV/c for central collisions. The observed RCP in intermediate px region are not explained by the hydrodynamic model alone, but some of theoretical model qualitatively agree with data. These observations can be explained by the hydrodynamical model with jet fragmentation (hydro + jet model) 4 and the parton recombination at intermediate px (recombination model) 5 . Both theoretical models reproduce the binary collision scaling observed in the data.

References 1. 2. 3. 4. 5.

P H E N I X Collaboration, S.S. Adler et al., P h y s . Rev. C 6 9 034909 (2004). K. Adcox et al, Nucl. I n s t r u m . M e t h o d s A 4 9 9 469 (2003). E. S c h n e d e r m a n n , J. Sollfrank, a n d U. Heinz, P h y s . R e v . C 4 8 2462 (1993). T . H i r a n o a n d Y. N a r a , P h y s . R e v . C 6 9 034908 (2004). R. J. Fries, B . Miiller, C. N o n a k a , S. A. Bass, P h y s . Rev. C 6 8 044902 (2003).

S U S Y SEARCHES AT LEP

A.C. KRAAN University of Pennsylvania, Department of Physics and Astronomy, 209 S 33rd Street, PA 19104, Philadelphia, USA Searches for SUSY particles have been performed with 3.6 f b - 1 e+e~ data collected by the LEP detectors at ^/s between 90 GeV and 209 GeV. This talk reviews some of the relevant searches for SUSY particles at LEP. No excess of events is observed in any channel. Results are interpreted in the context of the MSSM.

1. Introduction Supersymmetry x (SUSY) is an attractive candidate as a theory for physics beyond the Standard Model (SM). In the simplest SUSY implementation, the Minimal SuperSymmetric Model (MSSM), containing the minimal number of additional particles, each SM particle has a supersymmetric 'partner', differing in spin by 1/2. The superpartners of fermions, gauge bosons and the two MSSM Higgs doublets are called sfermions, gauginos and Higgsinos, respectively. An important quantity in SUSY phenomenology is R-parity. In R-parity conserving (RPC) models, sparticles are only pair produced, and the Lightest SUSY particle (LSP) is stable. Most naturally the LSP is a neutralino Xo (a mixture of the neutral gauginos and higgsinos), or sneutrino v (superpartner of neutrino), although the latter is cosmologically disfavoured. Widely accepted frameworks are the constrained Minimal SuperSymmetric Model (cMSSM) and the Minimal supergravity (mSUGRA). In the former masses and couplings can be derived from a few parameters: tan/3, the ratio of the vacuum expectation value of the two Higgs doublets; n, the Higgs mass parameter, M2, the EW scale common gaugino mass; mo, the GUT scale common scalar mass; and A0, the trilinear couplings which enter in the prediction of the sfermion mixing. In the even more constrained mSUGRA framework the parameters are: tan/3; the sign of /j; mo; mi/2, the GUT scale common gaugino mass that replaces 7712; and A0, the GUT scale common trilinear coupling. 189

190

To search for SUSY, LEP data have been analysed. Results shown here are mainly based on the second phase of running, LEP 2, when roughly 775 p b - 1 of data per experiment was collected at -Js of 130-209 GeV. This paper reviews a selection of LEP SUSY searches. First searches for sleptons, squarks and charginos are summarized, and a limit on the neutralino LSP is shown. When available the SUSY LEP working group 2 results are used, based on combinations of ALEPH, DELPHI, L3 and OPAL (ADLO). No signal has been observed and results will be given in the form of 95% C.L. exclusion domains in the space of the relevant parameters. Also, DELPHI and ALEPH searches for a gluino LSP will be reviewed. Finally a few remarks will be given about alternative SUSY models. 2. Slepton searches If mo is small, the sleptons (I, SUSY partners of the leptons) can be light. In particular the stau (f, SUSY partner of the r) may be light, because for the 3rd generation sfermions large mixing can occur between "left-" and "right-handed" partners, resulting in a heavy and a light mass eigenstate, the latter possibly in the reach of LEP. Sfermions would be pair produced via s-channel Z/7 exchange, whereby for selectrons (e, superpartners of electrons) t-channel u exchange contributes also. The four experiments have searched for sleptons decaying into a lepton and a xo LSP, where the signature was two acoplanar leptons and missing energy due to the two escaping LSP's. The missing energy signal is closely related to the mass difference AM between the slepton and the LSP: small AM values imply large missing energy and vice versa. No excess of events was observed, and in Fig. 1 the mass limits are shown. 3. Squark searches Due to sfermion mixing, the third generation squarks may be light. Squarks would be produced via s-channel Z/7 exchange. Decay channels with a xo and v LSP have been studied. In the channels i -> cx° and b ->• b + x°, the topology is missing energy and acoplanar quark jets. In the channel i —)• blv, isolated leptons are additionally searched for. The four-body decay channel i —> 6/1/2X0) characterised by multi-jets and missing energy, was studied by ALEPH. No excess of events was observed in any channel, and Fig. 1 shows examples of excluded regions. The case in which the squark has a sizable lifetime (small AM), is addressed by ALEPH, and resulted in an absolute limit on the stop mass of 63 GeV/c 2 for a v or xo LSP.

191 Vs= 183-208 GeV

ADLO

Figure 1. Left: excluded region (final) for pair produced sleptons decaying via I —> l + Xo- The parameter space point is fi = —200 GeV/c 2 , tan(/3) = 1.5. Middle: excluded regions (preliminary) for pair produced stops decaying via i —> c\o- Right: excluded regions (preliminary) for pair produced sbottoms decaying via b —• bxo- Only squark masses above 50 GeV/c 2 are shown, since lower values have been excluded at LEP 1.

4. Chargino searches The charged gauginos and Higgsinos mix to form charginos, x ± ; which would be pair-produced via s-channel Z/7 exchange and t-channel eexchange. If m 0 is small the sleptons are light, and thus the decay X^ —> lu -» xo could dominate. Also, light sleptons can lead to t-channel destructive interference in the production cross section. At large mo, the search channel is x^ -¥ x°^± only, and in that case the topology, besides missing energy, depends on the decay mode of the W. Searches have been done for different values of AM between x * and x°: prompt decays, longlived and stable charginos have been searched for. In Fig. 2 the exclusion plot is shown.

5. LSP limits The above searches can be combined with the cMSSM Higgs boson searches, and Fig. 2 shows results. In the cMSSM framework the lower mass limit on the LSP is 47 GeV. For mSUGRA (not shown) the limit is 50 GeV. The effect of f mixing in the cMSSM, possibly causing the stau mass to be in between the x° a n d the x*, has been investigated by ALEPH. Searches have been done for e+e~ ->• x+X~ ~> TUTU -> TUX°TUX°, e+e~~ —• X2X1 ~~> T r an TTXA -^ X? Xi d e + e~ -> X2X2 ~^ TTTT -4- TTX\TTX\, where in all cases missing energy and a number of taus was searched for. Fig. 2 shows the LSP limit as function of tan /? when f mixing is included.

192

Figure 2. Left: exclusion plot of charginos as function of sneutrino mass (preliminary result). Middle: mass limit on the neutralino LSP as function of tan/3 (final result). Right: mass limit on the neutralino LSP as function of tan/3 including f-mixing (final).

6. Searches for gluino LSP In contrast to conventional SUSY models predicting heavy gluinos decaying promptly, models exist with a gluino (g, superpartner of the gluon) LSP. A stable gluino would hadronize into stable charged and neutral particles called R-hadrons, interacting hadronically and possibly electromagnetically in the detector. Searches for gluino LSP's have been done by DELPHI and ALEPH. Gluinos would be produced via squarks, e + e - ->• qq. The decay channels i -> c + g and b -> b + g have been studied. The signature is two acoplanar jets and missing energy (due to the missing mass of the particle plus the poor hadronic interaction in the detector 4 ) . Figure 3(left) displays the results for the decay channels b -» 6 + g, studied only by DELPHI 3 . The channel i -> c + g has been studied by DELPHI and ALEPH. The ALEPH search is based on a combination of four different analyses: 1) the Z hadronic width, resulting in an exclusion of gluino masses below 6.3GeV/c 2 and squark masses below 1.3GeV/c2; 2) LEP 1 searches for acoplanar jets and missing energy; 3) stable squark search with LEP2 data; 4) a direct search for i -> c + g, where the search topology is again missing energy and acoplanar jets. Issues addressed in the Monte Carlo simulation are stop hadronization, stop decay inside the stop-hadron, gluino hadronization into R-hadrons and the R-hadronic interaction in the detector 5 . The result of the interplay of the four analyses is shown in Fig. 3. The ALEPH analyses allowed a mass limit of 80 GeV to be set on the stop mass in case of a gluino LSP.

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7. Other S U S Y searches In GMSB models, the LSP is naturally the gravitino, while the neutralino or the slepton is the next-to-LSP (NSLP). Different NLSP decay lengths have been studied. Fig. 3 shows the excluded mass regions in the case of a f NLSP. Searches for RPV topologies have also been done at LEP. Contrary to RPC models, the phenomenology of It-parity violating (RPV) models is different, because the LSP decays into SM particles. Since LSP decaying into SM particles, the usual missing energy signal is absent, and instead, multi-jets and multi-leptons are searches for. No excess of events was observed. Acknowledgements I thank Giacomo Sguazzoni for many useful comments for the talk and for this paper. Thanks also to Stefania, who fortunately could not come to the conference, and to Paolo Azzurri for nicely reviewing this paper. References 1. H.P.Nilles, Phys. Rept. 110, 1984 (1); H.E.Haber and G.L.Kane, Phys. Rept. 117, 1985 (75); R.Barbieri, Riv. Nuovo Cim. 11N4, 1988 (1). 2. See http://lepsusy.web.cern.ch/lepsusy/ and references therein. 3. The DELPHI Coll., Eur. Phys. J. C 26, 2003 (505). 4. ALEPH Coll., Eur. Phys. J. C 31, 2003 (327). 5. A.C.Kraan, Eur. Phys. J. C 37, 2004 (91).

SEARCH FOR N E W PHYSICS AT CDF II

AMITABH LATH Rutgers, The State University of New Jersey E-mail: [email protected] (for the CDF II Collaboration)

Searches for new physics at hadron colliders present unique challenges and opportunities. We present searches with the CDF II detector using pp collisions at •/s = 1.96 TeV at the Tevatron collider at Fermilab. These searches include Standard Model (SM) and the Minimally Supersymmetric Standard Model (MSSM) Higgs bosons, as well as supersymmetric particles, 2 and W bosons decaying to leptons, and large extra dimensions. We discuss the major backgrounds and techniques to overcome them. We present several new results from CDF.

Searches for new physics at hadron colliders have to contend with significant backgrounds. Signatures for processes that produce particles such as the Higgs boson, supersymmetric particles, large extra dimension excitations, or extra vector bosons tend to have cross sections of a few fb up to 104 fb. In contrast, background processes from quark and gluon jet production occurs with 1012 fb. Bottom quark production from QCD at 10 11 fb can swamp 6-quark signatures from new physics. W, Z bosons are produced with 107 fb cross section, and the top quark - background for many searches for new physics - is produced with a cross section of 104 fb. We present searches for new physics using leptons, photons, b and light quark jets, as well as missing transverse energy in the event, fr1. Standard Model Higgs The SM Higgs is produced mainly in the gluon fusion mode, gg —> ho. For Higgs masses below ~ 135 GeV/c 2 the prominent decay mode is ho —* bb. Above that mass, decay to pair of on/off-shell W bosons dominates 1 . The searches for lower mass SM Higgs used Higgs production in association with a W boson to combat QCD backgrounds. The SM Higgs search channels are: Wh0 —> Ivbb, ho —> WW* for lower mass and higher mass Higgs bosons. The data (162 p b _ 1 ) show no excess over SM background predic194

195 MSSM Higgs-m Search, tanp Exclusion

mA(GeV/c2)

Figure 1. The left plot shows cross section times branching ratio limits for both lowmass and highmass SM Higgs searches. The SM expectations are also shown. The right plot show the tan /3 vs. mass exclusion for the MSSM higgs decaying to tau pairs.

tions. Figure 1 (left) shows the cross-section times branching ratio for SM Higgs production limits for both the light and heavy Higgs searches and the SM expectation. Our limits are approximately an order of magnitude from the SM expectation for Higgs boson productions. 2. Searches for Supersymmetry Supersymmetry (SUSY) solves many of the problems inherent in the SM but requires a spectrum of partner particles citemartin. We present a few of the searches for SUSY partners, gg —> bbbb, it production, and an R-parity violating search for it —> br. 2.1. Gluino decays to

Sbottom

We search for events with large pT, a signature of the lightest supersymmetric particle (LSP) leaving the detector without interacting. Events with fir greater than 80 GeV, and two 6-tagged jets are selected as potential signal events. Four events are observed in the data, compared to a SM expectation of 2.63 ± 0.23 ± 0.66 events, where the first error is statistical and the second systematic. Figure 2 (left) shows the excluded contour in gluino vs. sbottom mass. 2.2. MSSM

Higgs Decaying

to Tau

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The MSSM (minimally supersymmetric standard model) is the simplest realistic SUSY theory. It provides an extra channel for Higgs production, namely bb —> A/H/h where A, H, and h are the P-odd, heavy P-even, and

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light P-even Higgs bosons of the theory 2 . We search for the MSSM Higgs bosons decaying to TT. We concentrate on events in which one r decays to e or fx (called r e and rM respectively) and the other one decays to hadrons (called T/I). The largest backgrounds are due to T/» from Z —> TT events - an irreducible background to the Higgs. Other backgrounds include diboson, top quark, and QCD jets that appear to be T^. We see no evidence for a higgs decaying to tau pairs, and we set limits on higgs production times branching ratio to tau pairs. We interpret these limits in the MSSM framework and make an exclusion curve in the MA VS. tan/3 plane. Figure 1 (right) shows this exclusion. The SUSY parameters used for this exclusions are taken from suggestions by Carena et. al. 5 . 2.3. Stop Pair

Production

We search for i pairs decaying to c-quarks and a neutralino (LSP). We select events with large $T and tag a jet as containing c-quarks by a jetprobability algorithm. The largest SM background is from a real W boson plus a real or fake charm jet. No excess of events above SM expectations are seen, figure 2 (right) shows the limit (at 95% CL) for this search. 2.4. R-Parity

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Conservation of R-Parity in decays of supersymmetric particles leads to a stable LSP which leaves the detector without interacting. However, if Rparity were not conserved in supersymmetric decays, searches that require large fx would not work.

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R-parity violating decays lack the large $T signature crucial to SUSY searches citerpv. We have performed a search for i pairs decaying to br without any large 1£T requirement. Events with 0, 1 jet are dominated by Z —> TT but those with two or more jets are i decay candidates. Results of the search are consistent with SM background expectations, we place a limit of mj > 129 GeV/c 2 for the RPV stop squark. 3. Searches using Lepton and Photon Pairs We show results from searches for Z and W bosons decaying to leptons. Figure 3 (left) shows the invariant mass of two electrons. The Z peak is prominent. We search for a Z signal in the high mass regions. We have carried out this search with /J, and r as well. Figure 3 (right) shows the cross section times branching ratio limit for the ee and Hfi channels combined, using 200 p b - 1 of data. We set 95% CL limits on a sneutrino of 725 GeV/c 2 , on a neutral SM-like gauge boson of 815 GeV/c 2 , and on a little Higgs model ZH of 875 GeV/ 2 . We also use these results to exclude a Randall-Sundrum 6 extra dimension graviton below 700 GeV/c 2 . In the TT we can exclude a Z below 394 GeV/c 2 , and sneutrino (with r couplings) below 370 GeV/c 2 at 95% CL. We also search for W bosons decaying to ev, and place a limit o n a f f at 842 GeV/c 2 at 95% CL. Figure 4 (left) shows the transverse mass of e and f-r- As in the dilepton invariant mass plots, we see agreement over four orders of magnitude. We search for new physics in di-photon events, and figure 4 (right) shows the results as interpreted in the Randall-Sundrum

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Figure 4. Transverse mass of electron and I£T showing the W peak (left) and exclusion contours in graviton mass vs coupling showing the ee, pp, and 77 exclusions.. extra dimensions model. 4. Conclusion The Tevatron has accumulated over 1 fb _ 1 of integrated luminosity, and the results presented here are from the first ~ 200 to 350 p b - 1 of that data, collected by the CDF experiment. We have analyzed this data for evidence of new physics, and so far all our results agree with Standard Model predictions. We have surpassed the limits on new physics processes set by Run 1 of the Tevatron, and the limits shown either exceed published limits or are the first analyses ever on a given topic. The Tevatron is poised to collect approximately 4 fb _ 1 of data in the next few years. We will use this data to search for new physics, as well as understand the detectors better which will make the searches more sensitive to new physics. We hope to find evidence of new physics soon. Up to date results are posted on the CDF Exotics web pages 7 . References 1. J. Gunion et a l "The Higgs Hunter's Guide", Addison-Wesley; New York, (1990). 2. D.J.H. Chung et al., Phys.Rept. 407, 1 (2005), and references therein. 3. S. P. Martin, "A supersymmetry primer," arXiv:hep-ph/9709356, (1997). 4. H. Dreiner, hep-ph/9707435; F. de Campos et al., hep-ph/9903245. 5. M. Carena et a)., Eur. Phys. J. C26, 601 (2003). 6. L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999). 7. http://www-cdf.fnal.gov/physics/exotic/exotic.html

S E A R C H FOR F E R M I O P H O B I C HIGGS AT LEP

V. LEMAITRE Universite catholique de Louvain, E-mail: Vincent. Lemaitre@fynu. ucl.ac.be ON B E H A L F O F T H E A L E P H , D E L P H I , L3 AND OPAL COLLABORATIONS Searches for fermiophobic Higgs boson decaying into photon or weak boson pairs have been performed at LEP with the data collected at center of mass energies up to 209 GeV. A summary of several analyses allowing to cover some hundred different final state topologies is presented. No statistically significant evidence of fermiophobic Higgs boson has been found. A lower limit on the Higgs boson mass is presented.

1. Introduction and Motivation A fundamental hypothesis of the Standard Model is the Brout Englert Higgs (BEH) mechanism responsible of the spontaneous SU(2)L XV(l)y electroweak symmetry breaking into U(1)Q. An important consequence of this BEH mechanism is the prediction of a Higgs particle which has not been detected so far. The minimal representation of the scalar field associated to this particle is realized by assuming a SU(2) doublet complex field. The origin of W and Z boson masses as well as fermion masses can then be explained by means of interactions between the gauge bosons and charged fermions with the scalar field respectively through gauge couplings and Yukawa couplings. Several extensions of the standard model predict the presence of additional multiplets which could shed some lights on important experimental observations such as coupling constants unification and fermion mass hierarchy. Other important features such as the origin of CP violation in the weak interactions and the stability of the Higgs mass at the electroweak scale can find elegant explanations in such models. In this context, the two Higgs doublet models offer the most natural and non trivial extensions. The free parameters arising from the new higgs potential and possible mixing angles between the gauge and mass eigenstates can give rise to many 199

200

models. An important class of models are characterized by Higgs particles exclusively coupling to gauge bosons. Such a higgs boson is therefore said to be fermiophobic. In these models, the fermion mass is then explained by the presence of a non zero coupling between another neutral higgs boson. The fermiophobic models are parameter dependent, but in a large class of models, the fermiophobic higgs is the lightest scalar boson and is produced with near-Standard Model strength. Therefore one defines a "benchmark" fermiophobic higgs boson with SM production rates and decays, but with fermionic channels closed. Branching fraction of benchmark fermiophobic Higgs boson into boson pairs is illustrated in Fig. 4a.

2. Fermiophobic Higgs boson decaying into a photon pair The four LEP experiments have been looking for the reaction e+e~ —> XY, with X, a scalar particle decaying into a photon pair and Y, a vector particle decaying into a fermion and an anti-fermion. The ALEPH collaboration assumes Y to be a Z boson but the analysis is then mainly based on the detection of photons (inclusive approach) [1]. The DELPHI collaboration optimizes the selection for two scalar final states topologies resulting from minimal supersymmetric models [2]. In particular, topologies arising from the decay of a CP-odd heavy Higgs to bb quarks (X being the heavy CPeven Higgs) and topologies resulting from a heavy CP-even higgs decaying into light fermiophobic higgs are also taken into account. L3 collaboration assumes Y = Z and performed a detailed selection according to the Z final state [3]. OPAL collaboration assumes Y = Z or another Higgs boson (like in MSSM) and adopt also an inclusive approach [4]. The background is largely dominated by the two fermion final states with initial and/or final state radiative photons. The analyses use data collected in e + e~ collisions at center-of-mass energies between 88 and 209 GeV. A reasonable agreement is observed between the distribution of selected events and Standard model expectation shown in Fig. l a as a function of the di-photon mass. The Fig. l b shows the 95% C.L. upper limit on B(H —• "fj)a(e+e~ —> HZ)/a(SM) obtained by combining the candidates events from the four experiments. A 95% C.L. lower mass limit of a benchmark fermiophobic Higgs is set at 109.7 GeV [5].

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3. fermiophobic higgs boson decaying into W W or ZZ For fermiophobic Higgs boson mass heavier than 90 GeV, the predicted H —» 77 branching fraction becomes small relative to the predicted H —> WW branching fraction motivating a search in this channel. ALEPH and L3 have performed a detailed analysis of the many topologies resulting from the six fermion final states. For most of the studied topologies, the main background comes from the W pair production, where NLO QCD effects have to be taken into account.

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202

rate the various event topologies and relies on discriminant variables which are Higgs mass dependent. Although the analysis is optimized for a higgs boson mass of 110 GeV, the cuts are mainly motivated by background rejection criteria and optimization is therefore relatively insensitive to the Higgs boson mass hypothesis. As an exemple, distribution of the reconstructed Higgs mass is shown in Fig. 2a after all selection cuts, for events with a topology where the on-shell W decays into a muon or an electron and the other gauge bosons decay hadronically.

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The L3 analysis [6] makes use of neural network dedicated for background rejection and optimized for each Higgs mass hypothesis. Event kinematics is also fully exploited. The distribution of signal to noise ratio extracted from the final discriminant variable is shown in Fig. 2b for data, expected signal and background events. The L3 analysis also considers the possibility that the Higgs decays into ZZ final states when this channel is relevant. The expected exclusion region for a fermiophobic Higgs are [98-105] GeV and [88,108] GeV for ALEPH and L3 respectively. The difference of sensitivity is mainly due to the fact that the optimization procedure for ALEPH is only realized for a 110 GeV Higgs mass hypothesis. A small excess is observed in the ALEPH data such that a fermiophobic Higgs cannot be excluded with these data alone. The results from both ALEPH and L3 are presented in Fig. 3a and Fig. 3b as the 95% C.L. exclusion region in the plane defined by £2 = B{H -> WW)a{e+e~ -* HZ)/a{SM)

203

and the Higgs boson mass. The combination with the channel H —• 77 has been made by the L3 experiment and a 95% C.L. limit for the branching fraction into gauge bosons as a function of the Higgs mass and the branching fraction into photons has been derived and is shown in (Fig. 4b).

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Figure 4. a) Expected Fermiophobic higgs branching fraction b)95% C.L. limit on branching fraction and cross section as a function of th Higgs mass

4. Conclusion A search for fermiophobic Higgs has been performed at LEP using data collected at centre-of-mass energies between 88 and 209 GeV. Combining the four results for H -+ 77 from ALEPH, DELPHI, L3 and OPAL, the fermiophobic Higgs mass has been measured to be higher than 109.7 GeV at 95%C.L.. L3 and more recently ALEPH have performed a search for H —* WW with data collected at energies up to 209 GeV and no statistically significant evidence of such a decay mode has been found. L3 also combined their two analyses to further constraint the various couplings between the Higgs and the gauge bosons. References 1. 2. 3. 4. 5. 6.

ALEPH collaborationP%s. Let. B544, 16-24 (2002). DELPHI collqborqtion, Euro. Phys. J.C35, 313-324 (2004). L3 collaboration, Phys. Let. B534, 28-38 (2002). OPAL collaboration, Phys. Let. B544, 44-56 (2002). LEP Higgs working group LHWG Note 2001-08, (2001). L3 collaboration, Phys. Let. B568, 191-204 (2003).

M E A S U R E M E N T S OF P R O T O N S T R U C T U R E AT H E R A

V. LENDERMANN* Kirchhoff Institute of Physics, University of Heidelberg Im Neuenheimer Feld 227, 69120 Heidelberg, Germany E-mail: [email protected]

Measurements of proton structure functions in deep inelastic ep interactions are presented. The data were recorded with the HI and ZEUS detectors at the HERA ep collider at DESY in the years 1994-2000 (HERA I) and 2003-2004 (HERA II) at the center-of-mass energy of v ^ = 300 GeV in 1994-1997 and 319 GeV in 1998 onwards. The HERA I data were used to extract quark and gluon parton distribution functions (PDFs) and to determine the strong coupling as. During the HERA II data taking period the lepton beam was longitudinally polarized.

1. Measurements of Structure Functions F2 and xFs Deep inelastic scattering (DIS) is an ideal process with which to study the proton structure and to test Quantum Chromodynamics (QCD). Neutral current (NC) interactions are mediated by photons and Z° bosons. In NC ep events at HERA, the scattered lepton and the hadronic final state are measured in the HI and ZEUS detectors with almost 4ir solid angle coverage. The main contribution to the cross section for the dominant photon exchange is given in terms of the proton structure function i*2(a;, Q2), which provides the total quark content of the proton at given values of the Bjorken scale variable x and of the modulus of the four-momentum transfer squared Q2. Both experiments have shown that the Q2 evolution of F2 is well described by perturbative QCD (pQCD) throughout five orders of magnitude in x and Q2, as illustrated in Fig. 1.1.2.3.4.5 While at low to medium Q2 up to 3% precision is reached, the high Q2 range is statistically limited. To improve the statistical significance at high Q2, a luminosity upgrade of HERA in the HI and ZEUS detector regions was performed in 2001. After initial background problems, the experiments are currently collecting data aiming roughly at an order of magnitude larger *On behalf of HI and ZEUS collaborations 204

-3 1

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,

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integrated luminosity for the HERA II period than was collected during HERA I. At Q2 > M | , the electroweak effects, especially the jZ interference, become significant leading to different NC cross-sections for e+p and e~p scattering (see Fig. 2a). 2,6 ' 7 The difference is described in terms of the proton structure function xF^{x, Q2). In pQCD, xF$ is given by the difference between the quark and anti-quark density functions, and thus allows an extraction of the valence quark content of the proton. At present, the uncertainties are dominated by the limited statistics of the e~p event samples. In order to increase the e~p statistics, HERA has been operating in the e~p mode since December 2004. 2. Comparison of Neutral Current and Charged Current Cross-Sections in e + p and e~p Scattering In charged current (CC) interactions, mediated by W± bosons, the resulting neutrino escapes the detection. The CC events are thus recognized via imbalanced transverse momentum of the hadronic final state. At Q2 > Mf w, CC and NC cross-sections, driven by respective boson propagator terms, become of similar size, as shown in Fig. 2b. The measurements at HERA have confirmed the Standard Model predictions. 2,5 ' 6,7 As high Q2 and high x ranges are kinematically correlated, the high Q2

206 HERA Neutral Current at high x

io 2

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measurements cover mainly the x region of valence quarks. At high x, the CC e~p cross-section is dominated by the contribution of u quarks, while the CC e+p is dominated by d quarks. Hence, the valence u and d PDFs are separated via the difference between e+p and e~p cross-sections. 3. Determination of Parton Densities and aa The quark and gluon PDFs are extracted via next-to-leading order (NLO) pQCD fits independently by HI and ZEUS using somewhat different approaches. 2 ' 4 The differences lie in the functional forms of the parametrizations, the densities parametrized, constraints imposed on the densities, the treatment of heavy quarks, phase space limits, Q2 start scales, treatment of experimental uncertainties, the data sets used, etc. It is possible to extract PDFs from the HERA data only, without input from other experiments. 2,8 Results of both collaborations agree broadly, as shown exemplary in Fig. 3 for Q2 = 10 GeV 2 . From the fits, the valence u quark distribution is best known (up to 3% precision), followed by the valence d distribution (typically 3 — 10% precision) and the gluon distribution (5 — 20%), which is obtained from the F2 scaling violations. A precise knowledge of proton PDFs in the kinematic range of HERA is

207 0" = 10 GeV2

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of crucial importance for LHC data analyses, as the HERA data provide the only way to obtain PDF values in the LHC range via pQCD Q2 evolution and thus to determine parton luminosities in pp reactions at the LHC. The pQCD fits to the proton structure functions allow a precise determination of the running strong coupling, as(Q2), reaching currently the experimental uncertainty of 2 - 3%. Recently, a new NLO QCD analysis was presented by ZEUS, in which as and the gluon PDF at high x were constrained using data on inclusive jet production in e+p DIS and di-jet photoproduction. 8 This has allowed an improved determination of a.s.

4. Extraction of FL The contribution of longitudinally polarized photon exchange to the ep cross-section is described by the structure function FL(X,Q2). In pQCD a non-zero value of FL results from gluon emission. Measurements of Ft, can thus provide constraints on the gluon PDF. This is especially important at low Q2, where non-perturbative effects hamper the pQCD-based PDF extraction. The FL dependent term in the DIS cross-section becomes significant only at very high values of the 7*p center-of-mass energy W. An overview of FL values, obtained by HI from the shape of the cross section at high W, is presented in Fig. 4 for fixed W — 276 GeV. 1,2,9 The measurements span over three orders of magnitude in Q2. They are in agreement with NLO QCD fits. Non-zero FL values are measured for the whole kinematic range down to the lowest Q2 values.

208 T r " i | i i i | i i i

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HERA II Figure 5. CC cross-sections of e+p collisions measured by HI and ZEUS during the years 2003-2004 of the HERA II data taking period for different e + beam polarizations. The solid line represents the Standard Model prediction involving proton PDF parametrizations by the MRST group. 0

0.2

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5. First results with longitudinally polarized leptons After the upgrade, HERA has provided longitudinally polarized leptons reaching currently up to 40% polarization. First results are obtained with polarized leptons for CC and NC inclusive cross-sections. In the Standard Model only left-handed electrons and right-handed positrons take part in CC interactions, and the CC cross-section depends linearly on the polarization P: cr°fp{P) = (1 + P)of^(O). A test of this assumption for three different values of the e + beam polarization is presented in Fig. 5. The results are well described by the predicted dependence on P and thus compatible with the absence of right-handed charged currents. 10 ' 11 NC reactions are also sensitive to the lepton polarization. When more statistics is collected, this can provide a new possibility to disentangle individual quark flavors at high Q2. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

C. Adloff et al. [HI Collaboration], Eur. Phys. J. C 21, 33 (2001). C. Adloff et al. [HI Collaboration], Eur. Phys. J. C 30, 1 (2003). S. Chekanov et al. [ZEUS Collaboration], Eur. Phys. J. C 21, 443 (2001). S. Chekanov et al. [[ZEUS Collaboration], Phys. Rev. D 67, 012007 (2003). S. Chekanov et al, [ZEUS Collaboration], Phys. Rev. D 70, 052001 (2004). C. Adloff et al. [HI Collaboration], Eur. Phys. J. C 19, 269 (2001). S. Chekanov et al. [ZEUS Collaboration], Eur. Phys. J. C 28, 175 (2003). S. Chekanov et al. [ZEUS Collaboration], DESY-05-050, hep-ph/0503274. HI Collaboration, contributed paper to ICHEP'04, Beijing, Abstract 161. HI Collaboration, contributed paper to ICHEP'04, Beijing, Abstract 756. ZEUS Collaboration, contributed paper to ICHEP'04, Beijing, Abstract 256.

TOP PHYSICS AT THE LHC

STEVEN LOWETTE Vrije Universiteit Brussel - IIHE, Pleinlaan 2, 1050 Brussel, Belgium E-mail: [email protected] The physics of the top quark has an important role, both in verifying the Standard Model (SM) and in the search for physics beyond the SM. Its mass and Yukawa coupling to the Higgs boson are major parameters in studies of the electroweak symmetry breaking. Also the cross section of top-pair and single-top processes are important measurements to test the consistency of the SM. On the other hand, top quarks are a major source of background for almost all future searches for new physics. Therefore a precise understanding of the top signal is crucial. A review is given of the top physics programme for the CMS and ATLAS detectors at the Large Hadron Collider.

1. Introduction The Large Hadron Collider (LHC), currently under construction at CERN, will start its operation in 2007. It will collide protons onto protons at a center of mass energy of 14 TeV and at a luminosity ranging from 10 33 c m - 2 s _ 1 in the initial phase up to 1034 c m - 2 s _ 1 at a later stage. Two general purpose detectors are being constructed and installed: A Toroidal LHC Apparatus (ATLAS) 1 , and the Compact Muon Solenoid (CMS) 2 . Within the Standard Model physics program at the LHC, top physics plays an important role. The top quark is the least known SM particle. It was discovered in 1995 at the Tevatron, and the latest combined measurement of its mass 3 is 178.0 ± 4.3 GeV/c 2 . It is the most massive elementary particle known to date, and therefore it induces important electroweak corrections to for example the Higgs boson mass. Accurate measurements of the top quark mass and other top related properties allow for further constraining and testing of the Standard Model. At the same time top quarks are a major background for many new physics searches. The LHC will be a 'top factory': tt production reaches a cross section at NLO of about 800 pb. At a low luminosity of 10 33 c m - 2 s _ 1 , corresponding to 10fb _ 1 /y. over 8 million tt pairs are expected each year. As a con209

210 sequence most measurements will be very quickly limited by systematics rather than statistics. The decay of the top quark t —• Wb has a branching fraction of ~ 100% in the Standard Model. Due to the very short lifetime (~ 10~ 24 s) the decay happens well before hadronization takes place, excluding top hadrons. The signature of a tt pair is hence given by the decay topology of the W pair in addition to the two b-quarks in the final state. 2. Top Quark Mass Measurement in tt Events 2.1. The golden channel:

the semileptonic

decay

The decay channel tt —> bbqq'^i/ where one W decays into a muon or electron and the other hadronically, is called the semileptonic channel. It is the golden channel for the measurement of the top mass as the isolated lepton can be used to trigger the events and the top mass can be measured on the hadronic side of the decay. The most important background sources are shown to be combinatorial and originating from tt —> T+X and W+jets. One method to measure the top quark combines the two light quark jets with the W mass constraint and then adds one of the b-tagged jets. In the left plot of Figure 1 the resulting invariant mass distribution 4 is shown for CMS with 10 fb" 1 . Another method, exploiting the complete kinematics of the reconstructed event, involves the use of a kinematic fit5. In this case a x 2 function is minimized by variation of the reconstructed particles' kinematics. In the technique followed by ATLAS, events are classified as a function of the x 2 value of the kinematic fit. The top mass is estimated in subsamples in each x 2 slice and the top mass measurement is obtained by extrapolation to x 2 = 0. The estimated top mass as a function of the x 2 value is shown in the right plot of Figure 1 for 10 f b - 1 . A detailed estimation of systematic uncertainties has been performed for ATLAS for both methods 5 . For the first method the main contributions come from the b-jet energy scale (0.7GeV/c 2 ) and final state radiation (FSR) (1.0 GeV/c 2 ). The second method shows a large improvement on the uncertainty due to FSR (< 0.5GeV/c 2 ). After 10fb - 1 a total uncertainty on the top mass measurement of 1.4GeV/c 2 and 1.0GeV/c 2 is expected for the first and second method respectively. 2.2. Top mass measurement

in other

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The fully leptonic decay channel tt —> \fol\V\l2V1 is a cleaner channel, but the kinematics are underconstrained due to the two neutrinos. The top

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mass can however still be measured indirectly 5 . A first method looks at the number of solutions to the kinematical equations assuming a top mass. With 10 f b - 1 an accuracy of 1.7GeV/c 2 is expected. Another proposed method exploits the correlation between the invariant mass of the leptons and the top mass. Here an accuracy of 2GeV/c 2 is expected after 10 f b - 1 . The fully hadronic decay channel tt ->• bbqiq'1q2q2 suffers from trigger inefficiency and large combinatorial ambiguities. These problems can be tackled 5 by demanding each jet combination forming a top candidate to have a large total transverse momentum (e.g. pr > 200GeV/c). Combinatorics are then reduced due to hemisphere separation between the tops. A last proposed method 5,6 uses J / * -> fJ.+(J.~ decays in tt -» W(-> qq')6W(-^ &/)&(-> J / * ) . Here the top mass is correlated to the invariant mass of the J / * and the lepton from the corresponding W. Although low in statistics (~ 1000events/y expected at high luminosity), this channel is free from jet energy scale systematic uncertainties. The expected precision of 1 GeV/c 2 is limited by theoretical uncertainties on b fragmentation.

3. Topics in Top Physics 3.1. Single top

production

Single top quarks will be produced at the LHC either in the t channel processes qb -> tq' and qg ->• tq'b (245 pb) or through the s channel processes gb ->• Wt (60pb) and qq' -> tb (10pb). The largest contribution from the t channel is characterized by an isolated lepton, a b jet and a forward jet.

212

Single top production is an important test of the SM. Additionally the matrix element Vtb can be measured to the percent level and a less accurate but independent top mass measurement can be made 7,8 . 3.2. Top spin

correlations

Due to its fast decay, the spin information of the top quark is not diluted by hadron formation. When defining A as the asymmetry of finding top and anti top in the same or different polarization states, the SM predicts an asymmetry A = 0.31 at the LHC. In fully leptonic tt decays the angles 6*t± between the leptons in the top rest frames and the tops in the tt frame can be used to measure A, using 1

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polarization

Top decays offer the possibility to study W bosons in the longitudinal polarization state, only present for massive bosons. The SM predicts 70% of the W to be in this state, with the rest being left-handed. This prediction can be verified using the angle 6*t between the lepton in the W rest frame and the W in the top rest frame. In the right plot of Figure 2 the distribution of cos 6*t is shown at parton level for left and longitudinal polarization and the SM expectation. With 10 f b - 1 in the semileptonic decay, the fraction of longitudinally polarized W bosons is expected to be measured with a 0.023 statistical and a 0.022 systematic uncertainty 9 . 3.4. Other

topics

The tt cross section measurement is interesting in itself, but it is additionally sensitive to the top mass as 11 ml. Also differential cross sections are interesting to study: da^i/dpr and datt/dr] constrain PDFs and dati/dmti can be used to search for resonances, like heavy MSSM Higgs bosons. Many other measurements are being investigated within the framework of top physics. A non-exhaustive list of undiscussed topics: assignment of

213

Figure 2. Double differential distribution of cos 0*± for 30 fb 1 (left) and distribution of cos0£ at parton level for different W polarization states (right). the top charge, charged Higgs boson search in t -> H ± b , rare top decays and many detector related studies like b-tagging algorithm calibration. 4. Conclusions Top quarks will be copiously produced at the LHC, allowing for a broad physics program involving top quarks, already at startup of the accelerator. Many precision measurements will considerably increase our SM knowledge, and will be crucial for searches of physics beyond the SM. Acknowledgements I would like to warmly thank the organizers of this wonderful Institute, along with all collegues who helped me, in particular Michel Lefebvre. References 1. Homepage of the ATLAS collaboration: http://atlas.web.cern.ch/ 2. Homepage of the CMS collaboration: http://cmsinfo.cern.ch/ 3. The CDF collaboration, the D0 Collaboration and the Tevatron Electroweak Working Group, hep-ex/0404010. 4. L. Sonnenschein, CMS NOTE 2001/001. 5. I. Borjanovic et al, hep-ex/0403021. 6. A. Kharchilava, CMS NOTE 1999/065. 7. D. Green et al, CMS NOTE 1999/048. 8. A. Ahmedov et al, ATL-PHYS-2003-015. 9. L. Sonnenschein, PhD Thesis, 2001.

SPATIAL C O N F I N E M E N T A N D T H E R M A L D E C O N F I N E M E N T IN T H E COMPACTIFIED GROSS-NEVEU MODEL*

J. M. C. MALBOUISSONj F. C. KHANNA*AND A. E. SANTANA5 Department of Physics, University of Alberta, Edmonton, AB T6G 2J1, Canada [email protected], [email protected], [email protected] A. P. C. M A L B O U I S S O N 1 Centre

de Physique

Theorique,

Ecole Poly technique, [email protected]

91128 Palaiseau,

France

Spatial confinement is shown to exist for the compactified 3-D massive Gross-Neveu model at T = 0. Compactification is engendered through a generalized Matsubara mechanism. Raising the temperature, a deconfining transition occurs. The values of the confining length and the deconfining temperature obtained are comparable to the proton charge diameter and the estimated deconfining temperature for baryons, if the fermion mass is taken as the constituent quark mass.

The Wick-ordered massive Gross-Neveu model in a D-dimensional Euclidean space is described by the Lagrangian density 1 £ = : $(x)(i/8

+ m)iP{x) : + £ (: $(x)i/>(x) :) 2 .

(1)

Here x G R and tp{x) is a spin \ field having N (flavor) components, ij)a{x) (a = 1,2,..., N), summation over flavor and spin indices being implicit. We shall consider the large-A'' limit (N ->• oo), which permits considerable simplifications. In this paper, natural units (h = c = &B = 1) are used. This Lagrangian has been used in the literature as an effective model describing strong interactions. Our proposal in this note is to consider the •This work was supported by CNPq and FAPERJ (Brazil), and NSERC (Canada). Unstituto de Fisica, Universidade Federal da Bahia, 40210-340, Salvador, BA, Brazil t T R I U M F , 4004, Wesbrook Mall, Vancouver, BC V6T 2A3, Canada §Instituto de Fisica, Universidade de Brasilia, 70919-9700, Brasilia, DF, Brazil ^Centro Brasileiro de Pesquisas Fisicas, 22290-180, Rio de Janeiro, RJ, Brazil

214

215

effect of full compactification of the model in D = 3. The method is based on a generalization of the Matsubara imaginary-time formalism.2 This approach has been used to compactify field theories in spatial dimensions, considering the topology S1* x • • • x S 1 D , and has been used to treat the Gross-Neveu model at T = 0, compactified in one spatial dimension.3 Here we extend such a result to deal with the 3-D Gross-Neveu model at finite temperature, compactified in two space dimensions. To describe the fully compactified model, with Euclidean coordinates, say Xi, restricted to segments of length Lt (i = 1,2, ....£>) and the field %p{x) satisfying anti-periodic (bag model) boundary conditions, the Feynman rules should be modified following the Matsubara prescription

I

K g ' , ^HaptL. L

dki

(2)

Li

~2TT

n«=—oo

Then the X,-dependent four-point function at leading order in 1/N, at zero external momenta, has the formal expression .(4),-

~

,

.

«

(3)

where L^-dependent Feynman one-loop subdiagram is given by ^D({Li})

1

U

^ C

m 2 - £ i = i i/?

(4)

2

{n«}=-=o(E£l"?+"» )'

and Vi = 2(rii + |)7r/Lj. Introducing the dimensionless quantities 6» = (mLi)~2 and q — (2ir)~1, one can write ZD({bi})

=

mD-^'-1Wh---bD q Unis-AbM+^h—j

—

, (5) s=2

with zf(jr,b1,...M-YlZ?*fa-,4bi,...) »=i

+ ^

Zf

(»;...,4bi,...,4bj,...)----+(-l)dZ4d'>

(n;4bu...,4bd) (6)

216

where Z% (/^; {OJ}) is the multivariable Epstein-Hurwitz zeia-function.2 From now on, we restrict ourselves to the case of D = 3. Notice that, although the Gross-Neveu model is not perturbatively renormalizable for D > 2, it has been shown to exist and has been explicitly constructed for D = 3. 4 We will be considering fermions confined to a square box of side L (Li = Li = L) and at finite temperature T = / 3 _ 1 , with the confining length Lz = /?. Following similar steps as those for the T = 0 case,3 it can be shown after rather long calculations that the renormalized single-loop subdiagram is given by VR(L,P)

_ _ J_2_ lQg(1 + e_mL) + J _ i o g ( l + e-m0) + = 0 2TT

FI(JM)

m 4

I+1

*47r

e~m@

e-mL

- e[l +

mL

m ,+*(*.« +lr+f h e -= #

(7)

where Fr{L,P) = -2Gr{L,L)

+ 8Gr(L,2L)

- 8Gr(2L,2L)

-

4Gr(L,/3)

+8Gr{2L,P) + 8Gr(L, 2/3) - 16G r (2L, 20) +4Hr{L, L, /3) - 16Hr(2L, L, 2/3) - 8Hr(L, L, 2/3) +16Hr(2L, 2L, P) + 32Hr{L, 2L, 2/3) - Z2Hr{2L, 2L, 2/3), with the functions Gr and Hr (for r = 1,2) defined by "

Gr(x,y)

= 2_. (tnyx2™1

+ y2l2\

-2

exp (—m\Jx 2 n 2 + y2l2) ,

n,l=l oo

Hr(x,y,z)

)

= 2_. \jn\Jx2n2

2

+ y2l2 + z2k2 J

n,l,k=l

x exp ( —m^x2n2

+ y2l2 + z2k2 J .

Now, taking as usual Nu = A fixed and using Eq. (3), we obtain the large-iV effective renormalized coupling constant as

9^P,X) = NT»,L,P,u)=1 + JR{Ljy

(8)

Since l i m i ^ ^ o o S f i ^ , ^ ) = 0, we find that g(oo,oo,\) = A is the renormalized fixed coupling constant in free space at zero temperature. On the other hand, for either L -t 0 or /3 -> 0, T,R(L,/3) diverges implying that we have ultraviolet asymptotic freedom for short distances and/or for high temperatures, irrespective of the value of A.

217

Consider initially the situation at T = 0 (/? ->• oo); the behavior of Sfl(L), in this case, is shown in Fig. 1A. We find that T,R(L) is negative for L > L™in ~ 2.29 m - 1 and reaches a minimum ( E £ i n ~ -0.0624m) for Z, = L™ax ~ 3.13 m - 1 . This implies that, for A > Ac = - ( E ^ " ) - 1 ~ 16.03 m - 1 , \/g(L, A) has a non-positive minimum value and vanishes for a length L(c] (A) in the interval (L™n, L™ax]. This divergence of the effective coupling constant as L approaches Lh' (A) can be interpreted as the system being confined; that is, in the strong coupling regime (with large enough A), starting with L small (in the region of asymptotic freedom), the side of the square can not go above the length Lc° (A) since g(L,\) -4 oo as L -¥ Lrc'(\). Similar behavior has also been found for the 3D Gross-Neveu model compactified in a strip of width L at zero temperature. 3

0.1

0.08 0.06 0.04 0.02

-0.02 -0.04

Figure 1. A - P l o t of 5 = Sje(L, oo)/m as a function of mL. B - P l o t of G = \/g(L,(3,\) as a function of L, with A = 25.0 m 1 , for some values of /3: 3.0 m 1 , 2.34 m " and 2.2 m~1 (dashed, full and dotted lines respectively).

Let us now consider the effect of temperature, taking A > Ac. For )/ (0), low (fixed) T, \/g{L,/3,X) vanishes at a value Lf'(X) < L\- (u;0(A), its minimum (negative) value being slightly lower than the zero temperature case. Further raising the temperature, L c ' (A) and the minimum value of A/5 increase and, at the temperature ?d(A) = ^ 1 ( A ) , the minimum of \/g(L,/3,\) vanishes. For ft < /3d(A), X/g(L,(3,X) becomes positive for all values of L and then the system is unconfined. Thus, Td(X) corresponds to the deconfining temperature for the given fixed coupling constant A > Ac. The behavior of X/g is illustrated in Fig. IB. The above discussion demonstrates analytically that, in the strong coupling regime (A > Ac), the compactified 3D Gross-Neveu model presents simultaneously asymptotic freedom and spatial confinement. This can be

218 made clear if we consider a fermion-antifermion pair. Since we have just one color and g(L) is supposed to measure the intensity of the coupling between the constituents of the pair, which have colors of opposite signs, the potential between them is necessarily attractive. This means that, if we start with a system of a fermion-antifermion pair bounded within a square of side L (< LC(X)) at low enough temperature, it would not be possible to separate them a distance larger than Lc(\). This spatial confinement of the pair could be interpreted as the existence of bound ("baryon-like") states, characteristic of the model in the strong coupling regime. By raising the temperature, we find that the spatial confinement disappears at the deconfining temperature Td(\). To estimate the values of the confining length and the deconfining temperature, the fermion mass has to be fixed. Since, at most, the GrossNeveu model can be taken as an effective model for quark interaction, we will choose m « 350 MeV ~ 1.75 fm-1, the constituent quark mass. Taking for A the minimum strength for confinement, A = Ac ~ 16.03 m - 1 , we have Lc ~ 3.13m _ 1 « 1.79 fm. For this case, we find (3d — 2.76 m - 1 and so the deconfining temperature is T^ ~ 127 MeV. These values should be compared with the experimentally measured proton charge diameter (w 1.74 fm) and the estimated deconfining temperature ( « 200 MeV) for hadronic matter, respectively.5'8 The research is supported in part by the Natural Sciences and Engineering Research Council of Canada. JMCM thanks the Theoretical Physics Institute for partial support during his sabbatical stay at U of A. AES visited U of A for two months when part of this work was written. References 1. D.J. Gross, A. Neveu, Phys. Rev. D10, 3235 (1974). 2. A. P. C. Malbouisson, J. M. C. Malbouisson and A. E. Santana, Nucl. Phys. B631, 83 (2002). 3. A. P. C. Malbouisson, J. M. C. Malbouisson, A. E. Santana and J. C. da Silva, Phys. Lett. B583, 373 (2004). 4. C. de Calan, P.A. Faria da Veiga, J. Magnen, R. Seneor, Phys. Rev. Lett. 66, 3233 (1991). 5. Particle Data Group, Phys. Lett. B592, 1 (2004); see page 475. 6. S. G. Karshenboim, Can. J. Phys. 77, 241 (1999).

M E A S U R E M E N T S OF 7 IN BABAR

G. MARCHIORI (BABAR COLLABORATION) I.N.F.N. Sezione di Pisa, Largo B. Pontecorvo 3, 56100 Pisa, Italy E-mail: [email protected]

We report on the first measurements of the angle 7 of the Unitarity Triangle in B meson decays collected by the BABAR detector at the SLAC PEP-II asymmetricenergy B factory in the years 1999-2004.

1. Introduction A stringent test of the flavor and CP sector of the Standard Model can be obtained from the measurement, in B meson decays, of the sides and angles of the Unitarity Triangle, which are related to the elements of the Cabibbo-Kobayashi-Maskawa quark-mixing matrix V. Among the angles, VudV, v ytM is the most difficult to measure, since the B decay modes 7 = a rg that provide information on it are characterized either by very small branching fractions, small interference effects or low reconstruction efficiencies.

2. General strategies for measuring 7 from B meson decays 7 is the relative weak phase between the tree amplitudes b—tcuq, q — {s,d} (oc Vct,V*q), and b-^ucq (oc VubV*q), and can be measured using CPviolating B decays where the two processes interfere. Since no penguin amplitudes are involved, these approaches are unaffected by a large class of possible new-physics effects. In BABAR,1 B+B~ and B°B° pairs are produced in e + e~->T(45)->-B5 collisions at y/s = 10.58 GeV. The total amount of BB pairs collected in the years 1999-2004 is 232 x 106, equally divided into B+B~ and B°B°. Within this sample we search for CPviolation in B~^D^°K^(q = s) and B°-^D^±TT^ (q = d) decays. 219

220

3. Measuring 7 in charged B —> D^°K^

decays

Interference in charged B->D^°K^ decays occurs when D*°->D°ir0 or D°7, and the D° final state is also accessible to D°. This can be either a singly Cabibbo-suppressed CP eigenstate like K+K~ (GLW method 2 ), a doubly Cabibbo-suppressed flavor eigenstate like K+n~ (ADS method 3 ), or a Cabibbo-allowed multi-body state like K°S-K+-K~ (GGSZ method 4 ). By measuring the time-independent rates and CP asymmetries, 7 can be determined together with hadronic quantities (the ratio rs of the magnitudes of the B~-tD°K and B~-+D°K amplitudes and their strong phase difference 5B) that would otherwise need to be calculated from QCD. The 7-related experimental observablesa in the GLW method are: b =

r(B--^D°CP±K-)

+

r(B+^p°CP±K+)

T(B-^D0CP±K-)-T(B+^D0CP±K+) ~ T(B-^D°CP±K-) + T(B+->D°CP±K+)' =

CP±

l ;

where DQP± denotes a CP-even (+) or CP-odd (—) D° decay. The interference term sensitive to 7 is proportional to rs, which from CKM and color suppression is expected to be « 10%. The 7-related ADS observables are: c = ADS -

=

ADS -

r(B-^D°[K+n-}K-)

+

r(B--+D°[K-n+]K-)

+ T(B+^D0[K+IT-]K+)

T{B-^D°[K+TT-}K-)

-

r(B-_>£>o^+7r-]#-) + 0

T(B+^D°[K-Tr+]K+) '

{

'

(

'

T{B+->D°[K-TT+]K+)

r(B+^D°[K-K+]K+)' +

+

To extract 7, the quantity rD = \A(D ->K Tr-)/A(D°->K-7r )\ must also be known. The interference term is proportional to TBI^D = 0(1), but branching fractions are suppressed with respect to the previous case by a factor m 25. In the GGSZ method 7 is extracted from the Dalitz distribution, for positive and negative B->D°K candidates, of the D° decay products. d Interference and hence the sensitivity to 7 vary across the Dalitz plot. Branching fractions are 1-2 orders of magnitude higher than in previous cases, but a more complicated study is required and, within the present statistics, the full Dalitz D° decay amplitude must be known. "Here and throughout the text we write only the explicit formulae for b Rcp± = 1 + r\ ± 2rB cos7COS(5B, ACp± — ±2rB siwy sin 6B/RCp± C

# A D S = TB+T\>

+

2r

BrD

cos 7 cos S'B, A A D S = 2rBrD

s i n 7 sin S'B/RAUS,

B-^D°K. S'B =SB

+

arg[A(D° -> K+w~)/A{D° ->• K~-K+)] d A(B±-^D°[K^n+n-]K){m2_,m2+) <x [f(m2±,m\) + rBeiSB e±iri f{m\,m2±)]. m± are the K^n^ invariant masses, f{m^,m?_) is the Dalitz D°-+K®Tr+n~ amplitude.

221 In BABAR, the GLW analysis has been performed for the channels B-+D°CP±K (see Figure l ) , 5 B-+D%P±K*,6 and B^-DgP+K.7 The 0 0 ADS analysis has been performed for B-^D^°K, £>*°->£) 7r and £>°7, D°^-K+Tr~ decays. 8 The GGSZ analysis has been performed for B-+D^°K, D*°->D°Tr0 and D°1, D°^K0sit+vdecays.9 The full decay chains are reconstructed and B meson candidates with beam-energysubstituted mass (mEs) and center-of-mass (CM) energy (EB) consistent with TUB = 5.279 GeV/c 2 and \fs/2 are selected. Combinatorial background from e+e~-¥qq processes (q — u,d,s,c) is suppressed by exploiting the different CM topologies of BB (spherical) and qq (jet-like) events. Particle identification information allows to distinguish between B->D^°K and sw 12 times more abundant B-^D^TT decays. We reconstruct 93±15 B-*D°CP+[K+K-,-K+-K-]K and 76±13 B^D%P_[K%-K°]K 6 ± in a sample of 214xlO B , 35±7 B->D^P+[K+K~,n+'K-]K* and 15±6 B^D°CP_[K0sTr0,K%<j>,K°suj]K* in a sample of 227xl0 6 B±, and 30±7 B->D^p+[D%P+ir°]K, D^p+^K+K-,Tr+7rin a sample of 130xl0 6 B±. In the ADS modes no signal is found in a sample of 227xlO 6 B^. 282 ± 20 B^D°K, 83 ± 11 B^D*0[D0TT°]K and 40 ± 8 B^D*°[D°-f]K, ( + D°-^K g'K -K~ candidates are found in a sample of 211xl0 6 B±. The measured value of RCP, A-CP and RADS are summarized in Table 1; no A ADS measurement is possible with the current data sample, TD = 0.060±0.003 10 is measured on a clean sample of D*+—>D0TT+,D0—>KTT decays produced in e+e~—>cc events. In the GGSZ approach, the D°—>KgTr+rr~ amplitude is determined on a large, 97% pure sample of 81500 reconstructed D*+^D0TT+,D0^K^+TTdecays, and from the Dalitz distribution of D° mesons from B -> D^°K decays a 68% C.L. interval for 7 is found, up to a 180° ambiguity: 7 = (70 ± 26 ± 14)°. When combining this result with the information from the GLW and ADS measurements, the 68% C.L. interval for 7 - evaluated by the UTFit collaboration 11 - is, modulo 180°, 7 = (60 ± 29)° or 7 = (107 ± 6)°. The parameter rB is found to be < 0.16 for D°K and D*°K and < 0.74 for D°K* at 95% C.L.

Table 1.

Measured 7-related observables in B-^D^K^

D°K D°K* D'°(D°TT°)K

D*Q{D0~i)K

GLW and ADS analyses.

RCP+{%)

ACp+{%)

RCP-(%)

87±14±6

40±15±8

80±14±8

173±36±11

-8±20±6

64±25±7

106±26±10

-10±23±4

-

-

-

-

RADS(%)

ACp-{%) 21±17±7 -35±38±10

11 J3+1-1

-

"••••-o.e

- -0.9

-

1'-•'•-1.3 1+1-9

222

0.15 AE (GeV)

Figure 1. AE(= E'B -y/s/2) distribution of B-+D^p+K (right) and B-+D<£,p_K (left) candidates. Solid curves are projections of a maximum likelihood fit; dash-dotted, dotted and dashed curves represent the B-+D°K, B->£)°7r and background contributions.

4. Measuring 2/3 + 7 in neutral B° —> D^^ir^1

decays

B° — B° mixing can lead to interference between the (b-tcud) B°->D^~ir+ 12 + and (6->ucd) B°-^D^~TT amplitudes. When the other B from the same T(45) decay is reconstructed in a flavor-specific state (like D*+e~ve) and the proper time difference At of the two B decay instants is inferred from the measured distance between the decay vertices and from the known T(4S) boost (PT ~ 0.49), 2/? + 7 can be obtained from the time-dependent CP asymmetries: A±(At)

= ^0(A*HD(*>^) JV^A*)-^*)^) Ar(B°(Ai)->JD(*)±7r=F) + Ar(5°(A£)->£>(*)±7rF)'

^

where B°(At) means that the other B has decayed to a final state ach cessible only to B° and viceversa. Since /? = arg ' Vcdv: is accurately VtaV'. measured in neutral B° —¥ (cc)K^° decays (at present 073 « 1.5°), this leads to a measurement of 7. Branching fractions are at least an order of magnitude higher than in B —> D^K^*\ but the interfering amplitudes differ by a factor rB(D^7r) = \A(B0^D^-TT+)/A(B°^D^-T:+)\ = 0(1^6Kdl/l^cbV^I) « 0.02 and therefore the sensitivity to 7 is very small. In BABAR B°—>D*TT decays have been reconstructed on a sample of 89 x 106 B°B° pairs with a partial reconstruction technique. 13 The asymmetries A±(At) have been measured (see Fig. 2). From these asymmetries, fixing the value rB(D*Tr) = (1.5i°'.6 ± °- 5 )% obtained from the B°->D*+Tr~ and B°->D*~n+ branching fractions assuming SU(3) factorization, the limit I sin(2/3 + 7)| > 0.75(0.58) at 68%(90%) C.L. is found.

223

0.05

0

-0.05

-0.1

-10

-5

0

5

10 A t (PS)

Figure 2. B° —»• D*~-K+ time-dependent CP asymmetry for events in which the flavor of the other B is inferred from the charge of the high-momentum lepton produced in a semileptonic decay. Solid curves represent the projections of a maximum likelihood fit

5. Conclusions The angle 7 is the most difficult of the Unitarity Triangle angles to measure with B mesons. The interference terms sensitive to 7 are proportional to a small quantity TB (0.02 - 0.2 according to the B decay mode considered) . By combining several approaches BABAR has measured 7 with RJ 30° precision. The enlarged data sample available in the future and the measurement of additional 7-related observables will lead to a more accurate determination of 7, up to 12 — 15° by year 2008. A precise measurement of 7 is essential for a critical test of the Standard Model flavor sector. References 1. BABAR Collaboration, B. Aubert et al, Nucl. Instrum. Meth. A479, 1 (2002). 2. M. Gronau and D. Wyler, Phys. Lett. B265, 172 (1991); M. Gronau and D. London, Phys. Lett. B253 483 (1991); M. Gronau, Phys. Rev. D58 037301 (1998). 3. D. Atwood, I. Dunietz and A. Soni, Phys. Rev. Lett. 78, 3257 (1997); A. Bondar and T. Gershon, hep-ph/0409281. 4. A. Giri, Y. Grossman, A. Soffer and J. Zupan, Phys. Rev. D68, 054018 (2003). 5. BABAR Collaboration, B. Aubert et al, hep-ex/0408082. 6. BABAR Collaboration, B. Aubert et al, hep-ex/0408069. 7. BABAR Collaboration, B. Aubert et al., Phys. Rev. D71, 031102 (2005). 8. BABAR Collaboration, B. Aubert et al, hep-ex/0408028. 9. BABAR Collaboration, B. Aubert et al, hep-ex/0408088. 10. BABAR Collaboration, B. Aubert et al, Phys. Rev. Lett. 91, 171801(2003). 11. UTfit Collaboration, M. Bona et al, hep-ph/0501199 (2005). 12. I. Dunietz, Phys. Lett. B427, 179 (1998). 13. BABAR Collaboration, B. Aubert et al, hep-ex/0408038.

LEPTOGENESIS FROM P A R A M E T R I C R E S O N A N C E

B R U C E A. C A M P B E L L Department of Physics, Carleton University, Ottawa ON K1S 5B6, CANADA E-Mail: [email protected] DAVID W . MAYBURY Department of Physics, University of Alberta, Edmonton AB T6G 2J1, CANADA E-mail: [email protected]

The concordance of experimental observations on neutrino oscillations strongly favours the existence of neutrino mass. The supersymmetric see-saw mechanism not only provides neutrinos with light masses, but also supplies a natural mechanism for leptogenesis and hence the baryon asymmetry of the universe. CP violating effects in the lepton sector can produce a lepton asymmetry that becomes transferred to the baryon sector via sphaleron reprocessing. We will show from preliminary investigations that non-perturbative resonant production of sneutrino singlets from coherent infiaton decay can generate the BAU while avoiding the gravitino reheat bounds, even in the event that the sneutrino singlets are heavier than the infiaton mass (> 10 12 GeV) and Hubble dilution effects are ignored.

1. Introduction The solar and atmospheric, neutrino deficit observations, which imply neutrino mass and mixing, (and their confirmation by reactor, and accelerator experiments), presently provide the only direct observation of physics that cannot be accommodated within the Standard Model. The smallness of the inferred neutrino masses can be understood through the see-saw mechanism and in particular its supersymmetric extension, which involves the introduction of a heavy gauge singlet chiral superfield, containing the (s)neutrino singlet (UR, VR), for each generation. The light neutrino masses are then induced through a Yukawa interaction of the form N?Yvl° LjH, once the right-handed neutrinos are integrated out at the Majorana scale, MR ~ 1014 GeV, and once the Higgs acquires its vev. Assuming that the lepton sector contains CP violating phases, the supersymmetric see-saw can 224

225

also be used as a mechanism to generate the baryon asymmetry of the universe (BAU), 7js ~ 1 x 10~ 10 , via leptogenesis. The out-of-equilibrium CP violating decay of the (s) neutrino singlets produces a lepton asymmetry, s s where e is the CP asymmetry parameter given by, e = 6l

T(vm -+L + HU)- T{uRi ^L + Hu) T{vRi -+L + HU) + T{vRi -> L +

ffu)

U

and where I/JU, L, Hu denote both fermionic or scalar components of the corresponding supermultiplets along with L, Hu denoting the anti-particle states. Non-perturbative sphaleron effects arising from the weak SU(2) anomaly convert the lepton asymmetry, r/i, to a baryon asymmetry, VB

= ar)L

(3)

where a = - 8 / 2 3 in the MSSM. In thermal (s)neutrino production models (see for example 1'2 and references therein), integrating the Boltzmann equations determines the righthanded (s)neutrino number densities and hence the BAU. However, even if we assume a strong neutrino mass hierarchy and that the lightest righthanded (s)neutrino provides the dominant contribution to the CP asymmetry parameter, we will typically require M\ ~ 109 GeV resulting in a reheat temperature of Treheat > 108 - 1010 GeV in order to fit the neutrino oscillation data and to generate the BAU 3 . The gravitino overproduction bound, Treheat-gravitino ^ 109 - 1012 GeV, presents a problem for thermal production models within the supersymmetric see-saw over much of the available parameter space. 2. Parametric Resonance and VR It has been realized that the standard perturbative treatment of reheating with single particle inflaton decay may not provide the dominant mechanism for early universe particle production 4 . In the case where the inflaton is coupled to bosonic fields, coherent oscillations of the inflaton field can lead to a coherent enhancement of the transition to bosonic decay products. This process, called parametric resonance or pre-heating, leads to the exponential growth of mode occupation numbers of the product bosonic fields resulting in the non-thermal development of large number densities. Thus, parametric resonance may afford supersymmetric see-saw models of

226

leptogenesis a method for generating the BAU while evading the gravitino reheat bounds. As we are addressing the supersymmetric see-saw, we consider a complex inflaton, cj>, coupled to a complex scalar sneutrino field, PR through the superpotential term, W D g$NN.

(4)

In supergravity models with broken supersymmetry, phase dependent Aterms in the scalar potential can induce a torque on the inflaton field such that an out-of-phase fraction develops. Phase dependent terms also generically arise in minimal supergravity models for inflation 5 which can have the same effect. After the phase dependent terms cease to be efficient, the resulting out-of-phase fraction remains approximately constant. Following 6 , we can parameterize the out-of-phase fraction of the inflaton by, <j)(t) = $(i) sin(m^t) + if${t) cos(m$t)

(5)

where / is a constant confined to the interval [0,1] and $(£) denotes the amplitude of the real component of the inflaton field. The mode expansion of VR becomes, Xk + ( ^ + m2PR + f2g2$(t)2

+ (1 - / V * W

2

sin 2 (m 0 t)) Xk = 0

(6)

which can be re-written as a Mathieu equation, X* + (^fc-2 9 cos(2z))xfc = 0

(7)

with z = m^t

Ak = q

~

fc2/«2 + m l R + / V $ ( f ) 2 , o -j +2g

4^J

•

(8)

The Mathieu equation has exponential growing solutions which are often characterized by the stability/instability band structure in A^, q space. These growing solutions lead to explosive particle production and hence large co-moving number densisties of sneutrino singlets. The condition for resonant sneutrino production requires a departure from adiabaticity.

227

Following the semi-analytical approach of 4 , the violation of adiabaticity in this case reads, - m\R - fg2M2P

^—^gMpm*

> 0

(9)

which, assuming m^ ~ 10 -6 Mpi an k, leads to a condition on the out-ofphase fraction parameter, ~

/ v

l + 47r 2 (m i > H /m^) 2 '

Parametric resonance ends when q ~ 1/4. There are essentially two stages to parameteric resonance distinguished by whether or not back reaction effects are important. If parametric resonance ends during the first stage, back reaction effects are negligible and lead to the constraint g < 10~ 3 . If parametric resonance enters the second stage before ending, back reaction effects must be taken into account and again a condition on g appears, g > 10~ 3 . For illustrative purposes, we will only consider first stage resonance as our preliminary investigation indicates that second stage resonance typically leads to excessively high reheat temperatures. In our simple model, we assume prompt decay of the sneutrinos which results in the energy density relations p ~ paRK m-VRn-VR ~

200 _ ,

JJQ^TR.

(11)

This is a somewhat unrealistic assumption since the particulars of a given see-saw model determine the Yukawa couplings and hence the decay rate. In general Hubble dilution model dependent effects will be present which will generically lower the reheat temperature. In our preliminary investigation we have not taken these effects into account. For numerical results based on the semi-analytical approach of 4 , see the panels in figures 1 and 2. 3. Conclusions Our preliminary investigation of parametric resonance in our toy supersymmetric see-saw model with the superpotential term g$NN shows that, even in the worst case scenario where Hubble dilution effects have been ignored and large sneutrino singlet masses {moR = (2 — 5)m,f,) have been assumed, much of the available parameter space generates the BAU within two orders of magnitude of the gravitino overproduction bound and with an acceptable CP asymmetry parameter of e ~ 1 0 - 8 . It is plausible that given

228

Figure 1. P a r a m e t e r i c r e s o n a n c e e n d i n g in first s t a g e — mpR = 2m^: CP asymmetry parameter and reheat temperature as a function of the coupling g consistent with the BAU and over the available parameter space provide by eq.(10). The lower bound indicated in the second panel indicates the gravitino overproduction bound.

Figure 2. P a r a m e t e r i c r e s o n a n c e e n d i n g in first s t a g e — mpR = 5m,j,: CP asymmetry parameter and reheat temperature as a function of the coupling g consistent with the BAU and over the available parameter space provide by eq.(10) The lower bound indicated in the second panel indicates the gravitino overproduction bound.

a more realistic model where see-saw Yukawa coupling Hubble dilution effects are included, the reheat temperatures will come below the gravitino overproduction bound for most of the available parameter space. Thus, parametric resonance combined with supersymmetric see-saw leptogenesis may provide an excellent avenue for realistic mechanisms that generate the BAU. References 1. W . Buchmuller (2001), [arXiv:hep-ph/0107153]. 2. W . Buchmuller P Di Bari, a n d M. P l u m a c h e r , New J. P h y s . 6 (2004), 105. [arXiv:hep-ph/0406014]. 3. S. Davidson, a n d A. I b a r r a , P h y s . L e t t . B 5 3 5 (2002), 25-32. [arXiv:hepph/0202239]. 4. L. Kofman, A. Linde, a n d A. A. Starobinsky, P h y s . R e v . D 5 6 (1997), 32583295. [arXiv:hep-ph/9704452]. 5. M. Dine, L. R a n d a l l , a n d S. T h o m a s , Nucl. P h y s . B 4 5 8 (1996), 291. [arXiv:hep-ph/9507453]. 6. R. Allahverdi, B . A. C a m p b e l l , a n d R . H . D . Shaw, P h y s . L e t t . B 4 7 3 (2000), 246-257. [arXiv:hep-ph/9909256].

C U R R E N T S O N S U P E R C O N D U C T I N G S T R I N G S IN A N UNUSUAL ENVIRONMENT

MAX A. METLITSKI Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada E-mail: [email protected]

It is well known that fermion zero modes concentrated in the core of a topological defect can endow the defect with highly nontrivial physical properties. A particular example of this phenomenon due to Witten, is the so-called string superconductivity, when an application of an electric field along the string leads to an appearance of a persistent current in the string direction. In this talk, I will show that a current along the string can also be induced by placing the string in an environment with a non-zero fermion chemical potential and temperature. The resulting current is exactly calculable and topological in nature. I will also discuss how the interest in this problem was motivated by the study of topological defects in dense quark matter.

Topological defects are fascinating objects in field theory, which generically arise when some symmetry of the theory is spontaneously broken leading to a topologically non-trivial vacuum manifold. One example of a topological defect is a string. As the name suggests, strings are line-like objects, which appear when the vacuum manifold of the theory has noncontractible loops. Moving in a circle around the core of the string, one traces out a non-trivial loop in the vacuum manifold. In many cases, the long range topological properties of the defect lead to a rich internal structure. For instance, if one couples fermions to a topological defect in a certain manner, fermion zero modes appear in the defect core. The presence of such fermion zero modes often makes the defect carry quantum numbers associated with the fermions, most commonly fermion number or electric charge. In many models, the fermion number appearing on the defect is exactly calculable and topological in nature, in the sense that it depends only on the boundary values of the background fields and not on the particular details of the defect profile. 229

230

It has been first shown by Jackiw and Rossi1 that fermion zero modes can appear in the string core. Moreover, in his famous paper 2 , Witten has noted that such zero modes are free to move along the string leading to the phenomenon of string superconductivity. This means that an application of an electric field in the string direction, excites the fermion zero modes in the string core causing them to move along the string, inducing an electric current. Such an electric current would grow linearly with time while the electric field is turned on and will persist even after the field is turned off. The string, thus, becomes superconducting. There is, however, a caveat to the above description. Namely, if the current along the string exceeds a certain critical current, whereby the momenta of the fermion zero modes in the string core become comparable to the fermion mass at infinity m, one loses the analytical control of the problem. One expects that at the critical current it will become energetically favorable for the fermion zero modes to move off the string and the superconductivity will be quenched. The purpose of this talk is to describe the recent investigation 3 of a very different mechanism for inducing a current along the string. Namely, I consider the properties of Witten's strings in an environment with a finite fermion chemical potential n and temperature T. I show that for any value of the chemical potential and temperature, the current along the string can be calculated exactly and the result is topological in nature: at fixed values of fi and T, it depends only on the winding number of the string n, the magnetic flux through the string $ and fermion mass at infinity m. This result is quite curious from a theoretical viewpoint. Indeed, most previous works on the subject of quantum numbers on topological defects analyzed the fermion number, and found that although at zero chemical potential one could often calculate this topological quantity exactly, at finite chemical potential the fermion number becomes difficult to compute exactly and acquires non-topological contributions. I show that if one, instead, focuses on the current along the string, one obtains an exactly calculable and topological result for any value of the chemical potential and temperature. The physical motivation for analyzing the superconducting string in the background with a non-zero fermion chemical potential originally came from studying the so-called "Condensed Matter Physics of QCD? It is wellknown that at large baryon chemical potential, the ground state of QCD develops a diquark condensate, which spontaneously breaks the SU(3) color symmetry, as well as a number of global chiral symmetries. Such a state of matter may be realized in our universe in the dense interiors of neutron

231

stars. From a theoretical standpoint the dense quark matter with its large array of spontaneously broken global symmetries offers a wonderful thought laboratory for the study of topological structures (some of which may be relevant for neutron star physics). In particular, in the case of both two and three light quark flavors, it is believed that at sufficiently large baryon chemical potential, the axial U(1)A symmetry of QCD becomes spontaneously broken. As a result a light pseudo-Goldstone boson 77' appears, and strings associated with the spontaneous breaking of the U(1)A symmetry may exist. Recently, it was shown4 that such strings will carry an electric current given by, T _ V ^ eatJ-an Qa a

m

^

Here, the sum is over all the quark species, ea are the quark electric charges, /i a are the quark chemical potentials, n is the winding number of the string and ^ is the flavor content of the condensate supporting the axial string. This result was obtained 4 using a technical trick of fictitious chiral anomalies, which is not sensitive to the microscopic details of QCD and only depends on the pattern of spontaneous symmetry breaking and the existence of U(\)A strings. Thus, our goal is to understand the microscopic origin of the result (1) using the model of superconducting Witten's strings at finite chemical potential. The simple model in which Witten's strings arise is described by the Lagrangian,

C = JH-f^ - ieA„ -lJRrf)i>- ^ ( ^ i ± 2 l + 4}-^)^

(2)

Here A^ and i?M are gauge fields and <j> is a complex scalar field. The Lagrangian (2) has the following classical gauge symmetries: U{1) : ip ->• e iea ( a >V, Ali^Ali+ U(l) : V -»• e W ^ ' V , Rli^Rll+

d„a, 4> -> 4> 0^8, -> e ^ V

(3) (4)

The vector (7(1) symmetry and the A^ field are conventionally associated with electromagnetism. On the quantum level, the U(l) x U{\) symmetry suffers from chiral anomalies, which can, however, be removed by adding more fermion species to the problem. Alternatively, one can consider the C/(l) symmetry to be global, in which case the R^ field is absent and the theory is well-defined. We assume that the U(l) symmetry is spontaneously broken, the <j> field acquires a non-zero expectation value and strings of the fieldare possible.

232

We wish to consider the fermion tp in the background of an infinitely long static string uniform in the z direction. The string is characterized by a non-zero winding number n of the scalar field: f d l a <j>*da<j> n

J 2ni |0|2

^

j

where the integral is over a contour in the xy plane at infinity. If the i7(l) symmetry is local, then in most models the condition that the string energy is finite, implies the quantization of the string flux: $

= £f(fxeabRab

=n

(6)

Our objective is to calculate the expectation value of the electromagnetic fermion current in the string direction, J = e /"d 2 x(^7 3 V>

(7)

at finite fermion chemical potential // and temperature T. To do this, one first needs to find the spectrum of fermions in the string background. The most remarkable feature of the spectrum is that it has fermion zero modes, with energies, N+ : E = +k,

N-:E

= -k

(8)

Here, k is the momentum of the fermion mode along the string and N+, N^ denote the multiplicities of the modes. It can be shown that the difference between the number of "up-movers" and "down-movers" is given exactly by the winding number of the string, N+-N-=n

(9)

The rest of the fermion spectrum is gapped and has the dispersion, E = ±Vk2

+ A2

(10)

where the gap, given by the minimal value of |A| is of order of the fermion mass at infinity m = h\((j>)\. Thus, at low energies, the theory reduces to a 1 + 1 dimensional theory of chiral fermions living on the string. In particular, at small values of chemical potential (i < m, only the fermion zero modes contribute to the current along the string. Since the zero modes are chiral, their contribution to the electric current is particularly simple, and we find,

233

This agrees exactly with the result (1) based on the effective Lagrangian treatment and fictitious axial anomalies, which was first obtained in the context of dense QCD 4 . It is a little more surprising that one can calculate the current along the string for any value of chemical potential and temperature, when the nonzero modes contribute to the current. Indeed, the contribution of a gapped mode with energy E and momentum k to the current can be shown to be proportional to k/E. However, since the dispersion of the gapped modes is symmetric with respect to the interchange k —• — k, one expects that the contributions to the current of gapped modes moving with opposite momenta along the string cancel. For the case of local strings, obeying the flux quantization condition $ = n, this cancellation is, in fact, exact. Hence, for all /i and T the electric current is saturated by zero modes alone and given by the simple result (11). Note that the current (11) is temperature independent, which is due to special properties of chiral fermions in 1 + 1 dimensions. For global strings, the story is slightly more complicated. The long range nature of global string fields, implies some subtleties related to the density of continuum states, and the cancellation between contributions to the current of gapped modes is not exact. However, the current along the string still remains exactly calculable3 and one finds that the zero mode result (11) receives a modification from certain polarized modes at the continuum threshold. The resulting electric current at T = 0 becomes, PTI

i

J=—fa-0{n-m)y/i?=rt)

(12)

In conclusion, note that the current along the string at fixed values of chemical potential and temperature is topological in nature, depending only on the string winding number n, the magnetic flux through the string $ and the fermion mass at infinity m. It is precisely the fact that the current turns out to be topological that allows for its exact evaluation. References 1. 2. 3. 4.

R. Jackiw and P. Rossi, Nucl. Phys. B190, 681 (1981). E. Witten, Nucl. Phys. B249, 557 (1985). M. A. Metlitski, Phys. Lett. B612, 137 (2005). D. T. Son and A. R. Zhitnitsky, Phys. Rev. D70, 074018 (2004).

SEARCH FOR TECHNICOLOR AT LEP

N. M E Y E R * DESY -FLC22603 Hamburg, Germany E-mail: [email protected],

edu

This talk summarizes the searches for Technicolor signatures in electron-positron collisions with center-of-mass energy up to 209 GeV at LEP. No excess over Standard Model background is observed, hence mass limits on Technicolor resonances Pre and 7TTc are given at the 9 5 % confidence level. Using measurements of the cross section of W-boson pair production, a lower limit Mp > 600 GeV for the mass of Technicolor vector resonances is reported by the ALEPH collaboration. Interpretations of direct search results in the framework of the Technicolor Strawman Model, performed by the DELPHI and OPAL collaborations, yield a best lower limit MK > 79.8 GeV for the mass of scalar resonances and exclude vector states in the range 90 < Mp < 206.7 GeV.

1. Introduction The formation of strongly bound fermion condensates breaks chiral symmetry. Corrections to the W propagator from these condensates introduce effective mass terms and thus break electroweak symmetry. This dynamical symmetry breaking is already realized in Quantum Chromodynamics (QCD), however it yields a W-mass of only M w « SOMeV1. The measured W-mass could be explained with the same mechanism by a new strong interaction with a higher intrinsic energy scale. This concept is referred to as Technicolor (TC) 1 and comes along with the prediction of new TC fermions, which carry TC charge. Couplings between TC and SM fermions requires extended Technicolor (ETC) 2 , that is new gauge interactions at even higher energies. Analog to W-mass generation through Technicolor, ETC gives rise to fermion masses. Technicolor theories usually require additional modifications to be compatible with recent measurements, such as top color assisted TC to account *Now: The University of Iowa, SLAC, 2575 Sand Hill Rd, Menlo Park, CA-94025, USA

234

235

for the large mass of the top quark or walking TC (a slow evolution of the couplings with energy) to suppress flavor changing neutral currents. Due to this complexity, QCD inspired low-energy effective models are used for TC searches at LEP.

2. Search for Strong Interaction in W-Production The Goldstone bosons of chiral symmetry breaking in QCD are the ordinary QCD pions IT. The cross section for pion pair production is enhanced + by the presence of the p resonance via e+«e In Technicolor, the Goldstone bosons of chiral symmetry breaking are the longitudinal polarization states W i of the weak gauge bosons. In analogy to QCD, an enhancement of the cross section for e + e~ —> W j W £ is expected from a TC vector resonance p TC . In both cases, the additional contributions to the pair production cross section can be parameterized by a complex form factor FT, which is a function of mass Mp and width Tp of the intermediate resonance: FT

=

M£ - iTpMp

Ml

iTpMp'

(1)

where s is the center of mass energy.

0

200 400 600 800 1000 1200 1400 1600 1800 M 0 (GeV)

Figure 1. a) Shows the measurement of FT (shaded ellipse) and the physically allowed range from one-sided 9 5 % confidence levels (solid shaded triangle). The latter region translates to the shaded area in the Mp — Tp plane as shown in b). The white region indicates exclusion at 95 % confidence level.

236

The ALEPH collaboration performed a fit of FT to the cross section measurement of e + e - —> W + W ~ based on 683pb _ 1 of data recorded at y/s = 183 — 209 GeV 3 . Fig. la) shows the measured 95% confidence level contour for FT as shaded ellipse. However, as long as Mp > y/s, only values RC{FT) > 1 and Im(FT) > 0 are sensible. This assumption translates into the one-sided 95% confidence level contour shown as solid shaded triangle. The corresponding parameter space in the Mp — Tp plane is shown in Fig. lb), indicating that the white region is excluded at 95% confidence level. A lower limit Mp > 600 GeV is placed for Tp < Mp. 3. Search for 7rTC and p T C in the T C S M The Technicolor Strawman Model (TCSM) 4 is an effective low energy Techniclolor theory with richer phenomenology. It considers scalar and vector resonances of TC fermions, named technipion 7rTC and technirho pTC. The technipions mix with the longitudinal states W i of the weak gauge bosons to form TC eigenstates, where the mixing angle x is related to the number ND of TC fermion doublets via sinx — l/y/No- A large number No is favored by theoretical arguments, since this naturally causes a slow evolution of the TC couplings and suppresses flavor changing neutral currents. This corresponds to the scenario where the TC eigenstates have only small W L admixtures and thus is complementary to the Technicolor model used in the previous section, where the TC eigenstates are pure Goldstone bosons. Table 1. Processes used by the DELPHI and OPAL collaborations to search for technipion and technirho production. Channel "

"

e+e~

' ^TC

DELPHI

OPAL

TC

—• 7TTCWJ

e + e - - • ^r C — W + W ~

x

X

e + e - —> /9TC —> qq

X

e+e~ —> PTO —> 77r5c

X

X

The DELPHI and OPAL collaborations have used the TCSM framework to interpret searches for TC particles in a variety of modes listed in Tab. I 5 ' 6 . Figure 2 shows the excluded mass regions in the Mn — Mp plane based on 452pb~l at y/s = 192 - 208 GeV for the DELPHI results and 209.4 p b " l at y/s = 200 - 209 GeV for those from OPAL.

237

3.1. Search for 7rTC Technipions nTC decay via extended Technicolor interaction to pairs of SM fermions. The couplings are proportional to the mass square of the final state fermions, resulting in almost exclusive decays 7r^Tc —• bq with q = u, c and 7r°c —» bb. In e + e _ collisions, charged technipions are produced pairwise or in association with a Wx, boson. The production cross section is significantly enhanced by an intermediate pTC resonance for collision energies yfs « Mp. In the limit of Mp —* oo, the cross section at a given collision energy is finite and depends only on M„ and No- This enables to place absolute mass limits M„ > 79.8/62 GeV at 95 % confidence level from DELPHI and OPAL, respectively. These limits are obtained for ND = 2, and improve to 89.1/77 GeV for ND = 9. For the latter case, the excluded parameter space in the Mv — Mp plane is shown in Fig. 2.

r

H e'e'-MtjjtjjitjW,.

£.120

oV->p^7): g=j pT->hadrons B(y-»WtK.

2

- i

, - • --

.

|

•

|

,

!

i

|

OPAL Preliminary Dn'/y

tobyM^OOGeV

D.T ','Y-^bbYM^lOOGeV Drt7

rc.j.-»bqbq'

N„=9

r

t

excluded 300

350 tOO MlPr) [GeV/c 2 ]

250 300 350 400 450 500 550 600

mp/OJ [GeV]

Figure 2. Excluded parameter space for T C searches in the TCSM framework by DELPHI (left) and OPAL (right). Mass limits at 95 % confidence level are shown assuming ND = 9 technifermion doublets.

3.2. Search for p T C Technirhos are produced as s-channels resonance and decay into a large variety of final states. Searches are performed in the decay modes pTC —* qq, PTC —• W + W ~ , and p TC —> 7r5c7. The decay mode pTC —> 7r5c7 depends on a mass parameter My and the charge sum Q from the particles in one

238

technifermion doublet. These are free parameters of the model and prohibit model independent mass limits. From the other channels, the mass range 90 < Mp < 206.7 GeV is excluded at 9 5 % confidence level by the DELPHI results. The corresponding parameter space is also shown in Fig. 2. 4. Summary The electroweak measurements at LEP are in good agreement with the predictions of the Standard Model. Based on these results, limits on effective Technicolor models can be derived under different assumptions. The contributions of a TC vector resonance pTc to the cross section of e + e - -> W + W - yield a lower limit of Mp > 600 GeV at 95 % confidence level as reported by the ALEPH collaboration. The model used assumes no mixing between Wj, bosons and hypothetical TC mass eigenstates. The DELPHI and OPAL collaborations interpret direct searches for scalar and vector resonances 7rTC and p TC , respectively in the framework of the Technicolor Strawman Model. Due to larger theoretical freedom in this low-energy effective description, the mass bounds on the particles are weaker. DELPHI published an upper limit Mv > 79.8 GeV and excludes the mass range 90 < Mp < 206.7 GeV at 95 % confidence level. The OPAL collaboration is still finalizing the results and reports a preliminary limit of Mv > 62 GeV at 95 % confidence level from a reduced data set. References 1. S. Weinberg, Phys. Rev. D19, 1277 (1979); L. Susskind, Phys. Rev. D20, 2619 (1979). 2. S. Dimopoulos and L. Susskind, Nucl. Phys. B155, 237 (1979); E. Eichten and K. Lane, Phys. Lett. B90, 125 (1980). 3. S. Schael et al. [ALEPH Collaboration], Phys. Lett. B 614, 7 (2005). 4. K. D. Lane, Phys. Rev. D 60, 075007 (1999). 5. J. Abdallah et al. [DELPHI Collaboration], Eur. Phys. J. C 22, 17 (2001). 6. The OPAL Collaboration, OPAL Physics Note PN485, 2001.

SEMILEPTONIC DECAYS FROM B A B A R

AJIT K MOHAPATRA* 2575 Sand Hill Road, SLAC Menlo Park, GA 94025, USA E-mail : [email protected]

A summary of the measurements of the CKM matrix elements \Vcb\ and \Vut,\ using semileptonic B decays at BaBar is presented. While |VJ.(,| is measured with an accuracy of ± 2 % , the measurement of \Vui,\ is limited to an accuracy of ±10%, and is currently dominated by the theoretical uncertainties.

1. Introduction Accurate determination of |VC(,| and \Vub\, the CKM matrix elements that govern the b —>• c and b —> u weak transitions, play a critical role in testing the consistency of the Standard Model description of CP violation. Semileptonic decays of the B mesons provide the best access to these quantities as the leptonic current can be cleanly factored out from the hadronic. Parton level distributions from inclusive semileptonic decay (6 —> c and b —>• u) gets impacted by the "shape function", i.e., the distribution of the b quark momentum inside the B meson 1 , in addition to other effects. The decay rate can be estimated by operator product expansion (OPE) technique. OPE breaks down near the upper kinematic limit of lepton momenta due to non-perturbative effects in the theoretical prediction. OPE in the limit of heavy quark symmetry can be used to calculate the QCD corrections needed for the prediction of the inclusive rate T(B —> Xclv), where Xc refers to any hadronic system with a charm quark. Experimental observables i.e the moments of the lepton energy (E() and charmed hadron mass (nix) distributions can be calculated using OPE provided that the quantity in question is integrated over a large region of the phase space. These observables can be used to extract the branching fraction B —> Xc£u and \Vcb\*On behalf of the BABAR Collaboration.

239

240

2. Measurement of \Vcb\ The following eight moments are measured in the BABAR data : M

°~

rB '

1 _

JdT '

i _

JdT

V-Z>6h

(1)

where TB is the total B decay rate and cfl? is the differential B -> Xctv decay rate. The integrations are done in the phase-space region in which Ei is greater than an energy threshold Ecut. 2.1. Measurement

of the lepton-energy

moments

The lepton-energy moments were measured 2 using electrons found in the BABAR data that correspond to 47.4 / 6 _ 1 on the T(4S) resonance and 9.1 / & _ 1 below. The selected events were required to have two electrons: one with a large center-of-mass momentum identified the event as a likely T(45) -> BB decay with a B -> Xlv decay; the other was used to measure the lepton energy spectrum. The charge and angular correlations between the two electrons were used to separate the contribution of the primary B -)• Xcev decays from the other sources. After correcting for the experimental efficiencies and for the Bremsstrahlung in the detector material, four moments Mf were calculated with Ecut varying between 0.6 and 1.5 GeV. Corrections were applied for the difference between the T(45) and B rest frames, for the effect of the final state photon radiation, and for the B -> Xulv decays. 2.2. Measurement

of the hadron-mass

moments 3

The hadron-mass moments were measured in 81 fb~1 of on-peak BABAR data. Only those events were selected in which one of the B meson was fully reconstructed {Breco) in a hadronic decay channel. The remaining part of the event contains the other B meson (Brecou), whose flavor (except for B°-B° mixing) and momentum are known by the conservation laws. The Brecou sample was used to search for a lepton accompanied by a missing 4-momentum compatible with a neutrino. The invariant mass of the hadronic system was determined by a kinematic fit assuming the 4-momentum conservation, equal mass of the B mesons, and zero neutrino mass. Residual bias in the measured mass, due mainly to the undetected

241

particles, was corrected using Monte-Carlo simulation. Four moments M* were calculated with Ecut varying between 0.9 and 1.6 GeV. 2.3. Fit to the Moments

and extraction

of \VCb\

The value of \Vcb\ along with the masses m&, m c and several nonperturbative parameters were obtained from a simultaneous fit to the moments of lepton-energy and hadron-mass 4 in the kinetic-mass scheme 5 , \Veb\ = (41.4 ± 0 . 4 exp i 0-^HQB i 0.6th) X 10 This measuremet is conistent with the present world average value obtained from exclusive B semileptonic measurements 6 . 3. Measurement of |V^b| It is experimentally challenging to separate the b -> uiv decays from the more abundant b —> civ decays. Selection criteria applied to achieve this separation generally make the theoretical extrapolation to the full decay rate more difficult. Experimentally, inclusive B —> Xuiv decays can be studied using three independent kinematic variables : lepton energy (Ee), hadron mass (mx), and invariant mass of the i and v combination (q2). Four different techniques based on the above variables are used to measure \Vub\ with BaBar data, as described below. 3.1. Lepton End Point

(Ei)

The inclusive electron-energy spectrum was measured 7 using electrons found in the BABAR data that correspond to 81.4 fb^1 on the T(45) resonance and 9.6 fb_1 below. Electrons in the momentum range of 2.02.6 GeV were selected for this purpose. The raw electron spectra from T(45) was subtracted from the non-resonant continuum backgrounds using both ON- and OFF-resonance data [ref]. The BB background from the dominant B —> Xcev decays and backgrounds other than B —> Xuev processes were subtracted using Monte-Carlo estimations. After correcting for the experimental efficiencies, the Bremsstrahlung in the detector material and final state radiation the final electron spectrum was obtained in the momentum range of 2.0-2.6 GeV, from which the partial branching fractions (BF)for B —> Xcev decays was obtained. Using the shape function parameters from the Belle b —> sj measurement, the partial branching fraction was translated to the total branching fraction for B —» Xuev which was then used to calculate \Vub\ which is given in Table 1.

242

3.2. Ei vs q2 Semileptonic B decays were selected using energetic electrons and simultaneously making requirements on q2, the invariant mass squared of the ev pair 8 . The neutrino 4-momentum is reconstructed from the visible 4momentum and knowledge of the e+e~ beam momenta. The dominant charm background is then suppressed by selecting a region of the q2-Ee phase space where properly reconstructed B —\ Xcev events are kinematically suppressed. Background contamination in the signal region is due to resolution effects and was evaluated by Monte Carlo (MC) simulations. The fraction of B —> Xueu phase space accepted was RJ 15%. The value of \Vub\ obtained with data corresponding to 81.4 fb"1 on the T(45) resonance and 9.6 fb"1 below is given in Table 1. The theoretical uncertainty on the determination of \Vub\ arises from limited knowledge of the 6-quark mass and the non-perturbative shape function.

3.3. Hadron mass

mx

Selection of BB events was based on the criteria in which one of the B mesons decays hadronically and was fully reconstructed (Breco)Q. The semileptonic decay of the recoiling B meson (Brecou) was detected by a charged lepton above a threshold momentum. Requirements on various kinematic correlation between the lepton and the B flavor was used to reduce contamination from events in which some of the hadrons accompanying the lepton and the neutrino go undetected. The invariant mass mx of the hadronic system recoiling against the t and the v was estimated from the remaining particles in Brecou. A binned x2 fit to the mx distribution was performed to subtract the MC modelled B -» Xcev and other backgrounds. The number of B —> Xueu signal events were extracted from the fit for mx < 1-55 GeV/c and used to derive the ratio of branching fractions Br(B -»• Xulv)I'Br(B -> Xlv) and to determine |VU|,| which is given in Table 1. The fraction of B —> Xuev phase space accepted was between 7080% of the total charmless semileptonic decays, thus considerably reducing acceptance corrections. But the extraction of |VU(,| is systematically limited by the dependence on the shape function.

3.4. mx

vs q2

In this method the variable q2 is used in combination with the mx in order to reduce the dependence on the shape function 9 . Following an event

243

selection that is similar to the mx method as described above, the mx-q2 distribution was obtained from the semileptonic events in Brecou. Using 81.4 / 6 _ 1 on the T(4S') resonance data the background subtracted B -> Xulv signal events were extracted from a 2D fit to the mx-q1 distribution for mx < 1.7 GeV/c and q2 > 8 GeV 2 /c 4 . This resulted in a partial branching fraction for B —> Xutv decays. This partial branching fraction was then used to determine the value of \Vub\, which is given in Table 1. Table 1.

\Vui,\ values from four different techniques.

Technique Et > 2.0 GeV 2

Ei vs q mx

< 1-55 GeV mx vs q2

\Vub\

x 10 3

4.40 ± 0.13 a t o t ± 0.25 S j, s 4.99 ± 0.23stat

±0.38theo

± 0A2ays

±0.32 t f c e o

5.22 ± 0.30 s t o * ± 0.3lsys

±0.43iheo

4.98 ± 0.40 stO i ± 0.39sys

±0A7theo

4. Conclusion The CKM matrix element \Vcb\ is measured from a simultaneous fit to the moments of lepton-energy and hadron-mass with an accuracy to ±2%. The measurement of |VU&| is done using four methods based on the variables : Ei, mx, and q2 and is limited to an accuracy of ±10%. Both theoretical and experimental uncertainties at present are at the same level. It is expected that this uncertainty will be improved in future with better precision of the theoretical calculations, and reduced experimental error. References 1. 2. 3. 4. 5. 6. 7. 8. 9.

M. Neubert, Phys. Rev. D49, 3392 (1994). BABAR Collaboration, B. Aubert et al., Phys. Rev. D69, 111104 (2004). BABAR Collaboration, B. Aubert et al., Phys. Rev. D69, 111103 (2004). BABAR Collaboration, B. Aubert et al, Phys. Rev. Lett. 93, 011803 (2004). I. I. Bigi, M. Shifman, N. Uraltsev, and A. Vainshtein, Phys. Rev. D56, 4017 (1997); D. Benson, I. I. Bigi, T. Mannel, and N. Uraltsev, Nucl. Phys. B665, 367 (2003). Averages of b-hadron Properties as of Summer 2004, HFAG, hep-ex/0412073. BABAR Collaboration, B. Aubert et al, hep/ex-0408075. BABAR Collaboration, B. Aubert et al, hep/ex-0408045. BABAR Collaboration, B. Aubert et al, hep/ex-0408068.

QCD RESULTS AT CDF

OLGA NORNIELLA* Institut de Fisica d'Altes Energies, Edifici Cn. Facultat Ciencies UAB, E-08193 Bellaterra (Barcelona), Spain E-mail: [email protected]

Recent QCD measurements from the CDF collaboration at the Tevatron are presented, together with future prospects as the luminosity increases. The measured inclusive jet cross section is compared to pQCD NLO predictions. Precise measurements on jet shapes and hadronic energy flows are compared to different phenomenological models that describe gluon emissions and the underlying event in hadron-hadron interactions.

1. Introduction The Run II at the Tevatron pp collider will define a new level of precision in the knowledge of QCD processes in hadron collision. The large amount of data to be collected in Run II, together with the increase in the center-ofmass energy (from 1.8 to 1.96 TeV) and the upgrade of the CDF detector [1] will allow to perform stringent tests of the QCD predictions in extended regions of jet transverse momentum, i^ e t , and jet rapidities, y j e t . This contribution presents recent results on inclusive jet production, as well as studies on non-perturbative QCD phenomena related to jet fragmentation and the underlying event. 2. Inclusive Jet Cross Section The measurement of the inclusive jet production cross section is one of the pillars of the QCD program at CDF. It probes very small distances (10~ 19 m) and thus is sensitive to new physics. In the Run II, the cross section has increased (by a factor of 5 for jets with Pjf* > 600 GeV/c) compared to the Run I. This has allowed already to increase the kinematic * On behalf of the CDF Collaboration.

244

245

region in Pjf* by more than 150 GeV/c. Following theoretical work, CDF is exploring the KT algorithm [2] in order to search for jets:

K{

pi

.

min{PT,,P?

Ki,

(1)

D2

•j)

where the jets are separated according to their relative transverse momentum. The algorithm includes a D parameter that approximately controls the size of the jet in the — 77 space. Unlike the Run I cone-based jet algorithm [3], the KT algorithm is infrared and collinear safe to all orders in perturbative QCD and does not need an experimental prescription to resolve situations with overlapping cones. Figure 1 shows the inclusive jet cross section using the KT algorithm, in the region 0.1 < | y j e t | < 0.7 and based on the first 145 p b _ 1 of Run II data.

ICDF Run II Preliminary | K T D=0.7-0.1<|Y|<0.7 — • — Data Systematic Errors NLO(CTEQ61) NLO Uncertainties

10

ICDF Run II Preliminary I ~ 8r K T D=0.7-0.1<|Y|<0.7 Systematic Errors NLO Uncertainties NLO: JETRAD uR =u F = P?"72 No Had. / Und. Event Correction

I

1

L=145pb"'

No Had. / Und. Event Correction

100 200 300

400 500

600 700 P T [GeV/c]

100

200

300

400

500 600 700 PT [GeV/c]

Figure 1. Measured inclusive jet production cross section compared to pQCD NLO predictions for a D parameter equal to 0.7.

The measurement is compared to pQCD NLO calculation as determined using JETRAD program [4], with CTEQ 6.1 PDFs [5] and the renormalization and factorization scale set to PJ? a x /2. The data uncertainties are dominated by the energy scale determination in the calorimeter, while the NLO errors mainly come from the gluon PDFs. The agreement between data and NLO is good. At low P^ et , the data tends to be above the prediction and the effect increases as D increases (see Figure 2). This indicates the presence of underlying event contributions and fragmentation effects that have not been taken into account yet.

246 |CDF Run II Preliminary I

Q

.

I CDF Run II Preliminary |

KTD=0.5-0.1<|Y|<0.7 ., Systematic Errors L = 145 pb NLO Uncertainties NLO: JETRAD H„ = HF = P™72 No Had. / Und. Event Correction

co

O

3

UJ

o 2-5 o „

1

1

KTD=1.0-0.1<|Y|<0.7 , L Systematic Errors = 1 4 6 Pb NLO Uncertainties NLO: JETRAD nR = |i F = P ^ / 2 No Had. / Und. Event Correction

_n±i.

0 . 5 r. • • • i • • • • i • • • • i • • • • •. •.. i • • • • i . . . . • • • • • i • • • • i . • • • I 0.51 0 50 100150 200 250 300 350 400 450 500 0 50 100150200250300350400450500 P T [GeV/c]

Figure 2. tively.

P T [GeV/c]

Data divided by pQCD NLO predictions using D=0.5 and D=1.0, respec-

3. Study of the Underlying Event As mentioned, the final states in hadron collision are affected by the presence of soft gluon emissions. The underlying event receives contributions from initial and final-state soft gluon radiation, beam-beam remnants and multiple parton interactions. These processes must be modeled using MC programs tuned to describe the data. In CDF, the underlying event has been studied in dijet production by looking at different regions (in ) well separated to the direction of the leading jet (see Figure 3-left). The "transverse" region is perpendicular to the direction of the hard 2-to-2 scattering and is assumed to be mostly sensitive to the underlying event. Figure 3right shows the average charge particle density in the transverse region as a function of the E^ of the leading jet. The jets are defined by the Run I cone-based jet algorithm with a cone size R=0.7. The measurement has been restricted to events in which the leading jet is in the region |r^ et | < 2.0 with Ej,1 > 15 GeV. The measurements are repeated using dijet events with nearly back-to-back configuration in , with the aim to suppress extra hard gluon radiation. The measurement is compared to different MC models: Pythia tune A [6] and Herwig [7]. It shows that the underlying event contribution in the transverse region is well described by Pythia tune A, while Herwig does not describe the low Pjf* region as well as Pythia. The latter can be attributed to the absence of multiple parton contributions in Herwig. 4. Studies on Jet S h a p e s The study of the jet shape is also sensitive to the underlying event. The shape of the jet is dominated by multi-gluon emission from the primary

247 'AVE Transverse" Charge Density: dN/dnd<|> Jet #1 Direction

CDF Preliminary data uncorrected theory + CDFStM

I PY Tune A [

Swift

JTii^ii^{wp[ Charged Particles (fol<1.0, PT>0.5 GeV/c) 100

150

ET(jet#1) (GeV)

Figure 3. Left: Definition of the transverse region in 4>. Right: Measured average charged particle density in the "transverse region" as a function of E^ of the leading jet compared with different MC models.

parton and it constitutes a test of the parton shower models and their implementation in the MC programs. The integrated jet shape is defined as the average fraction of the jet transverse momentum that lies inside a cone of radius r concentric to the jet cone:

*(r) =

N.jet

£ Pr(0,r) PT(0,RY

0
(2)

Figure 4-left presents the measured integrated jet shape for jets defined using the Midpoint algorithm [9] with a cone size R=0.7 in the region 37 GeV/c < Pjf* < 45 GeV/c. The measurements have been done for jets with PJ?' in the region 37 GeV/c < J^ et < 380 GeV/c. The measurements have been compared to the prediction from Pythia-tune A and Herwig MCs. In addition, two different Pythia samples have been used with default parameters, with and without multiple parton interaction, in order to study the importance of a proper modeling of soft-gluon radiation. Figure 4-right shows, for a fixed radius r=0.3, the average fraction of the jet transverse momentum outside r=0.3 as a function of Pj? • The measurements show that the jets are narrower as P^ increases. Pythia tune A predictions describe all of the data well, while Herwig produces too narrow jets at low JRjf*. The comparison between Pythia and Pythia (no MPI) indicates that the contribution from the multiple interactions on the jet shapes is relatively small but relevant at low P^ .

248 CDF II Preliminary

CDF II Preliminary ' • DATA -

Midpoint Algorithm ( R = 0 . 7 )

PYTHIA Tune A

-•0^^*^''^

--F1TH1A

' - HERWIG

,

• DATA

O

.-•••;•'-"joi^**^

- ... P*rTHiA(noMPI),'

fT)0.35

0

>

- . ' - ^ ^

••,

I

''''si™

: T

/•'.'/

0.2 -

/:'/A /-]//

PMHIA

0.15

•V 0.1 < I Y

H

PUHIA (no MPI)

'% \_ \ T

HERWIG 0.1 < I Y**1! < 0.7

"% N ^

3 7 < P , " < 4 5 GeV/c

/

PYTHIA Tune A

:

* ~ 0.25 7 \

':'':--c*^

r

I<0.7

^""^^Ss^-^-k-i

0.1

--3=E={

0.05

0.2

0.4

0.6

50

0.8

r/R

100

150

200

250

300

350

P,m (GeV/c)

Figure 4. Measured integrated jet shape compared to different MC predictions. 5.

Conclusions

Preliminary results on t h e inclusive j e t cross section have been presented in this contribution. T h e measurements are in agreement with p Q C D calculations. Several studies have been done in order t o test t h e modeling of t h e soft gluon radiation a n d t h e underlying event in t h e different M C programs. T h e results show t h a t P y t h i a t u n e A prediction provides t h e best description of these non-perturbative Q C D phenomena.

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

R.Blair et al., CDF Collaboration, FERMILAB-Pub-96/390-E, (1996). S.D. Ellis and D.E.Soper, Phys Rev., D 4 8 , 3160 (1993). F.Abe et al, CDF Collaboration, Phys Rev., D 4 5 , 1148 (1992). W.T.Giele et al., Phys Rev.Lett, 73, 2019 (1994). J.Pumplin et al, JHEP, 0207 (2002). R.D.Field, ME/MC Tuning Workshop., Fermilab, October 2002. G.Marchesimi et al., Comp. Phys. Comm., 67, 465 (1992). Hans-Uno Bengtsson and Sjostrand, Comp. Phys. Comm., 46, 43 (1987). S.D.Ellis, J.Huston and M.Toennesmann, hep-ph/0111434 (2001).

H A D R O N S P E C T R O S C O P Y IN ELECTRONS-PROTONS COLLISIONS AT H E R A

BOB OLIVIER DESY, Notkestrasse 85, 22607 Hamburg, Germany E-mail: [email protected]

Recent HERA and of results

results from HI and ZEUS on searches for exotic baryons in ep collisions at are reviewed. Evidence for the production of the strange pentaquark 0 + a narrow anti-charmed baryon decaying to D*~p together with negative of pentaquark searches at HERA are presented.

1. I n t r o d u c t i o n Experimental evidence for an exotic baryon first came in 2003 from the observation of a S = + 1 narrow resonance 1 at 1540 ± 1 0 MeV which can be associated with an exotic pentaquark state with content uudds. Confirmation came quickly from a series of experiments, with the observation of sharp peaks 2-3>4>5 in the nK+ and pKg invariant mass spectrum near 1540 MeV, in each case with a width limited by the experimental resolution. Strong evidence in support of a baryon decuplet comes from the reported observation of an exotic S = — 2, Q = — 2 baryon resonance in pp collisions 6 . A narrow peak at a mass of about 1862 MeV in the 5~7r _ invariant mass spectrum is proposed as a candidate for the predicted exotic S 7 - baryon with a quark content dsdsu. At the same mass, a peak is 2

observed that is a candidate for S | 2

At HERA electrons (or positrons) of energy 27.5 GeV are collided with 920 GeV protons providing a center of mass energy i/s of 318 GeV. In the following we present the results of the searches for strange and charmed pentaquarks performed by the HI and ZEUS experiments with an integrated luminosity of up to 126 p b _ 1 accumulated from 1995 to 2000 during the HERA-I data taking period. 249

250

2. Search for 0 + and 0 + + ZEUS performed a 6 + search 7 ' 8 at high energies using the ep data taken in the years 1996-2000 with an integrated luminosity of 121 p b _ 1 . The kinematic region is restricted to the exchanged boson virtuality domain Q2 > 1 GeV 2 and the inelasticity domain 0.01 < y < 0.95. The decay chain 9 + —> pKs —> p7T+7r~ has been used. About 866800 Kg candidates are selected. They are combined with proton candidates selected via the energy-loss measurement dE/dx. The Mn+n- mass distribution shows sign of structure below about 1600 MeV. For Q2 > 10 GeV 2 , a peak is seen in the mass distribution around 1520 MeV. In Fig. 1 the M ^ - i s shown for Q2 > 20 GeV 2 . The figure includes the Monte Carlo expectation from ARIADNE u scaled to the data for M„.+w- > 1650 MeV. After scaling ARIADNE does not describe the data at low masses, maybe due to the absence of the E bumps in the simulation. A fit to the data of a smooth background function and two

M(GeV)

M(GeV)

Figure 1. (left) Invariant mass distribution M +n- observed by ZEUS at Q2 > 20 GeV 2 . (right) Invariant mass distribution M K+ (open dots) and M K- (full dots) observed by ZEUS.

Gaussians, also shown in Fig. 1, gives a signal of 221 ± 48 events at a mass of 1521.5 ± 1.5(stat.) MeV with a significance of 4.6(7. The Gaussian width of 6.1 MeV is found to be consistent with the experimental resolution. The signal is observed at similar rate for protons and for antiprotons suggesting the existence of the anti-pentaquark 0 ~ .

251 ZEUS has also measured the cross section for the production of the 0 + baryons and their antiparticles in the kinematic region Q2 > 20 GeV 2 , 0.04 < y < 0.95, pT > 0.5 GeV and |r/| < 1.5, a(ep - • eQX -> eK°sp(p)X) = 125 ± 27(stat.)1lll(syst.) pb. ZEUS also measured the 9 + production cross section for higher Q2 thresholds 30, 40, and 50 GeV 2 . The 0 + cross section shows no significant dependence on Q2. After the presentation of this talk were released results on the 0 + search performed by HI 9 in a similar phase space region than ZEUS. No peak was observed in the M„.+„.- mass distribution. At a mass of 1522 MeV, HI sets an upper limit on the 0 + production cross section of the order of 100 pb. This upper limit is compatible with the ZEUS observed cross section due to the large error on the latter one. ZEUS has also searched for the 0 + + signal via its possible decay ©++ —> + + K ir . Fig. 1 shows the MpI<- and M p #+ mass spectra. No peak structure is observed in the Mpx+ spectrum but in the MVK- spectrum the well established resonance A(1520) —> pK~ is clearly seen. As no signal is found in the 0 + mass range, this suggests that the 0 + could be isoscalar. 3. Search for S 7 _ and S ° 2

2

ZEUS has performed an analysis in the channel E - ^ to search for the strange pentaquark S and its neutral partner 10 . The decay chain 5 —> E~TT~ —> An~n~ has been considered. A baryons were identified by the charged-decay mode, A —> pir~, using pairs of tracks from secondary vertices. These are then combined with another pion from the primary vertex. Fig. 2 shows the Ms% mass distribution for all possible S-zr charge combinations for Q2 > 1 GeV2 . While the H°(1530) is clearly visible, no signal is observed around 1860 MeV as observed by the NA49 collaboration 6 . Even when restricting to Q2 > 20 GeV 2 , where the 0 + signal was best seen by ZEUS, no signal is observed. 4. Search for 0 C The production of a charmed pentaquark 0 C has been studied via its decay into D*p by HI 12>13 and ZEUS 14 . The analysis of HI is based on the DIS data taken in the years 1996-2000 with a luminosity of 75 p b - 1 in the kinematic region 1 < Q2 < 100 GeV2 and 0.05 < y < 0.7. The D**1 charmed meson has been reconstructed via its decay chain D*+ -»• D°TT^ -» (K^n+)ir^. Around 3400 D* candidates are selected, and are combined with proton candidates selected via dE/dx.

252

M(D«p) [ GeV ]

Figure 2. (left) Invariant mass distribution M H7r observed by ZEUS for Q2 > 1 GeV 2 and for all four charge combinations combined, (right) Invariant mass distribution Mo*p from HI for Q2 > 1 GeV 2 compared to the fit results with two hypotheses: signal plus background (solid line) and background only (dashed line).

The resulting MD.-p distribution in Fig. 2 shows a clear narrow peak close to the threshold. The signal is both observed in the D*~p and in the D*+p sample with compatible mass, width and rate. Log-likelihood fits to the Mr>,p distribution are performed. The background is parametrised by a power law while a Gaussian is used for the signal. A signal of 51 events is observed with a mass of 3099 ± 3(stat.) ± 5(syst.) MeV and a width of 12 ± 3(stat.) MeV consistent with the experimental resolution. The background fluctuation probability has been estimated to be less than 4 x 10- 8 . A similar search has been performed by ZEUS in both photoproduction and DIS regimes. Data from the years 1995-2000 with an integrated luminosity of 126 p b _ 1 have been analyzed. About 9700 D* candidates are selected for Q2 > 1 GeV2 and 43000 candidates for all data. No signal is observed at 3.1 GeV. Upper limits on the fraction of D* mesons originating from the 0 C decays, R = N(QC —» D*p)/N(D*p), were set by ZEUS in the signal window of 3.07 < MD»P < 3.13 GeV. This window covers the HI measurement. The 95% confidence level upper limit on the fraction R is 0.23%. The upper limit for DIS with Q2 > 1 GeV2 is 0.35%. Thus, the ZEUS results are not compatible with the report of the HI collaboration of a charmed pentaquark which contributes to l.59±0.33(stat.)to'%l(syst.)% of the D** production rate 13 .

253

5. Conclusions Recent results from HI and ZEUS on searches for exotic baryons in ep collisions at HERA have been presented. ZEUS has found evidence for the production of the strange pentaquark © + . HI on the contrary has not found any signal compatible with the 0 + and has obtained limits for its production. ZEUS has not found any evidence for the signal seen by the NA49 collaboration attributed to the £ 7 ~ . 2

HI has found evidence for the existence of a narrow anti-charmed baryon decaying to D*p. This result has not been confirmed by the ZEUS search which has been performed in a similar kinematic region. Pentaquark searches are still an open issue. Of the colliding beam experiments that are currently taking data, the HERA experiments HI and ZEUS are the only ones which have reported the observation of pentaquark signals to date. Pentaquark production may be suppressed in e+e~ annihilation due to the lack of any particles carrying baryon number in the initial state colliding beams. The complicated and high multiplicity hadronic final states produced in pp and pp scattering may obscure any pentaquark signal, especially if it is dominantly produced at low transverse momentum. The search for pentaquarks at HERA using the high statistics data from the HERA-II data taking period, to be completed in 2007, may thus represent a unique opportunity to make progress in the field of exotic hadron spectroscopy. References 1. T. Nakano et al. [LEPS Collaboration], Phys. Rev. Lett. 91, 012002 (2003). 2. V. V. Barmin et al. [DIANA Collab.], Phys. Atom. Nucl. 66, 1715 (2003). 3. S. Stepanyan et al. [CLAS Collaboration], Phys. Rev. Lett. 91, 252001 (2003); V. Kubarovsky et al., ibid. 92, 032001 (2004). 4. J. Barth et al. [SAPHIR Collaboration], Phys. Lett. B 572, 127 (2003). 5. A. E. Asratyan et al., Phys. Atom. Nucl. 67, 682 (2004). 6. C. Alt et al. [NA49 Collaboration], Phys. Rev. Lett. 92, 042003 (2004). 7. S. Chekanov et al. [ZEUS Collaboration], Phys. Lett. B 591, 7 (2004). 8. ZEUS Collaboration, Contributed paper to ICHEP04, Beijing, China, Abstract 10-0273 (2004). 9. HI Collaboration, Contributed paper to DIS05, Madison, USA. 10. ZEUS Collaboration, Contributed paper to ICHEP04, Beijing, China, Abstract 10-0293 (2004). 11. L. Lonnblad, Comput. Phys. Commun. 71, 15 (1992). 12. A. Aktas et al. [HI Collaboration], Phys. Lett. B 588, 17 (2004). 13. HI Collaboration, Contributed paper to DIS05, Madison, USA. 14. S. Chekanov et al. [ZEUS Collaboration], Eur. Phys. J. C 38, 29 (2004).

COULOMB CORRECTIONS TO R-CORRELATION IN T H E POLARIZED N E U T R O N DECAY

ANDRZEJ CZARNECKI AND ALEXEY PAK University

of Alberta,

Edmonton,

Canada

We study the final state interaction effects on the electron transverse polarization correlation JR in the Standard Model. We present numerical calculations of the proton recoil effects, second-forbidden terms, and radiative corrections. These corrections are presently beyond the reach of experiment.

1. I n t r o d u c t i o n Historically, studies of nuclear /3-decay have played an important role in establishing the Standard Model. From the theoretical point of view, neutron decay is a convenient place to test weak interactions, as the nuclear structure model uncertainties are minimal. However, only recently intensive neutron sources appeared which made these experiments possible. We

Figure 1. Neutron decay kinematics: s n - neutron polarization, p p - proton momentum, p e - electron momentum, s e - electron polarization.

consider the standard neutron /3-decay n —> p, e, Pe (Fig. 1) in an experiment where electron momentum p e and electron polarization direction s e are measured, and the neutrons are polarized along s n . We study the measurable quantity R related to correlation s n [p e x s e ], which violates T- and 254

255

P-invariance. Traditionally, decay width in this process is parameterized as follows: dT(sn, s e , p e ) = ——rEepe(AM x

- Ee)2dEedSle

q l + &-=- + A L

-fre

n(SePe)(SnPe)

+

(1)

h G— Pe

1- N (s„s e )

-&e (se [sn X pe])

y

£ e ( £ e + m) +U Ee where Ee is the electron energy, m = 0.511 MeV/c2 is the electron mass, and A M = M„ - Mp = 1.2933 MeV/c 2 is the neutron and proton mass difference, and R is the coefficient of interest here. The general weak decay Hamiltonian allows for (Pseudo)Scalar, (Pseudo)Vector, and (Pseudo)Tensor interactions. In the Standard Model Scalar and Tensor interaction vanish, and the Hamiltonian becomes the common (V-A) law. In the SM at the tree level R = 0, and a non-zero value would imply the existence of Scalar and Tensor interactions 2 . A number of experiments were aimed to constrain Scalar and Tensor interaction in various weak decays. An experiment at SINQ spallation facility in Paul Sherrer Institute will measure R to the accuracy of ~ 5 • 10~ 3 . 2. Corrections to R in the Standard Model The measured value of R is affected by the Coulomb interaction of the electron and the proton in the final state. The true T-violating value is the difference between the measured R and calculated value of the final state effects. One-loop correction to R has been found in Ref. 3 , it is accurate to the first power of a in the assumption of zero proton recoil and point-like nucleons. In the Standard Model this answer reads as R^=-2^^(gl-gA), Pe

£ = G%(1 + 3g2A), R ~ 8.3 x 1 0 " 4 ^ , (2) Pe

where a = 1/137.035 is the fine structure constant. Further terms in the expansion are determined by the following small parameters: a/n = 2.3- 1 0 - 3 - appears with radiative corrections, me/Mp « 5 • 1 0 - 4 - appears when the proton recoil effects are taken into account, a = 7.297352 • 1 0 - 3 - appears with the higher corrections to the lepton wavefunctions, and pmaxj^N ^ g 3 . J O - 4 - arises with the emission of higher angular momenta from a finite-size nucleus. In what follows we discuss these corrections and estimate the possibilities for further calculations.

256

2.1. Finite

size

effects

Non-zero size of the proton introduces two types of corrections. First, the electron wavefunction does not have a real singularity in the position of proton, and the second, emission of non-zero angular momenta becomes possible. These two effects have been implemented 4 to the first order in PURN, OL, VN/C ("normal approximation") using the notation of Konopinski5: £ = Q{[l-2eW-A(e

+ W)]

(3)

2

+3g A [1 + 2e(X + Y) + A{X - Y + e/3(l + 2Z))]} =

_2G|£eB ^ a

+ 2e(x

_

+

+ Y +

+

Pe

-gA [i + e(X-Y-W)

C

_ PVRN 3 '

y A

_ (iTsf) (<x) '

^ = 2gl/.2~ f"^"1»

g

+ C/2{X + Y-W-

v

_ (<* * f ) ^(a) '

v Z

2e/3(l - Z))]}

_ (o- - 3f(or)) _ (ior) (a) >W (1)

= H T ^ COS AT?, C -

glg

~* "

/l/

-1

where X , y , Z , W are combinations of nuclear beta-moments, the quantities gkjk are the electron radial wavefunctions (of particle and anti-particle, correspondingly), with k = ± 1 , ±2,... being the eigenvalues of the Dirac K ( Qk(r)xT \ operator and the electron spinor defined as VP = /? A l . Lepton

*

V*/fc(r)X-fc/

wavefunctions are estimated at the nuclear radius (for point-like nucleons) or in the center of the nucleus (for continuous distribution of charge). Ar? = S(—1) — 6(1) is the difference of the Coulomb phase shifts for states with k = — 1 and k = 1. On Fig. 2 we present the results obtained with numerically calculated electron wavefunctions and the nuclear matrix elements estimated in the MIT bag model 8 : (a x f) = 1.56, (i^f) = 0, (iar) = 0 , (a - 3f (or)) = —0.87. These numbers may be considered accurate to 10-20% basing on the accuracy of the MIT bag model prediction for gA2.2. Proton

recoil

effects

To account for the proton motion, we include next-to-leading terms in the me/Mp expansion of the one-loop calculation. Integrating over neutrino

257

pe/me 0.2 Figure 2.

0.4

0.6

0.8

1

1.2

Relative effect of the proton size.

directions, we obtain (Fig. 3): R£ = R£(°\l + Akinem), ^ e 2 (5 + 119A) + AM 2 (2 + 8gA) - AMEe(7 Akinem = 6gA(AM - Ee)Mn

Figure 3.

2.3. Radiative

+ 13gA) -

(4) 6gAm2

Relative effect of the proton recoil.

corrections

Correction arising from one-loop photon exchange were published in Ref. 6 , this result is presented on Fig. 4. 3. Conclusion We presented the corrections to the first non-vanishing terms of the transverse electron polarization coefficient R in the neutron beta-decay, including

258

Sf

0.0225

"e

0.015

0.02 § 0.0175 e 0.0125

•f

0.01

^

0.0075

<

0.005

Figure 4. Relative effect of radiative corrections.

the p r o t o n size effects, proton recoil contribution and the radiative corrections. Currently running experiments and t h e next generation experiments will not have enough sensitivity to hit this background.

References 1. I.C.Barnett, K.Bodek itshape et al., Fundamental Neutron Physics Research at SINQ: Search for Time Reversal Violation in the Decay of Free, Polarized Neutrons, PSI Proposal, 1997. 2. J.D. Jackson, S.B. Treiman, H.W. Wyld, Possible tests of time reversal invariance in beta decay, Phys. Rev. 106, 3 (1957). 3. J.D. Jackson, S.B. Treiman, H.W. Wyld, Coulomb corrections in allowed beta transitions, Nucl. Phys. 4 (1957). 4. P. Vogel, B. Werner, Final-state interactions and time-reversal tests in nuclear P-decay, Nucl. Phys. A 404 (1983). 5. E.J. Konopinski The theory of beta radioactivity, Oxford Univ. Press, 1966. 6. Y. Yokoo, S. Suzuki, M. Morita, Radiative corrections to asymmetry and energy spectrum of (3 rays from polarized nuclei, Progr. Theor. Phys. 50, 6 (1973). 7. A. Czarnecki, K. Melnikov Muon-electron conversion in the field of a nucleus, (unpublished). 8. A. Chodos, R.L. Jaffe, K. Johnson, C.B. Thorn, Baryon structure in the bag theory, Phys. Rev. D 10, 2599 (1974).

SIMULATING T H E SENSITIVITY OF k m 3 H Y D R O P H O N E A R R A Y S TO FLUXES OF ULTRA HIGH E N E R G Y NEUTRINOS

JONATHAN PERKIN for the ACoRNE Collaboration Department of Physics and Astronomy, University of Sheffield, Sheffield S3 IRE, United Kingdom We present the results of a preliminary simulation to predict the sensitivity of hypothetical arrays, of typically one thousand hydrophones, to a flux of ultra high energy neutrinos.

1. Introduction Ultra high energy (UHE) neutrinos {Ev > 10 18 eF) can interact in the sea a via deep inelastic scattering (DIS) off constituent quarks in water nuclei. Interactions can be neutral current: v + N —> v + X (where N is a nucleon) or charged current: v + N —> I + X, where I is a charged lepton. In each case an excited hadronic final state X is produced which develops as a particle cascade. The energy contained therein is imparted to the surrounding medium via ionisation and excitation. This forms the basis of the acoustic signal. Such a signal could be detected by a 3D array of hydrophones (underwater sound to electricity transducers). Reconstruction of the neutrino interaction vertex is performed via the difference in arrival times, of the acoustic pressure wave, at the different sensors in the array. 2. Acoustic Signal Generation Generation of the acoustic signal follows the quasi-instantaneous temperature increase, resulting from the fast thermal energy deposition, associated with the cascade. Knowledge of the thermal energy density allows the pressure wave at an arbitrary location in the far-field to be computed 1 . The a

or indeed Antarctic ice, and salt domes, etc, but here we shall restrict our discussion to interactions in sea water. 259

260

form of the pressure pulse originates from the second time derivative of the change in temperature; since this is essentially a step function, the pulse has a distinctive bi-polar shape. The cascade can be considered as a continuous distribution of point sources, from which the acoustic radiation is emitted coherently. The consequence of this is to confine the signal to a narrow pancake perpendicular to the shower axis 2 . This is analogous to the single slit diffraction of light and is illustrated in Fig. 1. Indeed, at angles greater than 5° out of the plane of the pancake, signal intensity is diminished to at least one hundredth of its original value.

Figure 1. Schematic of the energy deposition. At Ev = 10 2 0 eV, in water, a hadronic shower deposits 99% of its energy in a cylinder of length L = 10m and radius R = 20cm.

Investigations of hadronic shower shapes in water have been performed using the G E A N T 4 simulation toolkit 3 , thus providing information on thermal energy densities. Parameterisations of these results are an input to the detector simulation. 3. Signal Propagation The acoustic signal detected at a hydrophone is modified by three factors. Firstly, the geometric attenuation of the signal whereby intensity falls off as the reciprocal of the distance traveled from source. Secondly, the angular spread of the signal, modelled using Fraunhofer Diffraction Theory. Finally, the attenuation due to the bulk water properties as illustrated in Fig, 2. In our simulation, this latter effect is coupled to the output of a matched filter applied to a flat, Gaussian noise background, the performance of which enhances the signal by approximately a factor of three. A conservative pressure cut of 0.035Pa is imposed, i.e. hydrophones recording a peak pressure less than this are neglected. The magnitude of this cut has been calculated from a probability of false alarm (PFA) rate of one false signal

261 in ten years due to noise, with a five-fold coincidence. Distance 0.1 km

Distance 1 km

Figure 2. Variation of pulse shape, with increasing distance form source, due propagation through a dense medium.

4. Vertex Reconstruction Given the sound speed c and the hydrophone locations fi one can reconstruct the coordinates of the neutrino interaction vertex v = (vx,vy,vz) and its time ts, from the difference in arrival times of the signals U at each hydrophone in an array 4 : \v-ri\2=c2{ti-ts)2.

(1)

This can be expanded quadratically: (r? - r?) - c2[t2 - t)} + 2c2ts(U - ts) = 2v • (r- - r=})

(2)

and expressed in terms of a matrix equation: (3)

262

which allows for a solution of both v and ts where: i t = r? - r) - c2(t2 - tj) 2

T* = 2c (ti-tj)

(

(i,j = 1,2; 1,3; 1,4) (t,i = l , 2 ; l , 3 ; l , 4 )

dx12 dy\2 dzi2 \ dxi3 dyi3 dzi3 J dxu dyu dzu J

Here, in the limiting case of four hydrophones, the one with index 1 is taken as the reference hydrophone, dx, dy, dz are the difference in x, y and z coordinates respectively, between this phone and the other hydrophones hit.

5. Array Sensitivity In order to calculate the sensitivity of the array to a flux of UHE neutrinos we must first calculate the differential flux, incident upon our detector. The key equation 5 is:

*<£> = Evm

<4>

where $(E) is the differential flux [dNu /dEdAdQdt] in units of GeV~1cm~2sr~1s~1. Sup is the upper limit on the number of detected events. Assuming that no events are seen, then 95% confidence level upper limits correspond to setting Sup = 3.0. \(E) is the number of events that we would detect if a unit differential flux were incident on our detector at a unique energy E, for time T. It can therefore be written as: X(E) = avN(E)

XPXNAXVX2TTX

fMC(E)

xT

(5)

where a„^i{E) is the neutrino-nucleon cross section at energy E; this result is extrapolated from Fig. 3 in Ref. 6. p is the density of water; NA is Avogadro's number; V is the fiducial volume: IT X (Rcan)2 x Hcan; T is the exposure time: lyr; and fMc(E) is the fraction of Monte Carlo events generated at energy E that are detected and reconstructed (using the process described in Sec. 4). Having computed the differential flux, one can proceed with calculation of the detector's sensitivity by assuming that no events are seen after one year of running as illustrated in Fig. 3

263

Ev

IGeV)

Figure 3. Model independent flux limit (labelled "THIS STUDY"). The breadth of the band encompasses the range of performances of the different array geometries studied. The number of hydrophones was varied between 1000 and 1029; the number of hydrophones per cluster was varied between one and seven; and, there were a variety of geometries and inter-hydrophone distances simulated.

6. Summary A preliminary simulation designed to predict the sensitivity of an approximately kilometre-cubed hydrophone array to a flux of UHE neutrinos has been produced. Parameterisations of G E A N T 4 hadronic cascades provide an input to the simulation and permit computation of the predicted peak pressure signal on each sensor. The signal propagation is modified by three factors of attenuation and the detector response is coupled to the performance of a matched filter applied to a flat, Gaussian noise background. A conservative threshold of 0.035Pa is imposed, based on a PFA of one signal in ten years due to noise. The results in Fig. 3 indicate this is potentially a competitive technique, worthy of further study. References 1. 2. 3. 4. 5. 6.

J. G. Learned Phys. Rev. D, vl9, No. 11 (1979). N. G. Lehtinen et al, Astropart.Phys. 17 (2002) 279-292 (astro-ph/0104033). http://geant4.web.cern.ch/geant4/ I. Kravchenko et al, Astropart.Phys 20 (2003) 195-216 (astro-ph/9507078). N. G. Lehtinen et al, Phys.Rev.D 69 (2004) 013008 (astro-ph/0206371). J. Kwiescinski et al, Acta Phys.Polon.B 31 (2000) 1273-1285.

D 0 T O P PHYSICS

MARC-ANDRE PLEIER University of Rochester E-mail: [email protected] for the D0 collaboration The Tevatron proton-antiproton collider at Fermilab operates at a centre of mass energy of 1.96 TeV and is currently the only source for the production of top quarks. Recent D 0 results on the top quark's production cross section and its properties such as mass, helicity of the W in its decay and branching fraction B(t —> Wb) are presented, and probe the validity of the Standard Model (SM).

1. Introduction The top quark, which completes the quark sector of the SM, was discovered in 1995 at the Tevatron by the CDF and D 0 Collaborations [1]. Being the heaviest of all quarks with a mass of 178.0 ± 4.3 GeV/c 2 [2], it couples most strongly to the Higgs boson, and its lifetime of w 4 • 10~ 25 s means that it is the only quark that decays before it can hadronise, preserving spin information, and providing a way to study the decay of an essentially free quark. Measuring the production cross section of the top quark and its different properties such as mass, W helicity in its decay, branching fraction B(t -> Wb), etc., and comparing with predictions of the SM is a very powerful tool for searching for physics beyond the SM.

2. Top quark production at the Tevatron In pp collisions at a centre of mass energy yfs = 1.96 TeV, top quarks are produced predominantly in pairs: pp —> it + X via the strong interaction (85% qq annihilation and 15% gluon-gluon fusion). At next-to-next-toleading order, the corresponding SM cross section is 6.77 ± 0.42 pb [3]. According to the SM, the top quark decays predominantly into W bosons and b quarks. Hence, there are three event classes to be observed resulting from it decay, which depend on the decay mode of the W bosons: (i) a dilepton final state where both W bosons decay leptonically, resulting in two iso264

265

lated high-px leptons, missing transverse energy # r corresponding to the two neutrinos and two jets, (it) a lepton+jets final state where one W boson decays leptonically, the other one hadronically, resulting in one isolated high-pr lepton, $T and four jets, and (tit) an all-jets final state where both WTbosons decay to qq' pairs producing six jets. In all final states, two of the jets are &-jets, and additional jets can arise from ISR/FSR. The all-jets final state represents the biggest branching fraction of ti events («46%), but it is also difficult to separate from a big multijet background. The dilepton final state without r leptons constitutes « 5 % of the ti events and gives the cleanest signal, but also suffers from low statistics. The lepton+jets events in the e+jets or ^+jets channels yield «29% of the branching fraction and provide the best compromise between sample purity and statistics. In addition to ti pair production, top quarks can also be produced singly via the electroweak interaction through a Wtb vertex. A measurement of single top quark production consequently provides direct access to the CKM matrix element Vtb- Depending on the virtuality (squared four-momentum) of the participating W boson (Q\y), there are two contributions: the schannel q'q -» tb (Q\y > 0), with a predicted cross section of 0.88 ± 0.05 pb [4], and the t-channel q'g —> tqb (Qw < 0), with a predicted cross section of 1.98 IQ.22 P D [*>]• The contribution from single top production in both s and t channels of bg -> tW can be neglected at Tevatron energies [6]. We present only results from leptonic channels containing a muon or an electron, and W —> r decays are therefore included in a partial way, depending on the r decay mode.

3. Measurement of the tt production cross section The ti pair production cross section has been measured by D 0 in several decay modes, using either purely topological and kinematic event properties to separate the ti signal from background, or by adding identification of bjets based mainly on the long lifetime of B hadrons. Several algorithms are deployed for fe-jet identification, e.g., searching for muons in jets resulting from semileptonic B decays (soft-^ tag) or using reconstructed secondary vertices (SVT), or the significance of impact parameters of tracks within jets relative to primary vertices (CSIP). The probability to tag at least one jet in a ti lepton+jets event by its lifetime is ~60%, whereas the main background from W+jets production is tagged in only «4% of the cases, resulting in an improved signal to background ratio in tagged analyses. An advantage of topological analyses is that they do not depend on the

266

assumption of 100% branching of B(i -> Wb), and are therefore less modeldependent than tagging analyses. Analysing different decay channels helps to improve statistics of top events, and studies of properties, as well as probing of physics beyond the SM that could result in enhancement/depletion in some particular channel. Figure 1 shows an overview of all cross section measurements performed thus far at D 0 . We find that all measurements are in good agreement with the SM and with each other. 4. Measurement of the top quark mass The top quark mass is a fundamental parameter that is not predicted by the SM, but can be used together with the Wmass to constrain the mass of the Higgs boson via radiative corrections. D 0 has measured the top quark mass in the lepton+jets and dilepton channels using different techniques: In the lepton+jets channel, a kinematically-constrained fit is used to extract the top quark mass from preselected events, using either template mass spectra for signal and background (template method) or an analytical likelihood for calculating the probability for any event to be signal or background (ideogram method). In the dilepton channel, of the 6-particle final state, only four objects are detected together with $ T , which provides an underconstrained problem. As proposed by Dalitz, Goldstein [7] and Kondo [8], a hypothesised value of the top quark mass can be used to solve for the it momenta. The solutions yield a weight distribution for each preselected event as a function of the top quark mass. Using its peak as an estimator of the mass for each event, and comparing the resulting distribution from all preselected events to signal and background templates, provides an estimate of the top quark mass. All the measurements are shown in Fig. 1, and all are in agreement with the current world average [2]. The final goal is to measure the top quark mass with 1% precision in Run II. 5. Measurement of the W helicity in tit decays Top quark decay in the V - A charged current weak interaction proceeds only via a left-handed ( / ~ = 30%) and a longitudinal (/°=70%) fraction of W helicities, which is reflected in the angular distribution of the charged lepton relative to the line of flight of the top quark in the W rest frame in lepton+jets final states. Using data corresponding to integrated luminosities of 169 p b _ 1 (e+jets) and 158 p b _ 1 (jj+jets), and comparing the above mentioned angular distribution in data to templates, where we set f° to its SM value, and vary the right-handed fraction / + , and correspondingly

267 D0 Run II Preliminary

D0 Run II Preliminary dilepton L*146pb''

l+jets (ideogram)

"'

l+jets (topological^ L=230pb-'

' ' '' *

-1.3 -1.1

' '

, +4.1 +2.0

L=160pb* l+jets (template, topological)

l+jets (soft n t a g ) f % L=93pf'

e|i (Vertex tag) L=1S8pb-'

l+jets (template, b-tagged) I I • L=230pb~'

, ' *|"J

l+jets (Impact parameter) Xl

L=230pf'

IH—m-

L=230pb'1

>•'">

J*

-1.1 -0.9

] l

dilepton (matrix weighting)

H—

+15+1.1

•

H

l+jets (Vertex tag)

a-*-

L=230 pb'1 all hadronic

t W

7J

*" "

'

'" *

'

-;

'

| | Cacclarl et al. JHB* 0404 068(2004), m, * 175 GeV/e* . I . . . . I . . . . I . . . -I . . , , , , I , , ,

0

2.5

5

7.5

10 12.5 15 17.5 20

World average (Run I only) hep-ex/0404010

140

o(pp^tt)(pb)

160 180 200 Top Quark Mass (GeV)

Figure 1. Left: it pair production cross section as measured by D 0 in Run II, and the SM prediction. Right: Top quark mass measurements from D 0 in Run II compared to the world average based on Run I measurements.

/ _ , between 30% and 0%, we obtain an upper limit on / + from a binned likelihood fit of: / + < 0.24 (90% CL), in agreement with expectation from the SM. 6. Measurement of B(t ->• Wb) / B(t - » Wq) The ratio of branching fractions R = B(i -> Wb) / £<,=<*,»,& B(i -> Wq) is constrained within the SM to 0.9980 < R < 0.9984 at 90% CL [9], assuming three fermion generations, unitarity of the CKM matrix and neglect of nonW decays of the top quark. D 0 has measured R in the lepton+jets channel using data corresponding to integrated luminosities of 169 p b - 1 (e+jets) and 158 p b - 1 (/i+jets), by comparing the number of single to double btagged events, using one 6-jet to identify the it event and the second one for the measurement of the relative fraction of t —> Wb. For example, applying the SVT algorithm for 6-tagging, we obtain the following result for R from a simultaneous fit of R and the it cross section: R = 0.70±g;H (stat) 1 ° ; ^ (syst). This agrees with the SM expectation.

268

7. Search for single top quark production Thus far, the search for single top quark production has been performed only for the cases where the W boson decays into an electron or muon and neutrino, resulting in final states with one isolated high-py lepton, $T and two or three jets. Using data for an integrated luminosity of 230 p b - 1 , with selections optimised for leptonic W decays, maximal acceptance of signal and good modelling of the remaining backgrounds, a set of common discriminating variables is used to separate signal from the background. One analysis is based on classical cutoff criteria, optimised via a random grid search, and another on a multivariate (neural nets/decision trees) analysis. The neural network analysis gives the best limits: a, < 6.4 pb (95% CL),

at < 5.0 pb (95% CL).

These limits represent a factor of two improvement relative to all other measurements, and are in agreement with expectations from the SM. 8. S u m m a r y A wealth of top analyses is being pursued at D 0 , continuing to probe the validity of the SM. So far, all measurements are in agreement with the SM. More detailed descriptions of the analyses can be found online [10]. Continuously improving the analysis methods, and using the increasing integrated luminosity from a smoothly running Tevatron, expected to deliver more than 4 fb _ 1 by the end of Run II, we are moving towards precision measurements and hopefully discoveries within and outside the SM. References 1. CDF Collaboration, F. Abe et al., Phys. Rev. Lett. 74, 2626 (1995); D0 Collaboration, S. Abachi et al, Phys. Rev. Lett. 74, 2632 (1995). 2. CDF Collaboration, D0 Collaboration and Tevatron Electroweak Working Group, P. Azzi et al, preprint hep-ex/0404010, 1-7 (2004). 3. N. Kidonakis and R. Vogt, Phys. Rev. D 68, 114014 (2003). 4. M. C. Smith and S. Willenbrock, Phys. Rev. D 54, 6696 (1996). 5. B. W. Harris, E. Laenen, L. Phaf, Z. Sullivan and S. Weinzierl, Phys. Rev. D 66, 054024 (2002); Z. Sullivan, Phys. Rev. D 70, 114012 (2004). 6. A. S. Belyaev, E. E. Boos and L. V. Dudko, Phys. Rev. D 59, 075001 (1999). 7. R. H. Dalitz and G. R. Goldstein, Phys. Rev. D 45, 1531 (1992). 8. K. Kondo, J. Phys. Soc. Jap. 57, 4126 (1988) and ibid. 60, 836 (1991). 9. S. Eidelman et al. (Particle Data Group), Phys. Lett. B 592, 1 (2004). 10. http://www-d0.fnal.gov/Run2Physics/top/index.html

D 0 HIGGS PHYSICS RESULTS

K. J Y O T H S N A R A N I for D0 collaboration, Department of High Energy Physics, Tata Institute of Fundamental Research, Homibhabha Road, Colaba, Mumbai - 400005, INDIA E-mail: [email protected]

We have searched for the Standard Model (SM) and non Standard Model Higgs bosons using about 200-260 p b _ 1 of data collected with the upgraded Run II D 0 detector at Fermilab Tevatron. Low-mass SM Higgs boson is searched in the associated production with W or Z and limits are placed on the cross section and the kinematic properties of the W or Z plus heavy flavor production. SM Higgs boson with mass greater than 135 GeV is searched for in its dominant decay mode WW with I f ' s decaying into electron or muon final states. Non SM Higgs searches are done in the associated production of neutral SUSY Higgs with b quarks. Data are compared to various predictions and the limits are derived on model parameters.

1. Introduction Deciphering the mechanism that breaks the electroweak symmetry and generates the masses of the known fundamental particles is one of the most important missions of present and future high-energy colliders. These are believed to be generated by the Higgs mechanism. 2. Standard Model Higgs boson searches The strategies to search for the Standard Model Higgs boson is a function of production channels and its decay modes. Depending on the mass of the Higgs (H) boson there are two search strategies at Tevatron at -y/s = 1.96 TeV: • Associated production of H with W ox Z with H —> bb decay mode for mH < 135 GeV • Gluon fusion gg —> H with H —• WW* decay mode for TUH > 135 GeV 269

270

2.1. Higgs boson search for mn < 135 GeV The Higgs boson with mass run between 105 and 135 GeV is searched in the production channel pp —> WH —> evbb. The expected WH cross section is of the order of 0.2 pb for this mass range. Assuming that the six observed events are consistent with the SM, without contributions from Wbb and WH, we set a 95% C.L. upper limit of 6.6 pb on the Wbb cross section, for pbT > 20 GeV and ARbb > 0.75. The expected contribution from the 66 decay of a SM Higgs boson, with m/j = 115 GeV produced with a W, is also shown in Fig. 1 (left). In the absence of a signal, we set a limit on the cross section for a(pp —> WH) x BR(H -> 66) of 9.0 pb at the 95% C.L., for a 115 GeV Higgs boson. The limit on the cross section for other masses along with mj/ = 115 GeVis shown in Fig. 1 (right).

• D0,174 pb'\WH-» evbb

W + 2 b-tagged jets • Data • W + jets OQCD • tt HWbB - - • other HWH

100

150

200

250

300

Dijet M a s s ( G e V )

105 110 115 120 125 130 135

0

Higgs Mass (GeV)

Figure 1. Left: Distribution of the dijet invariant mass for W + 2 6-tagged events, compared to expectation (cumulative). The expectation for a 115 GeV Higgs boson from WH production is also shown. Right: 95% C.L. upper limit on a(pp —• WH) x BR(H —• 66) compared to the SM expectation at y/s = 1.96 TeV, and to CDF results, which were obtained at ^/s = 1.8 TeV. T h e predicted WH cross section at 1.96 TeV is approximately 15% larger than that at 1.8 TeV.

We have measured the ratio of inclusive cross sections for pp —> Z + b jet to pp —• Z+jet production. The inclusive Z + 6-jet reaction is an important background to searches for the Higgs boson in associated ZH production at the Fermilab Tevatron collider. Our measurement is the first of its kind, and relies o n Z - > e+e~ and Z —• n+p,~ modes. The combined measurement of the ratio yields 0.023 ± 0.005 for hadronic jets with transverse momenta pr > 20 GeV and pseudorapidities |rj| < 2.5,

271 consistent with next-to-leading order predictions of the standard model. 2.2. Higgs boson search for mn > 135 GeV Higgs boson for mH > 135 GeV is searched in the channels H -> WW^ -> l+vl*~v (I = e, //). The number of events observed is consistent with expectations from standard model backgrounds. Limits from the combination of the ee, fi/j, and e/x channels on the production cross section times branching ratio a x BR(H -»• W < ' ) ) are shown in Fig. 2.

Figure 2. Excluded cross section times branching ratio c x BR(H —> WW^) at 95% C.L. together with expectations, the 4th generation model, and the topcolor model.

3. N o n Standard Model Higgs boson searches We searched for neutral Higgs bosons produced in association with bottom quarks in pp collisions, using 260 p b _ 1 of data. The cross sections for these processes are enhanced in many extensions of the Standard Model, such as in its minimal supersymmetric extension (MSSM) at large tan/3. The results of our analysis agree with expectations from the SM, and we use our measurements to set upper limits on the production of neutral Higgs bosons in the mass range of 90 to 150 GeV.

272

We search for an excess in the invariant mass distribution of the two leading transverse momentum (px) jets in events containing three or more b quark candidates. Fig. 3, shows the expected MSSM Higgs boson production cross section as a function of UIA for tan/3 = 80, and the median expected limit with the background-only hypothesis along with its ±lcr range. The MSSM cross section shown in Fig. 3 corresponds to no mixing in the scalar top quark sector, or Xt = 0, where Xt = At — /^cot/3, At is the tri-linear coupling, and the Higgsino mass parameter \i = —0.2 TeV. We also interpret our results in the "maximal mixing" scenario with Xt = V6 x MsusYi where MSUSY is the mass scale of supersymmetric particles, taken to be 1 TeV. Results for both scenarios of the MSSM are shown in Fig. 3 as limits in the tan/3 versus TUA plane.

mA ( G e V )

m A (GeV)

Figure 3. Left: The expected and measured 95% C.L. upper limits on the signal cross section as a function of TCIA- The band indicates the ±1
Acknowledgments We thank the staffs at Fermilab and collaborating institutions, and acknowledge support from the DOE and NSF (USA), CEA and CNRS/IN2P3 (France), FASI, Rosatom and RFBR (Russia), CAPES, CNPq, FAPERJ, FAPESP and FUNDUNESP (Brazil), DAE and DST (India), Colciencias (Colombia), CONACyT (Mexico), KRF (Korea), CONICET and UBACyT

273

(Argentina), FOM (The Netherlands), PPARC (United Kingdom), MSMT (Czech Republic), CRC Program, CFI, NSERC and WestGrid Project (Canada), BMBF and DFG (Germany), SFI (Ireland), A.P. Sloan Foundation, Research Corporation, Texas Advanced Research Program, Alexander von Humboldt Foundation, and the Marie Curie Fellowships. References 1. V. M. Abazov et al, Phys. Rev. Lett. 94 091802 (2005); hep-ex/0410062; FERMILAB-Pub-04-288-E. 2. V. M. Abazov et al, Phys. Rev. Lett. 94, 161801 (2005); hep-ex/0410078; FERMILAB-Pub-04-297-E. 3. V. M. Abazov et al, submitted to Phys. Rev. Lett. (2005); hep-ex/0504018, Fermilab-Pub-05/058.

M E A S U R E M E N T S OF Rb AT LEPII ENERGIES

Y. R O Z E N A N D H. L A N D S M A N F O R THE OPAL COLLABORATION Physics

Dep.,

Technion - Israel Institute of Haifa 32000 Israel E-mail: [email protected]

Technology,

Measurements of R^, the ratio of the bb cross-section to the qq cross-section in e + e _ collisions, are presented. The data were collected by the OPAL experiment at LEP at centre-of-mass energies between 182 GeV and 209 GeV. Lepton, lifetime and event-shape information is used to tag events containing b quarks with high efficiency. The data are compatible with the Standard Model expectation. The mean ratio of the eight measurements reported here to the Standard Model prediction is 1.055 ± 0.031 ± 0.037, where the first error is statistical and the second systematic.

1. Introduction The cross-section for bottom-quark pair production in e + e~ annihilation relative to the quark-pair cross-section, _ cr(e+e~ -» 7/Z -»• bb) 7 / Z ->• qq)'

b =

is a sensitive probe of the Standard Model 1. Measurements of Rb have been made at the Z peak and at higher energies 2 . At the Z resonance, where fermion-pair production is dominated by Z decays, measurements of Rb provide a precise determination of the ratio of the Z -» bb partial width to the hadronic width a i?° = r b b -/r n ad- This quantity is of particular interest because of its unique sensitivity to electroweak radiative corrections; while sensitive to the top-quark mass, its dependence on other parameters, for example the Higgs boson mass and the strong coupling constant, a

R ° is the partial width ratio for Z decays and not the cross-section ratio measured in this paper. In the Standard Model it is smaller than the cross-section ratio at the peak of the Z resonance by 0.0002.

274

275

is negligible 2 . Above the Z peak, the pure Z cross-section decreases and the contributions of photon exchange and 7-Z interference become important. Possible new physics at a high energy scale might manifest itself as a deviation from the Standard Model prediction. In this paper, measurements of Rb at energies above the Z resonance are presented. The data were taken by the OPAL detector at the LEP e + e~ collider, at centre-of-mass energies, y/s, ranging from 182 GeV to 209 GeV, during the LEP2 programme. A more detailed description is given in 3 . Above the Z peak a significant fraction of the observed fermion-pair events comes from radiative return to the Z through initial-state photon radiation. Only non-radiative events are considered here, according to the definition used by OPAL in the analysis of fermion-pair production at LEP2 4 : An effective centre-of-mass energy y/s' > 0.85-y/s, where s' i s defined as the square of the mass of the 7/Z propagator. The Standard Model predicted contribution of interference between initial- and final-state photon -radiation is removed. At high energies, additional background sources also arise, mainly from W + W _ and ZZ decaying to four-fermion final states. Because of the limited statistics due to the low cross-section at LEP 2, the double-tag technique as used at the Z resonance 5 is not optimal. Instead the measurement reported here relies on a single-tag method, and uses a sophisticated tagging algorithm based on lepton, lifetime and eventshape information to identify bb events. This algorithm is more efficient and has a higher purity than the one used in our previous measurement 6 , where R\> was measured up to 189 GeV.

2. Analysis procedure The measurement of Rt> starts by selecting non-radiative hadronic events, applying fiducial cuts and rejecting four-fermion background events. The number of selected events, Nhad, is corrected for background and for the efficiency of the selection cuts to yield a corrected number of non-radiative hadronic events, JVqq. The background includes the residual four-fermion background and feedthrough of events with lower effective centre-of-mass energy, y/s*. The contribution from interference between initial- and finalstate radiation is also removed. A b-tagging algorithm is applied to the selected events, and the number of tagged events, Nt&s, is similarly corrected for the same background contributions and interference to obtain Nh^, which still contains contributions from cc and light-quark-pair events.

276

i?b is then calculated using: Rh

=

^ b b / ^ q q ~ € c#c ~ (1 - -Rc)6uds ^b "~ ^uds

,^

where £b,c,uds are the efficiencies for non-radiative bb, cc and light-quarkpair events to pass the selection criteria and the b-tagging algorithm. 2.1. Hadronic

event

selection

Hadronic events, e+e~ -> 7/Z -> qq, are selected based on the number of reconstructed charged particle tracks and the energy deposited in the calorimeters 7 . Further requirements follow, demanding at least seven tracks and that the polar angle of the thrust axis, 0thr, satisfy I cos #thr| < 0.9; the thrust axis is calculated from all tracks and clusters and corrected for double-counting. The effective centre-of-mass energy, v ^ , of the e + e~ collision is estimated as described in Ref. 4 , and non-radiative hadronic events are selected if \/s'/s > 0.85. 2.2. Four fermion

background

rejection

For the centre-of-mass energies analysed in this paper, the production crosssection of W + W ~ events is comparable to that of non-radiative qq events. The production cross-section of ZZ events is about an order of magnitude smaller. Using the same techniques as in 8 , events are rejected if they are identified as W + W ~ events in any of the following channels: W + W ~ —> i+i/l-u, W + W - -4 qqqq or W+W~ -> q o > . 2.3. B +

_

tagging

In e e —> 7/Z —>• bb events, the quark and the anti-quark are typically boosted in opposite directions, and the subsequent hadronization is largely independent. In this analysis, each event is divided into two hemispheres defined by a plane that is orthogonal to the thrust direction. We use a hemisphere-based b-tagger designed for LEP2 Higgs searches 9 , where the tagging of bb events is based on three nearly independent properties of the b-hadron and its decay products: a lepton from a semileptonic b-hadron decay, the long lifetime, and kinematic differences between b-hadron decays and fragmentation in uu, dd, ss events, due to the hard fragmentation of the b-hadron and the high multiplicity of its decay products.

277

In each hemisphere, the output of the lepton tag, a lifetime based ANN and a kinematic based ANN are combined with an unbinned likelihood calculation, and the likelihoods iLmil.^hemil-^hemil^hen^, •^hemi2 are obtained. The likelihood -Lhemii 1S the probability for the first hemisphere to contain a b quark, etc. The two hemispheres' outputs are then combined into a single event b-tagging likelihood variable Invent, using r

•^event — r

b ^hemil-^hemi2 •^hemil-^hemi2 c re _i „ , ruds ruds b ^'hemil^'hemi2 + c ^h 'hemil-^hen^ "^ ' u d s - ^ h e m i l ^ h e n ^ r

The normalization parameters are arbitrarily set to r\, = 0.165, r c = 0.253 and ruds = 0.582. The number of events, Ntag, satisfying a b-tagging cut of •^event > 0.3 is determined; this cut value minimizes the total uncertainty in the measurement of R\>. Typical efficiencies for the b-tagger in the hadronic event sample are 65%, 6.3% and 1.5% for bb, cc and light-quark pair events respectively. The distribution of £event for the 182-209 GeV data is shown in Figure 1, together with the expectation from the Monte Carlo. Good agreement between the data and the Monte Carlo is observed.

i i i II ii ii ii ii

42 s

£ io 4

Figure 1.

i

i

I

I I

I

I

OPAL

I

I

I

I

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I

I

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|

I

1 I I

I

1

I

I

I

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I

I

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I I

Data 2-fermions b 2-fermions c N\\\N 2-fermions uds 4-fermions

L ev ent distributions for selected non-radiative hadronic events.

278

3. Systematic uncertainty Understanding of systematic effects is a major issue for a measurement that aim at a comparison to the SM. A large section is devoted to this in 3 . In short, we estimate the total effect of physics modelling to be 1.3% of the measured value of i?b while detector effect are larger and amount to 3.3% bringing the total relative systematic uncertainty to 3.5%. It was checked separately for each center-of-mass energy and was found to be uniform in the energy range investigated. 4. Results and conclusion The e + e~ —> bb production rate per non-radiative e + e~ —> qq event has been measured using data collected by the OPAL detector at LEP at centreof-mass energies between 182 GeV and 209 GeV. The results are summarized in Table 2. The measurements are shown in Figure 2, where they are compared with the predictions of the Standard Model, calculated using Z F I T T E R 1 0 . Good agreement between the Standard Model and the measurements is observed. A comparison of the eight measurements reported here to the Standard Model prediction gives: x 2 = 5.0, or 76% probability of obtaining a larger difference than observed. Since the x 2 test only uses the absolute difference between the prediction and measurement, we also made another test assuming that the ratio of the measurement to the prediction is constant. We perform a x 2 fit for the ratio using only the statistical uncertainties and add the systematic uncertainties, which are assumed to be fully correlated, to the result. We obtain a ratio of 1.055 ± 0.031 (stat.) ± 0.037 (sys.). Both tests suggest that these measurements are consistent with the Standard Model. Table 1. Measured R^ values with statistical (first) and systematic uncertainties.

yfi (GeV) 182.7 188.6 191.6 195.5 199.5 201.6 205.3 206.8

Rb ± stat ± sys 0.207 ± 0 . 0 1 8 ± 0 . 0 0 7 0.165 ± 0 . 0 1 0 ± 0 . 0 0 6 0.174 ± 0.025 ± 0.006 0.181 ± 0 . 0 1 7 ± 0 . 0 0 6 0.164 ± 0 . 0 1 6 ± 0 . 0 0 6 0.154 ± 0.024 ± 0.005 0.158 ± 0 . 0 1 8 ± 0 . 0 0 6 0.169 ± 0 . 0 1 4 ± 0 . 0 0 6

279 i i i i I i i i i I i i i i I i i i i I i i i i I i i i i I i i i i I i i i i I i i i i I

OPAL

0.25 0.2 0.15

H-—1—Ui^ • This measurement

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Figure 2. The measured R\, values and the Standard Model prediction (solid line). The error bars represent the combine statistical and systematical uncertainties

5.

Acknowledgment

We would like to t h a n k the organizers for a fruitful discussion in a splendid environment. References 1. G. Altarelli, T. Sjostrand and F. Zwirner, Physics at LEP2 CERN-TH/96-01, Vol. 1, 1996. 2. For a recent overview, see: CERN-EP/2004-069, November 2004 and references within. 3. OPAL Collaboration, G. Abbiendi et al, Phys. Lett. B 6 0 9 (2005) 212. 4. OPAL Collaboration, G. Abbiendi et al, Eur. Phys. J. C 3 3 (2004) 173. 5. OPAL Collaboration G. Abbiendi et al, Eur. Phys. J. C 8 (1999) 217. 6. OPAL Collaboration, G. Abbiendi et al., Eur. Phys. J. C16 (2000) 41. 7. OPAL Collaboration, G. Alexander et al., Z. Phys.C52 (1991) 175. 8. OPAL Collaboration, G. Abbiendi et al., Phys. Lett. B 4 9 3 (2000) 249. 9. OPAL Collaboration, G. Abbiendi et al, Eur. Phys. J. C26 (2003) 479. 10. D. Bardin et al., Comp. Phys. Commun. 133 (2001) 229;

QUANTIZATION OF GALILEAN COVARIANT FIELDS

E.S. SANTOS A , M. DE MONTIGNY A ' B , F.C. KHANNA- 4 ' 0 a

Theoretical Physics Institute, Univ. of Alberta Edmonton, Alberta, Canada T6G 2J1 Faculte Saint-Jean, Univ. of Alberta Edmonton, Alberta, Canada T6C 4 G9 C TRIUMF, 4004, Wesbrook Mall Vancouver, British Columbia, Canada V6T 2AS E-mails: esantos,montigny,[email protected]

We quantize Galilei-covariant field theories by using the canonical method and fivedimensional Lorentz-like covariant expressions of non-relativistic field equations. First, for a complex scalar field we calculate the scattering cross-sections for the Coulomb interaction and for the self-interacting A^4 term. Then, we turn to the Dirac equation and calculate the scattering and cross-sections for the Coulomb interaction, the electron-electron and the electron-positron scattering.

1. Introduction The quantization of Galilei-covariant theories has been presented in 1 and 2 . The program exploits a five-dimensional Galilean covariant formulation in order to understand the non-relativistic field theories 3 - 7 . A wealth of non-relativistic phenomena, particularly in condensed matter physics, low-energy nuclear physics, and many-body theory, are likely to benefit from any such convenient tool. Indeed, although it is usually understated, Galilean invariance is crucial for the applications of the methods of quantum field theory to many low-temperature systems such as superfluids, superconductors and Bose-Einstein condensation. A first advantage of the extended space approach is that Galilean covariance is manifest throughout the calculations. Therefore, the various procedures involved are carried out in the same way as in the relativistic case. Another, rather technical, advantage is that projective representations may be avoided when one is willing to pay the price of working in ( 4 + 1 ) dimensional space-time. The formalism begins with the fact that the (centrally extended) Galilei group in (3 + 1) space-time is a subgroup of the Poincare group in (4 + 1) 280

281 dimensions Hereafter, we will be working with Galilean five-vectors X^ = (X, X4, X5), which transform as X1' = Xi - V{XA, X*' = X\ X5' = 5 2 4 X - V • X + | V X . This transformation leaves invariant the scalar product : A • B = A • B — A4B5 - A5B4, so that, we use the Galilean metric gM„ where the non null terms are gu = -545 = - 554 = 1- The canonical conjugate variables provide the five-momentum : p^ = —\d^ = (—iV, — idt, —ids) = (p, —E, —m). When it comes to projecting the fields from G(4ii) to 3 + 1 dimensions, the relation ds = — \m implies the ansatz <E>(x) = e _ i m s y ( x , t). The invariant p^p^ = —k2, where k is some constant, leads to the dispersion relation : E = 2^;|p| 2 + 2m^ 2 ' where k — ±y/2m. In Section 2, we quantize the Schrodinger field and compute the scattering cross-sections for the Coulomb interaction and the self-interacting A<&4 term. In Section 3, we quantize the Fermi field and calculate the scattering cross-sections for Coulomb interaction, electron-electron and electronpositron scattering. 2. Complex Scalar Field : Schrodinger field The Lagrangian defined on extended space G(4,i) for Schrodinger field and its respective equation of motion are given by 8 L=

" 2 ^ ( ^ W ^ W + k2 Mx)\2) , 2

(0 M 0" - k ) *(*) = 0.

(1) (2)

The conjugate momenta of the field $(x) is -K{X) — ^$*(x). Thus, we find the following commutation relation, at equal times: [ $ ( z ) , $ V ) ] = <5(x-x')e-im(*5-*'5),

(3)

whereas the other commutators vanish. 2.1. Coulomb

interaction

The Coulomb interaction is described by introducing a minimal coupling between the scalar and the Coulomb field : d^ —> D^ = d^ + ieA^, where Ap = (0, — 0coui,O) and coui = — iff- The interaction Hamiltonian is 2 written as Hi = e
282

2.2.

Self-interacting

fields ; A * 4

In second order, the contribution to the 5-matrix is given by

5(2) = - I ( A / 2 ) 2 Jd5xd5y

:\$(x)\*\*(y)\*:

.

This expression contains some terms which represent the two trivial and independent first order processes, as well as terms for which the charge conservation is not respected, and, thus, such terms do not describe physical processes. In the centre of mass system, we have for the cross-section da dn

m4 A4 |p| 2 sin(0/2). 512 7T

3. Fermi Field We begin with the Galilean covariant Dirac Lagrangian, L = -V(x)(-y'ldli+k)9(x).

(4)

The Dirac equation for $ and its adjoint take their usual forms : (7"0M + k) *(*) = 0,

¥(a0)(7" 0 „ - f c ) = 0,

(5)

where [i = 1, ...,5. The adjoint spinor is given by 9(x) = ^(x) rj, with f] = —m (l4 + 7 5 )- The matrices 7^ are four-dimensional and we choose them as 7

V 0 -oa)'

7

\-V20J'

7

\o 0

They obey the Clifford algebra : {7",7"} = 2g»". We define the anticommutators at equal times as

{*„(*), *J(l/)} = i <W
-y

').

Interactions

In this section, we just show the final expressions for the scattering crosssection for the interaction of the Galilean Fermi field with a Coulomb field, electron-electron and electron-positron in the centre of mass system. a) Coulomb interaction da dO

=

a2 / 2p 2 4m 2 v 4 sin 4 (0/2) V ~ (E + m)2

. 2/a/o\ ^

283

The first term of this formula is identical to the one obtained in the relativistic theory in the low-velocity limit 9 . Moreover, the first term coincides with the previous cross-section for the scalar field and . the sin 2 (9/2) term is a signature of a spin 1/2 particle in a Coulomb interaction. b) Electron-electron scattering 4

da

dn

7+1 -3(7 - l)2

.

1 1 16w4 sin 4 (0/2) +' cos4 (6/2) sin 2 (9/2) cos2 (9/2) 4 8(7 - 1) ( 87 1+ -37-4 (6) 12 9 sin2 9 + sin 2 0

where 7 = E/m. If the limit E m, or 7 = 1, is taken, then we obtain the standard result da _ f a \ 2 1 1 1 2 dh ~ \m) 16i>4 sin 4 (9/2) +' cos4 (9/2) sin (9/2) cos2 (9/2), This is the Rutherford formula, taking into account the quantum effects. The cross-sections obtained here in this limit are identical to the corresponding limits of the relativistic case. However, no simple expansion of relativistic results seems to provide the cross-section formula in E.g. 6. c) Electron-positron scattering In this process and the previous one we use the intermediate field as the Galilean covariant five-dimensional Proca field, A^. da ~dH

4

(-)

(7

+

7+ 1 327

1 87D2 sin2 (9/2) +

3sin 2 (<9/2)-(7 1) sin2 9 -+ 16u4 sin4 (9/2) 2 (67-10)cos<9-10(37 1) 1) cos 9 2 + 87 8 7 v 2 sin2 (9/2)

+ (7- 1)

+

16w4 sin 4 (6>/2)

7+1 27

This result, in the limit 7 = 1 with low velocities, we obtain the well known non-relativistic expression da

dn

(a \mJ

1 IQv4 sin 4 (9/2)

Conclusion The manifest covariance of the Galilean symmetry of the field equations has been preserved throughout the calculations, as it is the case with the Lorentz symmetry of relativistic theories. We have presented the canonical quantization of the complex scalar fields, and computed the scattering

284

cross-sections for two examples : interaction with a Coulomb field, and quartic self-interaction. Then, for the Fermi fields, the Coulomb scattering, electron-electron and electron-positron scattering are calculated. The cross-sections obtained in the last two cases are interesting because, although they allow one to recover the corresponding results for the spinless fields and agree with the low-velocity limits of relativistic results 9 , there does not seem to be a way to obtain our cross-section formulas, for a small, but non-zero, value of the non-relativistic kinetic energy. Therefore, it seems that the Galilean covariant approach is more reliable than expansion of relativistic formulas in powers of p / m . This point deserves further investigation. Acknowledgments We acknowledge partial support by the Natural Sciences and Engineering Research Council of Canada. References 1. 2. 3. 4. 5. 6. 7. 8. 9.

L. Abreu, et al, Ann. Phys. (N.Y.) 308 (2003) 244. E. S. Santos, et al, to appear in Annals of Physics (N.Y.). M. de Montigny, et al, Ann. Phys. (N.Y.) 277 (1999) 144. M. de Montigny,et al, J. Phys. A : Math. Gen. 34 (2001) 8901; M. de Montigny,et al, J. Phys. A : Math. Gen. 33 (2000) L273; M. de Montigny, et al, Int. J. Theor. Phys. 42 (2003) 649. M. de Montigny, et al, J. Phys. A: Math. Gen. 36 (2003) 2009. Y. Takahashi, Fortschr. Phys. 36 (1988) 63; ibid Page 83. M. Omote, et al, Fortschr. Phys. 37 (1989) 933. E.S. Santos, et al, J. Phys. A: Math. Gen. 37 (2004) 9771. M.O.C. Gomes, 'Teoria Quantica dos Campos', Editora da Universidade de Sao Paulo, SP, Brazil, 2002.

ELECTROWEAK M E A S U R E M E N T S AT CDF *

A. SIDOTI t Laboratoire de Physique Nucleaire et de Hautes Energies Universite "Pierre et Marie Curie" (Paris VI) 4, Place Jussieu 75252 Paris Cedex 05, France

We present some recent measurements on electroweak physics using data collected by the CDF experiment at the Tevatron proton anti-proton collider (^/s = 1.96TeV) at Fermilab (Batavia, 111, USA).

1. Introduction The CDF electroweak physics program is one of the key components of the Runll. Electroweak measurements are complementary to those performed at e+e~ machines (LEP and SLD). The former can produce a larger number of W bosons and can produce Z/j* at higher invariant mass with respect of the latters. We will review CDF electroweak physics measurements using data collected from February 2002. The integrated luminosity of data ranges from 64 p b _ 1 to ~200 p b _ 1 depending on the measurement. 2. W and Z inclusive cross section measurements Due to the high branching ratios and clean signature W and Z bosons are identified through their leptonic decays. Inclusive cross sections of both W and Z have been measured using all the three leptons: electrons, muons and taus and using all the available subdetectors of CDF extending in particular the geometric acceptance at high pseudorapidity rf. All the measurements *On behalf of the CDF collaboration t Work supported by Research Training Network of E.U. "Probe of New Physics" HPRNCT-2002-00292 Contract a ?7 is related to the azimuthal angle through the relation rj = — logtan(0/2) 285

286

performed are shown in Fig.l and are in agreement with the theoretical predictions 1 . ' ' 'aid

\ n e (plug e+fi e

n

•

Stirling 2620± 7 0 ± 2 1 0 ± 1 6 0 (L= 72pb')

4-

Stirling, Van Neerven et al. (NNLO)

V .

i h I-

2786± 1 2 ± K ± 1 6 6 (lj*194pb )

r

1 ' ' ' ' 1 ' ' ' ' 1 ' ' ' ' 1 ' ' ' '

1

, , , ,|Van Neerven et al. (NNLO)

i

253.1 ± 4.2 ±J2 ±15.0 11

• *

(L= 194pb'')

e + u.

• r-

254.9 ± 3 . 3 ± 4 . 6 ±15.0 (i= 72pb~')

e

' •*

255.8 ± 3 . 9 ± 5 . 6 ±15.0 (L= 72pb')

2874± 3 4 ± 1 6 7 ± 1 7 2 (b* 64pb ) 2775± 10± 5 3 1 1 6 7
t

242.0 ±48.0 ±26.0 ±15.0 | U ,2pb )

2768 ± 14 ± 60 ± 1 6 6 (L= 72pb ) 2768± 1 4 ± 6 0 ± 1 6 6 (L. 72pb")

•< -

H

l.... I ... i ... I 1000 2000 _ 3000 4000 5000 6000 o(pp-»W)*BF(W-»lvlMpb)

, 1 , , , 200

248.0 ± 5 . 9 ± 7 . 6 ±15.0 (L= 72pb1)

300

400

500

o(pS->Z)xBF(Z->ll)(pb)

Figure 1. a(pp -» W) x BF(W -* tue) (left) and a(pp -> Z) x BF{Z - • it) (right) measured at CDF. The grey band indicates the theoretical (NNLO) predictions.

A stringent test of the Standard Model can be performed by evaluating the ratio R of the W and Z boson cross sections: R =

a{pp -> W) x BF(W -»tvt) a(pp -> Z) x BF(Z -> It)

that can be written as R =

a(pp -» W) a(pp -» Z)

T(Z) T(Z -» « )

T(W — we)

r(w)

Inserting the theoretical values of the total cross sections and of the partial width W —» Ivi and the experimental partial and total widths of the Z boson from LEP, it is possibile to extract indirectly the total width of the W boson. The measured value by CDF is: T{W) = 2079 ± 41 MeV CDF e + \x channel / CM = 72 pb~ x T{W) = 2056 ± 44 MeV CDF /. channel / Cdt = 194 p b " 1 well in agreement with both the PDG world average 3 and the theoretical predictions: r(W)pDG = 2118 ± 41 MeV

T(W)Th.

= 2092.1 ± 2.5 MeV

287

3. W Boson Asymmetries A precise charge asymmetry as a function of rapidity of the W boson provides constraints on the parton fluxes of the incoming protons and therefore provides a better determination of the parton distribution functions (pdf). The leptonic decay of the W boson makes difficult to measure directly the W rapidity itself. Instead, the electron asymmetry is measured that is the convolution of the W production charge asymmetry and the V-A asymmetry from the W decay. The lepton charge aymmetry is defined as: (da+/dr]e) -

(da-/dr)e)

Mve) = (da+/dr]e) + (d<j-/dr) ) e

where rje is the pseudorapidity of the lepton. CDF has measured the W charge asymmetry in the electron channel. The result as a function of the electron rapidity is shown in Fig.2. The measurement has been corrected for the effect of charge mis-identification and background contributions both dependent on the pseudorapidity. An additional selection 35 < ET < 45 GeV is applied on the electron energy to increase the sensitivity to different PDF. In fact the direction of an electron with higher energies is closer to the direction of emission of the W boson enhancing therefore the W production asymmetry 4 *-• CD

05

<

73 0 •*-* O 0 1_

o O

miliiii

E E

E CDF-II, 170 pb"1 E 35 < ET < 45 GeV

' ^

"\ '

E E

—CTEQ6.1M •— MRST02

E

NLO RESBOS (F. Landry, et al. Phys.Rev.D67:073016,2003)

I

K\ Figure 2. W charge asymmetry as a function of the electron pseudorapidity, with 35 < ET < 45 GeV. Comparison with expectations from different pdf are shown.

4. Di-Boson Production Di-boson processes probe electroweak gauge bosons interactions as well as sources of physics beyond Standard Model.

288 4.1. W-y and Z~f

production

When one of the bosons is a photon the main backgounds are no and jets faking a photon. To reduce these, CDF exploits the high spatial resolution of the electromagnetic calorimeter provided by the ShowerMax detector 5 and a track isolation criterium. The Wj —> £vej process has been studied by CDF in the electron and muon channel. Candidate events are selected requiring a high-Pr momentum lepton with large missing transverse energy and MT(£, V) < 120GeV/c 2 . The presence of a photon with ET > 7 GeV well separated from the lepton (AR(£, 7) > 0.7b) is required. The cross section times branching fraction measured is: a x BF(W^7 - • tva)

= 18.1 ± 1.6(stat.) ± 2.4(syst.) ± 1.2(lum.)pb _1

The predicted cross section including the photon acceptance is 7 : a x BF(Wj

-> tvelhh.

= 19.3 ± 1.4 pb

The photon transverse energy is shown in Fig.3. 2 7 —• U'y candidates are selected requiring two oppositely charged high momentum leptons with a dilepton invariant mass such that Mtti > 40 GeV/c 2 . The photon selection is the same of the Wj —> ivel- The cross section times branching fraction measured is 6 : a x BF(Z7 -y U-y) = 4.6 ± 0.5(syst + stat) ± 0.3(lum.)pb _1 The predicted cross section including the photon acceptance is 7 : a x BF(W7 -* eua)Th. 4.2. WW

= 4.5 ± 0.3 pb

Production

WW production has been studied at CDF in the WW —> (.vt(.'v't channel looking for two oppositely charged high PT leptons and large missing transverse energy in the final state. Using and integrated luminosity of 184 p b - 1 17 candidate events have been found with an estimated background of 5.01Q;| events. The cross section measured is 8 : a(pp - • WW) = 14.6i 5 ; 8 (stat)+3^(syst) ± 0.9(lum)pb well in agreement with the predicted cross section: cr(pp -> WW)Th.

= 11-3 ± 1.3pb

289

Figure 3. Photon ET (left) and Cluster transverse mass (right) for Wf —> ivy shown for observed events together with signal and background expectations. Anomalous gauge coupling will increase the high energy tail of the photon ET distribution.

5. Conclusions CDF is producing interesting results in the electroweak sector. Most of them have a precision that is limited by statistics. Therefore we are approaching a period where, with the available datasets, CDF can produce electroweak physics measurements with the smallest single experiment uncertainties. We are also refining the analysis using new methods that will decrease the systematics uncertainties. So far, no SM deviations have been observed. Acknowledgments It is a pleasure to thank all those at CDF and at Fermilab that are working hard for the success of the Runll of the Tevatron. I would also like to thank the organizers of this wonderful Lake Louise Winter Institute. References 1. P.J. Sutton et al., Phys Rev D45, 2349 (1992); P.J. Rijken et al., Phys Rev D51 44 (1995); R. Hamberg et al., Nucl. Phys. B359 343, (1991), R.V. Harlander et al., Phys. Rev. Lett. 88 201801 (2002). 2. D. Acosta et al. [CDF II Collaboration], Phys. Rev. Lett. 94, 091803 (2005). 3. S. Eidelman et al, Phys. Lett. B 592, 1 (2004). 4. D. Acosta et al. [CDF Collaboration], Phys. Rev. D 71, 051104 (2005). 5. G. Apollinari, et al. Nucl. Instrum. Meth. A412,515-526, (1998). 6. D. Acosta et al. [CDF II Collaboration], Phys. Rev. Lett. 94, 041803 (2005). 7. U. Baur, T. Han and J. Ohnemus, Phys. Rev. D 53 (1996) 1098. 8. D. Acosta et al. [CDF Collaboration], hep-ex/0501050.

R A R E A N D RADIATIVE B M E S O N DECAYS F R O M T H E BABAR E X P E R I M E N T

JORG STELZER Stanford Linear Accelerator Center, 2575 Sand Hill Road, MS 61, Menlo Park, CA 94025, USA E-mail: [email protected], edu Since its start in 1999 the BABAR experiment has collected a vast amount of data. Electron - positron collisions at the energy of the T(4S) resonance have produced about 240 million coherent B°B° and B+B~ pairs, opening the doors for exploration of rare B meson decays. An overview of the electroweak penguin physics program of BABAR is given. The analysis of two specific decays is presented in detail.

1. Introduction One of the primary scientific goals in high energy physics is to measure the parameters of the Standard Model (SM). The aim is to confirm the model that describes the basic relations between the particles and forces, or to find evidence for its incompleteness, often termed New Physics (NP). So far all experimentally acquired data point towards the validity of the SM. However, new generations of particle accelerators and detectors are producing ever larger datasets enabling us to search for NP in the regime where the SM predicts only small signals. These rare decays include penguin decays, CKM suppressed decays, and pure leptonic decays of B mesons. Most have branching fractions of 1 0 - 4 or less. Penguin decays proceed through a Wq loop diagram with the emission of an additional particle to conserve energy and momentum. The twofold change of the quark flavor introduces an effective flavor changing neutral current into the SM, otherwise forbidden at tree level. Penguin B decays with a suppressed tree contribution may exhibit direct CP violation, the asymmetry in partial width between a decay and its CP conjugate. Outside the B meson system only weak evidence exists. Recent observation of direct CP violation in the decay B° —> K+ir~ has raised excitement within and outside the community.1 290

291

Ultimately the study of rare penguin decays, in particular theoretically clean leptonic final states, could lead to the discovery of NP. New constituents like the Higgs or SUSY particles could enter the penguin loop, leading to increased branching fractions or effects on other observables. The interplay of weak and strong forces in weak B decays is best described in the framework of the Operator Product Expansion (OPE) and the renormalization group. The OPE achieves separation of the longdistance contributions contained in the operator matrix element Qi and short-distant physics described by the Wilson coefficients C; (Eq. 1). The index i runs over the contributing operators; in the literature Qr ... QIQ are usually associated with the various penguin decays. ffeff = - % y ) C i ( M , M W ) Q i ( / i )

(i)

While the coefficients can be calculated by well established field theoretical methods, it is - with few exceptions - the matrix elements that impose as the primary source of theoretical uncertainty. There are however a number of rare decays (B-tXaj, B-tl+l~,B->Ki>9), where the matrix elements can be extracted from other measurements or calculated perturbatively. Those are of primary interest. 2. The Rare Electroweak Physics Program at BABAR Depending on the gauge boson coupling to the loop one distinguishes between electroweak - that particle being a W^, Z, or 7, - and QCD - gluonic - penguin diagrams. The focus of this article will be the electroweak penguin decays with a photon or a lepton pair emerging from the loop. These decays can be studied in an inclusive or an exclusive manner, each having its own set of advantages and disadvantages. The reconstruction of a particular channel, e.g. B -» K*j, gives a clean experimental signal. However, due to long-distance QCD effects, namely the exchange of soft gluons in the formation of the strange hadronic state, large theoretical uncertainties arise when relating the measured quantities to the parameters of the SM. On the contrary the theoretical description of an inclusive decay such a s B - 4 X s 7 is very clean, since it corresponds to the partonic weak decay b -> sj. Only short distance physics is of relevance here and has been calculated up to next-to-leading order (NLO). The challenge here is on the experimenters side, since the methods for inclusively identifying a clean strange-hadronic samples are limited. In the following the search for the exclusive decay channel B -»(p, w)7 and the inclusive measurement of the B->XJ+l~ will be presented.

292

3. Search for B —> (p, w)7 Decays of type b—td'j are Cabibbo suppressed by a factor |Vtd/Vts|2 relative to b —> S7. Their measurement provides a mean for the extraction °f |Vtd/VfS| complimentary to the lifetime measurements of the Bd and Bs meson. The relation between the measured branching fractions and the SM parameters and QCD correction factors is given by Eq. 2. B(B->(p,q;)7)

B(B^K*i) where £ =

(^(0)

Vtd

Vts

i^Yc2(l + A*) 3 ~ mK*

(2)

)

= 0.85 ± 0.1 is the transition form factor ratio reflecting

the SU(3) breaking in the B -> K* transition, and AR = 0.1 ± 0.1 the weak annihilation correction 2 . The individual branching ratios relate as \B(B+ -> p+7) = B{B° -> p°7) = B(B+ -> ory), the combined result is calculated as B{B ->• [p,u)i) = %{B(B+ -> p+7) + ^ [ £ ( £ ° -> />°7) + B(B+—>co^f)]} where ^ i - is the i? meson lifetime ratio. The signature of B -> (p, w)7 events is a high energy photon, required to be between 1.5 GeV and 3.5 GeV. The p and w are reconstructed in their major decay mode, p + (°) ->TT+-K0(~^ and w->7r + 7r _ 7r°, and combined with the photon to form B meson candidates. Backgrounds in this analysis include peaking B decays such as B - > K*f, combinatoric T(45) -»• BB background, and continuum events e+e~~ -t qq with q 6 {u, d, s,c}. Variables which are related to the rest of the event (ROE) are combined in a neural net (NN), to separate continuum events from B decays. Variables constrained by the kinematics of the event are put into a Fisher discriminant, to reduce backgrounds such as B —> (p, u, 7r)(7r°, 77). This includes e.g. the helicity angle of the daughters of the p and w, which are transversely polarized J = 1 states. The remaining peaking background are B —» K*-y events where the K± from K* has been misidentified as a 71^. They exhibit a shift in AE due to the misidentification. The signal yield is extracted by simultaneously fitting the four variables rngs = V^beam ~ $B-> AE = Eg — E%eam, the NN output, and the Fisher discriminant, using probability distributions derived from Monte Carlo events. The analysis was performed on a data sample of 191 f b - 1 . Figure 1 shows the result of the fit for the combined modes B -¥ (p, w)7. The signal yield is 269J^2oi45 e y ents, the significance 2.1CT. BABAR published an upper limit for the branching fraction B{B^(p,w)-y) < 1.2 x 10" 6 at 90% C.L.. Reaching the lower boundaries of some of the SM predictions 2 , this

293

5.22 B2& &26 5£S n^iQeWe)

4.3-0.2-0.1 0 Oil (U (L3 dE*(G«V)

Figure 1. Fit of signal and background (dashed) P D F ' s simultaneously in TOES) A E , NN, and Fisher on the

Figure 2. CKM constraint from B —> (p,u)f. [C.Afl] = [0.85,0.1] - solid, [0.75,0.0] - d a s h e d .

combined B—>(p,w)7 sample.

result puts pressure on the calculation tools and models. BABAR sets an upper limit | | ^ | < 0.19 at 90% C.L., putting new constraints on the apex of the unitary triangle. However, within the errors of the £ and Ai? it is consistent with the current CKM fit (Fig. 2). 4. Semi-inclusive measurement of

B—>Xal+l

The decay B -4 Xal+l~ receives short distance contributions from electromagnetic and Z penguin diagrams as well as W box diagrams. Long distance contributions are from the resonant process B->XaJ/ift() -*Xal+l~ which can be eliminated by suitable cuts in the invariant lepton mass spectrum. While the branching fraction B(B -*• Xs^f) depends on the magnitude of C%s, its combination with various distributions of B-+Xsl+l~ can be used to extract all short-distance physics from electroweak penguin diagrams (C| f f , Cg, and Cio-) The BABAR analysis of B->X8l+l~ is performed in a semi-inclusive fashion. Ten B decay modes with a K± or a Ks and a combination of up to three pions are reconstructed. Assuming the same rates for K\ as for Ks this accounts for about 70 % of the total branching fraction. The precise number depends on the fragmentation model used and is the source of a large systematic uncertainty in the final result. After passing a J/ip and ip' veto, lepton pairs with a minimum mass of 200 MeV/c2 are combined with the strange hadronic system to form B meson candidates. Several measures to suppress combinatoric background are taken. Among these the event shape variables i?2 and cos dthrust and the variables AE, &EROE, and m§$B prove to be most effective. The fit in the mEs distribution (Fig. 3) yields 40 ± 10 ± 2 events. This results in a branching

294

(a)

2 < £ 2 •a a 5.22

524

5.25

525

5.3

m„(GeV/c')

522

524

5.26

5.26

5.3

•o

o

m I S (GeV/c')

Figure 3. Fit to mBS for (a) B^Xsl+r (l = e,fj,) and (b) B —> Xse^fv? (lepton flavor violating).

•ti m a (GeV/c")

mtl (GeV/c*)

Figure 4. Differential branching fraction as a function of the (a) X3 mass and (b) l+l~ mass. Line - theory.

fraction measurement of B{B^Xsl+l~) = ( 5 . 6 ± . 1 . 5 ± 0 . 6 ± l . l ) x l 0 - 6 , the errors being the statistic, systematic, and the previously mentioned model uncertainty. The differential branching fraction as a function of mx, and mu (Fig- 4) and the direct CP asymmetry Acp are in good agreement with predictions. However, the precision of Acp is still about two orders of magnitude away from the theoretical uncertainty. 5. Summary The BABAR collaboration has undertaken a number of analyzes in the electroweak penguin sector (Tab. 1). Many have reached a sensitivity at the level of the SM predictions; for those the tasks ahead are precision measurements of the branching fraction and first measurements of CP, forwardbackward, polarization, and isospin asymmetries. BABAR has not yet seen evidence of NP, but with the large data sample and sophisticated analysis techniques it has the best tools for a discovery at hand. Table 1.

QJ

BAR4R B->Xs7

"S TJ

X

B^-XJ+l-

Measurements published by the BABAR collaboration.

Standard Model S = (3-88to-.56) x 1 0 _ 4 -3 ACP = (25 ± 52) x 1 0 6 B = (5.6 ±2.0) x 103 ACP = (220 ± 260) x 10"

B = (3.61+0;i{j|) x 10" 4 ACP = (*-2±2{.t) x 10- 3 B = (4.2 ±0.7) x 10~ 6 ACp = (1.9 ±1.9) x lO" 3

B^K*"/ B = (4.06 ± 0.26) x 10~ 5 B = (7 ± 2) x 1 0 " 6 B-»-(p,w)7 B < 1.16 x 1 0 - 6 B = (1.38 ± 0 . 4 2 ) x 1 0 " 6 B-+K*l+r B = (0.88 ± 0 . 3 3 ) x 1 0 " 6 B = (1.19 ± 0.39) x 10~ 6 B^Kl+lB = (0.65 ± 0.14) x 10~ 6 B = (0.35 ± 0 . 1 2 ) x 10~ 6 + + B + - > K / T T V V , B° - > i + ( / 7 7 , B° -*<jyy searches still 1-10 orders of magnitude away from SM predictions

References 1. B . A u b e r t et al. [BABAR Collaboration], P h y s . R e v . L e t t . 9 3 (2004) 131801. 2. A. Ali, E. L u n g h i a n d A. Y. P a r k h o m e n k o , P h y s . L e t t . B 5 9 5 , 323 (2004).

T H E LHCB R I N G - I M A G I N G C H E R E N K O V D E T E C T O R S

J. W. STOREY* University of Cambridge, Cavendish Laboratory, Madingley Rd, Cambridge, CB3 OHE, UK E-mail: [email protected]

The particle identification system of the LHCb experiment is presented. It consists of two ring-imaging Cherenkov (RICH) detectors, which provide pion/kaon separation over the momentum range 1 up to >100GeV/c. The system uses novel hybrid photon-detector (HPD) technology, providing single photon sensitivity and high spatial resolution, and high speed radiation tolerant readout electronics. Performance studies of this technology, including a system test in a prototype RICH-2 vessel at a CERN pion test beam, are described.

1. Introduction 1.1. The LHCb

Experiment

The Large Hadron Collider Beauty (LHCb) experiment is a forward onearm spectrometer dedicated to the study of CP violation and other rare phenomena in the decay of hadrons containing b-quarks at the Large Hadron Collider (LHC) 1 . The physics goals are to check the consistency of the Standard Model through precision measurements of the sides and angles of the Cabibbo-Kobayashi-Maskawa (CKM) triangle, and to search for new physics in decays that are rare, or forbidden, in the Standard Model. 1.2. Particle

Identification

The ability to distinguish between pions and kaons is vital at LHCb, as many of the decay modes of interest for CP-violation studies have significant backgrounds from decays that are identical in topology. For example, Fig.l shows the effect of RICH particle identification (PID) information on the 'results presented in this report are the work of the LHCb RICH group.

295

296

invariant mass spectrum of simulated B° —> DSK decays. Without particle identification (left plot) the signal, shown unshaded, is overwhelmed by the B° -> Dj"7r+ background. With the PID data (right plot) this background is removed significantly.

El B, -¥ D,JI

1

WiihoutRICH

1200

f

DB,->D,K

With RICH

.

13 B, -* D,w > 1000 O

Invariant mass [GeV/c 2 ]

800

3

600

w

400

1 Invariant mass

[GeV/c2]

Figure 1. DSK invariant mass spectra with (left) and without (right) RICH particle ID.

LHCb requires K/i: separation over the momentum range ~ 1 GeV/c to >100GeV/c. The upper limit in momentum is determined by tracks from the hadronic two-body decay of B-mesons, while the lower limit is set by the momenta of the Kaons used for B-flavour tagging. 2. The LHCb RICH Detectors Particle identification in LHCb, particularly pion and kaon separation, is provided by two Ring-Imaging Cherenkov (RICH) detectors 2 . This technique uses the emission angle of Cherenkov photons emitted by a charged particle, together with a momentum measurement, to infer the mass of a particle. The momentum range covered by a RICH detector depends on the refractive index of the radiator, and on the Cherenkov angle resolution. To cover the required momentum range, the LHCb RICH system employs three different radiators, split between two RICH detectors. The lowest momentum particles, ~ l G e V , are detected by a silicon aerogel radiator (n=1.03). Intermediate momentum particles (up to ~70GeV/c) are detected by gaseous C4F 10 (n=1.0014). Both radiators are part of RICH 1, which is located close to the interaction region. In order to detect high momentum particles (>100GeV) a second detector, RICH 2, uses a gaseous CF4 gas radiator (n=1.0005) and is placed further downstream.

297

Aerogel

C 4 F 10

g^g

1190

Figure 2. Optical layout of RICH1 (left) and RICH2 (right). The paths of Cherenkov photons for a particle traversing RICH 1 are shown. Only half of each detector is shown.

The optical layout of the two detectors, shown in Fig.2, are very similar. Both detectors use a secondary flat mirror, to enable the photodetectors to be placed outside the detector acceptance, and to allow room for the extensive iron structure that is required to shield the photodetectors from fringe magnetic fields. Beryllium mirrors are used in RICH 1 so as to minimise the amount of material in the acceptance of the detector, while lower-cost quartz mirrors are used in RICH 2. The Cherenkov light is detected by Hybrid Photon Detectors (HPDs), this novel technology is described in detail below. 3. The Hybrid Photon Detector 3.1. Photodetector

Requirements

The photodetector for the RICH system must be single photon sensitive, fast (1 bunch crossing every 25 ns), precise (~2mm resolution) and have a high active-to-total area ratio (~70%). In addition, the detectors must be radiation hard to exposures up to 3 kRad/year, able to tolerate fringe magnetic fields of 20-30Gauss, and affordable (cover 2.6m 2 ). A hybrid photon detector (HPD) has been developed, in close collaboration with industry, to meet these requirements 3 . 3.2. Hybrid Photon

Detectors

(HPDs)

An HPD consists of a vacuum tube with an S20 multi-alkali photocathode at the entrance window and a pixellated silicon detector at the anode. A

298

photoelectron, released by an incident photon, is accelerated by a 20 kV potential and focused electrostatically onto the anode, and releases ~5000 electron-hole pairs in the silicon. The anode assembly consists of a 300 /xm thick array of 32 x 256 reverse biased p-n junctions, bump bonded to a custom CMOS binary readout chip. 3.3. HPD Performance

Studies

The single photoelectron detection efficiency of a single isolated HPD has been determined using a pulsed low intensity light-emitting diode (LED) 4 . The test setup allowed for direct measurement of the total silicon detector charge (back-pulse), a fit to which enabled estimation of the average number of incident photoelectrons. Detection efficiency losses are caused by back-scattering of photoelectrons, the threshold setting and charge sharing between pixels. However, the measured value of ~88% is within the LHCb specification. Laboratory measurements made of a single isolated HPD exposed to magnetic fields of similar magnitude to that expected in the experiment, have verified that with appropriate corrections the original undistorted image can be fully reconstructed. Test beam measurements of HPDs in a prototype RICH detector, combined with detector simulations, have demonstrated the Cherenkov angle resolution and photon yield to be within expectations and to meet the LHCb specification of 0.35 mrad in RICH l 5 . 3.4. Cluster

Test of 6 HPDs

A prototype RICH 2 vessel was constructed to test a cluster of 6 HPDs, together with the (almost) final versions of the readout electronics, mechanics and power distribution systems. The test was conducted in a CERN lOGeV/c pion/electron beam with both nitrogen and C4F10 radiators. Data from six close-packed HPDs operating at 20 kV were read at the full 40 MHz LHC bunch-crossing rate, and transmitted to the offdetector electronics at 1.6 Gbit s _ 1 . The accumulation of 100,000 pions traversing the prototype detector is shown in Fig.3. This is the first time a close-packed cluster of HPDs has been operated successfully with full LHC-speed readout electronics. The test verified the operation at high voltage of the close-packed HPD geometry and provides a final verification of the system before commissioning. The same apparatus will be used to test a cluster of Mu-metal shielded

299

Figure 3. Cherenkov ring from 10 GeV pions traversing a C4F10 radiator.

HPDs in a magnetic field of strength similar to that expected. Finite element simulations of an array have been performed but are of limited accuracy due to the inherit errors of the simulation process. Therefore it is important to verify the predictions of the simulation and to demonstrate that the proposed shielding is sufficient. Finally, it is foreseen to test a full column of 16 HPDs. 4. Conclusions The particle identification provided by the RICH system is crucial to the LHCb physics programme. The two RICH detectors will provide significant kaon/pion separation over the momentum range ~ 1 GeV/c to >100GeV/c. Novel hybrid photon detectors have been developed to meet the RICH photodetector requirements. A system test of a prototype RICH 2 detector has demonstrated the successful integration of the HPDs, readout electronics and mechanics in a realistic LHC environment. References 1. 2. 3. 4. 5.

LHCb Collaboration, CERN/LHCC 98-4, LHCC/P4, (1998). LHCb Collaboration, CERN/LHCC 2000-0037, (2000). T.Gys, Nucl. Instrum. Methods A465, 240 (2001). M.Moritz et al., Trans. Nucl. Sci. 51, 1060 (2004). S.Easo, LHCb 2000-70 RICH, (2000).

PHYSICS OF HEAVY FLAVOUR AT C D F

STEFANO TORRE* Univerita degli Studi di Siena Dipartimento di Fisica Via Roma 56 - 53100 Siena - Italy and Istituto Nazionale di Fisica Nucleare sez. di Pisa Largo B. Pontecorvo 3 - 56100 Pisa - Italy E-mail: [email protected]

Results on physics of heavy flavour at CDF are reported. Selected measurements of Branching Ratios and CP asymmetry in B° and B°, lifetime difference of B° CP eigenstates and a precise measurement of the B c mass are presented.

1. Introduction The upgraded Collider Detector at Fermilab (CDF II) 1 has collected around 800 p b - 1 between February 2002 and February 2005 during the Tevatron Run II at Fermilab. At pp colliders a large amount of b and c mesons and baryons are produced within a background of hadronic particles. However the presence of heavy flavour particle decays can be detected by the presence of a displaced secondary vertex, because these particles have long decay lengths (O(100/jm)). The issue is to be able to extract this information at trigger level. For this purpose CDF uses the Silicon Vertex Trigger (SVT) 2 that reconstruct online the tracks providing the informations needed for the trigger decision. In this way CDF is able to efficiently select events in which the heavy meson decays in either leptonic or fully hadronic modes. The collected data samples allow to perform a wide range of measurements, from the observation of rare decays to lifetime measurement, through BR and CP asymmetry measurements. In the following we concentrate on some selected topics.

*On behalf of the CDF Collaboration. 300

301 2. Branching ratios and C P asymmetries measurements Fully hadronic b meson decays are very useful to understand the b sector of the CKM matrix. CDF is providing interesting measurement both on two body charmless and on pure penguins decays.

2.1. Two body charmless

decays (B —¥h+h'

CDF Run 2 Preliminory.L = 180 pb"'

)

CDF Run 2 Preliminary. L=-180 pb"'

nn Mass [GeV/cl

n n Mass [GeV/c^

Figure 1. The plot on the left shows yield of B —• h+h'~ events at CDF. The signal is given by several decays. By an unbinned likelihood fit the different contributions can be extracted and the plot on the right shows, in different colors, the different contributes.

These decays are the ones in which & B°, B® meson goes into charged Pions and Kaons. The theoretical prediction on their BR and CP asymmetries are strongly affected by uncertainties on hadronic contributions. These unknowns can be removed by combining the informations obtained in the different modes 3,5 . The mass resolution at CDF is not enough to directly observe the different signals, but their yields can be extracted via an unbinned likelihood fit that exploits both kinematic and energy loss information. The overall yield is shown in the left plot in Fig.l. The result of the fit is shown in the right plot of Fig.l. In 1 8 0 p b - 1 we observe 509 B° -> K+TT~, 134

B°

-» TT+TT- and 232

B°

-» K+K~.

We measure the ratio:

/dfi ( (B^g+^-) = 0.50±0.08(stot)±0.07(s2/st). We set also the limits on the BRs of rare B°s decays as: ftggbjfclj < 0.11 and ^(%"XK+1~-) < 0-10 both at 90%C.L.. We also measure the CP asymmetry in the B° -*• ^TT^ decay and we obtain -0.04 ± 0.08(stat) ± 0.01{syst).

302 CDF RUN II Preliminary

L = 160±10pb"'

CDF Runll Preliminary

L = l79±l0pb'

8 events in search window Expected BG events = 0.75 ±0.41 *

5

t 4

ill 5

5.2

5.4

5.6

5.6 6 , m [GeV/o1]

Figure 2. The plot on the left shows the signal of B * —> cfrK^ events. The blue line is the fitted distribution of signal and background events. The red line is the only signal contribution to the fit. The other lines are different background contributions. The plot on the right shows the evidence of B ° —> events.

2.2. Pure penguin

decays

B meson decays involving b —> sss transitions can provide evidences of deviation from the SM 4 . In particular direct CP asymmetry of B± -» fyK^mode is expected to be of the order of few percent within the SM 5 . Left plot in Fig. 2 shows the mass distribution containing the signal of this decays obtained at CDF. The number of signal events has been extracted from the background using an unbinned likelihood fit on the kinematics of the particle's energy losses. We measured B(B± —> (pK^) = 7.6 ± 1.3(stat) ± 0.6(syst) x 1(T 6 and aCp{B± -> QK*) = -0.07±0.17(stat)±° 0 ° 0 l(syst). The same b transition occurs in B® —t (jxp decay. First evidence of this decay has been found at CDF and the right plot in Fig. 2 shows the observed signal. We measure B{B± -> (jxj)) = lAto*(stat) ± 0.2(syst) ± 6 0.5(BR) x 10~ where the last error comes from the BR of the B° -» J/ip4> that has been used as normalization mode. Details of these analyses can be found in Ref.6.

3. Measurement of decay width difference of JB° C P eigenstates In B°s —• J/ip

303 I - 260 pb

Iw

B„ -»

JAK

Figure 3. Projection of the unbinned maximum likelihood fit on the lifetime distribution. The red/yellow lines correspond to the light/heavy mass eigenstate.

amplitudes. The plot in Fig. 3 shows the projections of the fit result on the lifetime. The yellow line is the lifetime of the heavy mass eigenstate while the lifetime of the light one is reported in red. We found -jf1 = 65l33% 7 . 4. Spectroscopy

CDF Run 2 Preliminary Bc Mass = 6-2B70±0.0048 GeWc* Resolution (fixed) = 15.5 MeV/c* Signal: 18.9±5.7 events Mean exp. backgd.: 10.0±1.4 evts under peak

*J/>lt*

6.3

6.35

6.4

6.45 ,

J/vnMass(GeV/cz)

Figure 4. Mass distribution of events in the search window for Bc —*• J/ipir. The red line is the fit applied to data to measure the mass.

In the field of spectroscopy the measurement of the Bc mass is important to validate the theoretical models that predict this quantity 8 . This meson has been observed at DO9 and CDF 1 0 in semileptonic modes. Because in this kind of decay the events are not fully reconstructed the achieved mass resolution was not enough to constrain the theoretical predictions. We look for evidence of the fully reconstructed Bc ->• J/tpn decay in the mass range between 5.6 and 7.2 GeV/c 2 corresponding to 2a window around the previously measured value.

304

We optimize the selections following a blind procedure. The plot in Fig. 4 shows the mass distribution in the signal region after applying the optimized cut. From the fit we measured a signal of 18.9 ± 5.7 events over a background of 10.0 ± 1.4. The value of the mass we obtain is 6287.0 ± 4t.8(stat) ± l.l(syst) MeV/c where the systematic error is mainly given by the parametrization of the background. 5. Conclusions We have reported some examples of the wide range of heavy flavour particles that can be detected at CDF and how their characteristics can be investigated. These analyses are still statistically limited. However the systematics are well under control and the results will be easily improved by increasing the data samples. References 1. D. Acosta et al., Phys. Rev. D71, 032001 (2005). 2. W. Ashmanskas et al., Nucl. Instrum. and Meth., A518, 532 (2004). 3. R. Fleisher, Phys. Lett. B459, 306 (1999); M. Gronau and J.L. Rosner, Phys. Lett. B482, 71 (2000); J.F. Sun, G.H. Zhu and D.S. Du Phys. Rev. D68, 054003 (2003); D. London and J. Matias, Phys. Rev. D70, 031502 (2004); Y. Li, CD. Lu, Z.J. Xiao and X.Q. Yu, Phys. Rev. D70, 034009 (2004). 4. A. Raidal, Phys. Rev. Lett. 80,231803(2002); A.Datta et al, arXiv:hepph/0406192; submitted to Phys. Rev. D. 5. M. Beneke and M. Neubert, Nucl. Phys. B675, 333 (2003). 6. D. Acosta et al., arXiv:hep-ex/0502044; submitted to Phys. Rev. Lett. 7. D. Acosta et al., Phys. Rev. Lett. 94, 101803 (2005). 8. W. Kwong and J. Rosner, Phys. Rev. D44, 212 (1991); E. Eichten and C. Quigg, Phys. Rev. D49, 5845 (1994); S.Godfrey, Phys. Rev. D70, 054017 (2004); N. Branbilla, Y. Sumino and A. Vairo, Phys. Rev. D65, 034001 (2002); I.F. Allison, C.T.H. Davies, A. Gray, A.S. Kronfeld, P.M. Mackenzie, J.N. Simone, arXiv:hep-lat/0411027 and arXiv:hep-lat/0409090. 9. DO Collaboration, DO note 4539-CONF. 10. CDF Collaboration, Phys. Rev. Lett. 81, 2432 (1998) and Phys. Rev. D58, 112004 (1998).

T I M E - D E P E N D E N T CP-VIOLATING A S Y M M E T R I E S IN B -»• SQQ A N D B -> S-y T R A N S I T I O N S

Y. USHIRODA (THE BELLE COLLABORATION) KEK,

1-1 Oho, Tsukuba-city

Ibaraki-pre.

Japan

We present measurements of CP-violation parameters in B° -> (j>K°, K+K~K^, / o ( 9 8 0 ) K ° , rt'K^, uK°, K%ira, K%K°K% and i
In the Standard Model (SM), CP violation arises from an irreducible phase, the Kobayashi-Maskawa (KM) phase 1 , in the weak-interaction quark-mixing matrix. In particular, the SM predicts CP asymmetries in the time-dependent rates for B° and B° decays to a common CP eigenstate fcp2- In the decay chain T(4S) ->• B°B° -> /cp/tag, where one of the B mesons decays at time tcp to a final state fcp and the other decays at time ttag to a final state / t a g that distinguishes between B° and B°, the decay rate has a time dependence given by ,1 e -|At|/r B o f r V(At) = — 11 + q- \Ssin(AmdAt) + Acos(AmdAt)\ V. (1) Here S and A are CP-violation parameters, TB° is the B° lifetime, Am<j is the mass difference between the two B° mass eigenstates, At is the time difference tcp — itag, and the 6-flavor charge q = +1 (-1) when the tagging B meson is a B° (B°). In b —> sqq transitions, to a good approximation, the SM predicts <S = — £/ sin20i, where £/ = +1(—1) corresponds to CPeven (-odd) final states, and A — 0. The value of sin2(/>i has already been determined rather precisely from time-dependent CP asymmetries in B° —> J/xpKg and related b —> ccs transitions by Belle 3 ' 4 and BaBar 5 ; the present world average value is sin2i = +0.726 ± 0.037 6 . This serves as a firm reference point for the SM. In radiative penguin processes such as 305

306

b —> S7, the mechanism of time-dependent CP violation is different from the case of b -> sgg. Within the SM, the photon emitted from a B° (B°) meson is dominantly right-handed (left-handed). Therefore the polarization of the photon carries information on the original 6-flavor and the decay is, thus, almost flavor-specific. As a result, the SM predicts a small asymmetry 7 . Significant deviations from these expectations would be a manifestation of new physics. At the KEKB energy-asymmetric e+e~ (3.5 on 8.0GeV) collider 8 , the T(45) is produced with a Lorentz boost of /3j — 0.425 along the z axis defined as antiparallel to the e + beam direction. Since the B° and B° mesons are approximately at rest in the T(45) center-of-mass system (cms), At can be determined from the displacement in z between the fcp and / t a g decay vertices: At ~ (ZCP — ztag)/(Pjc) = Az/(f2jc). The Belle detector 9 is a large-solid-angle magnetic spectrometer A 2.0 cm radius beampipe and a 3-layer silicon vertex detector (SVD1) were used for a 140 fb _ 1 data sample containing 152 x 106 BB pairs, while a 1.5 cm radius beampipe, a 4-layer silicon detector (SVD2) 10 and a smallcell inner drift chamber were used for an additional 113 fb _ 1 data sample that contains 123 x 106 B~B pairs for a total of 275 x 106 BB~ pairs. Among b —> sqq transitions, we reconstruct the following decay modes: $K% and r)'K% for £/ = - 1 , cj>K°L; / 0 (980)Kg, uK%, and K°STT° for ft = + 1 ; in addition, K+K~K$ which is a mixture of £/ = + 1 and £/ = — 1 states is used. We find that £/ = + 1 state is predominant. Among b —> sj transitions, we reconstruct B° —> Kgn0rY in two Kgir0 invariant mass ranges: 0.8GeV/c 2 < MKo o < 1.0GeV/c 2 targeting K*°(892), and the full region up to 1.8GeV/c 2 including other resonances and non-resonant contributions. Whenever necessary, we distinguish these two by referring to them as K*°j and Ksir°j, respectively. In the following, the outline of analyses is described. Any details can be found elsewhere 11 ' 12 ' 13 with the updated final results. We identify B meson decays using the momentum of the B candidate in the cms (jf™) for 4>K\. For other modes, we use the energy difference AE = EQ°S — £ ™ i i anc ^ t n e beam-energy constrained mass M b c = y/(E£™m)2 - (pg" s ) 2 , where E£™m is the beam energy in the cms, and .Eg"8 is the cms energy of the reconstructed B candidate. The main background contribution is from e + e~ -¥ qq with q = u,d,s,c. In order to suppress qq background, we form a likelihood ratio {TZs/b) based on the event topology, where we take an advantage of the fact that our signal from BB decay has a spherical event shape while qq event is jet-like.

307

The 6-flavor of the accompanying B meson is identified from inclusive properties of particles that are not associated with the reconstructed signal decay. We use two parameters, q defined in Eq. (1) and r, to represent the tagging information. The parameter r is an event-by-event flavor-tagging dilution factor that ranges from 0 to 1; r = 0 when there is no flavor discrimination and r = 1 implies unambiguous flavor assignment. For Ksir°, KSKSKS and KSTT°J analyses, the vertex position of the signal-side decay is reconstructed from the Ks trajectory with a constraint on the interaction point (IP); the IP profile (ax ~ 100/im, ay ~ 5/im, az ~ 3 mm) is convolved with the finite B flight length in the plane perpendicular to the z axis. For other modes, two charged tracks which originate directly from the B vertex are used together with a constraint on the IP. The other (tag-side) B vertex determination is done in an established way 1 1 . Figure l(a,b) shows the M^c (AE) distribution for the reconstructed Ks candidates within the AE (Mbc) signal region after flavor tagging and vertex reconstruction. The signal yields are determined from unbinned twodimensional maximum-likelihood fits to the AE-M^C distributions (PB" S for (f>Kl). Number of observed events in the signalbox, extracted number of signal yields are listed in Table 1.

»•

+

(0

S5-0.5 IS I E

-1

I 1 I 0.5 0.-

5.24

5.26

M „ (GeV/c2)

5.26

5.3

-0.2-0.15-0.1-0.05 0 0.05 0.1 0.15 0.2

AE(GeV)

At(ps)

Figure 1. (a) Mb c and (b) AE distributions for <j>Kg. Solid curves show the fits to signal plus background distributions, and dashed curves show the background contributions. Raw asymmetry in each At bin with 0 < r < 0.5(top) and with 0.5 < r < 1.0 (bottom) for 4>K° is shown in (c).

We determine <S and A from an unbinned maximum-likelihood fit to the observed At distribution. The probability density function (PDF) expected for the signal distribution, Vsig(At), is given by the time dependent decay rate [Eq. (1)] modified to incorporate the effect of incorrect flavor assignment. The distribution is convolved with the proper-time interval resolution function i?sig> which takes into account the finite vertex resolution.

308

For each event, the following likelihood function is evaluated:

Pi = (1 - /oi) J

[/.igTWAf JflrigtAti - At')

+ (1 - Us)Vhkg(At')Rhk&(Ati

- At') d(At')

+ foiPoi(Ati),

(2)

where P0\ is a Gaussian function that represents a small outlier component with fraction / 0 i 4 - The signal probability / s ; g is calculated on an eventby-event basis from the function which we obtained as the result of fit for the signal yield extraction. Parameters in Pbkg and i?bkg are determined by a fit to the At distribution of a background-enhanced control sample, i.e. events outside of the AE-MbC (pg"8 for .ftT°) signal region. We fix TBO and Arrid at their world-average values 14 . The only free parameters in the final fit are <S and A, which are determined by maximizing the likelihood function L = Y\i Pi{Atf,S, A) where the product is over all events. Table 1 summarizes the fit results of S and A. The systematic errors are carefully estimated; they are much smaller than the statistical errors for all modes. We define the raw asymmetry in each At bin by (JV 9=+1 — Nq=-i)/(Nq=+i +Nq=-\), where iV g _ +1 (_ 1 ) is the number of observed candidates with q = +1(—1). Figure 1(c) shows the raw asymmetries for the cj)K° candidates in two regions of the flavor-tagging parameter r. Note that these are simple projections onto the At axis, and do not reflect other eventby-event information (such as the signal fraction, the wrong tag fraction and the vertex resolution), which is in fact used in the unbinned maximumlikelihood fit for S and A. Table 1. Observed number of events in the signal box (Nau), extracted number of signal yields(iVsjg), and results. mode K+K~K<1 /o(980)K| ri'K^ uK% tfg7T°(high-rcs/b) K°sn°{low-Tls/b) K K K S S s K*°-y AT27r°7

Nau 221 207 715 715 178 178 842 842 56 56 309 516 167 167 92 92 227 227

N.SIR 139 ± 14 36 + 15 398 +± 28 28 94 ++ 14 14 512 27 512 +± 27

31 31 ++ 77 168 ± 16 79 + 19 88 ++ 13 13 88 57 ++ 99 105 +± 14 14

+0.06 ± 0.33 ± 0.09

+0.08 ± 0.22 ± 0.09

-0.49 + 0.18 + 0.04 +0.47 + 0.41 + 0.08 +0.65 + 0.18 + 0.04 +0.75 ± 0.65ioJ|

-0.08 + -0.39 + -0.19 + +0.26 +

+0.30 + 0.59 + 0.11

-0.12 + 0.20 + 0.07

+1.26 + 0.68 + 0.18 - 0 . 7 9 ^ ^ + 0.10 —0.58±g-_|| ± 0.11

+0.54 + 0.34 + 0.08 fixed at zero +0.03 + 0.34 + 0.11

0.12 + 0.27 + 0.11 + 0.48 +

0.07 0.08 0.05 0.15

309

In summary, we have performed measurements of CP-violation parameters for B° -> (j>K° (including both <j)K% and <j>K%), K+K~K°S, iK°s, B° -> f0(980)K%, uK%, K%TT°, and K%K%K% decays. These charmless decays are dominated by b -¥ s flavor-changing neutral currents and are sensitive to possible new CP-violating phases. The combined result differs from the SM expectation by 2.7 standard deviations. Measurements with a much larger data sample are required to conclusively establish the existence of a new CP-violating phase beyond the SM. We have also measured CPviolation parameters for B° -¥ Kg-ir0*/ decays in two regions of the Kgir0 invariant mass: between 0.8GeV/c 2 and 1.0GeV/c 2 for the K*° resonance, and the full region up to 1.8GeV/c 2 . The two results are consistent with each other and with no CP asymmetry. References 1. M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973). 2. A. B. Carter and A. I. Sanda, Phys. Rev. D 23, 1567 (1981); I. I. Bigi and A. I. Sanda, Nucl. Phys. B193, 85 (1981). 3. Belle Collaboration, K. Abe et al., Phys. Rev. Lett. 87, 091802 (2001); Phys. Rev. D 66, 032007 (2002); Phys. Rev. D 66, 071102 (2002). 4. Belle Collaboration, K. Abe et al., Phys. Rev. D 71, 072003 (2005). 5. BaBar Collaboration, B. Aubert et al, Phys. Rev. Lett. 89, 201802 (2002); hep-ex/0408127. 6. Heavy Flavor Averaging Group, hep-ex/0412073. 7. D. Atwood, M. Gronau and A. Soni, Phys. Rev. Lett. 79, 185 (1997). B. Grinstein, Y. Grossman, Z. Ligeti and D. Pirjol, Phys. Rev. D 71, 011504 (2005). 8. S. Kurokawa and E. Kikutani, Nucl. Instrum. Methods Phys. Res., Sect. A 499, 1 (2003), and other papers included in this volume. 9. Belle Collaboration, A. Abashian et al., Nucl. Instrum. Methods Phys. Res., Sect. A 479, 117 (2002). 10. Y. Ushiroda (Belle SVD2 Group), Nucl. Instrum. Methods Phys. Res., Sect. A 511, 6 (2003). 11. Belle Collaboration, K. Hara et al., hep-ex/0504023. 12. Belle Collaboration, K. Sumisawa et al., hep-ex/0503023. 13. Belle Collaboration, Y. Ushiroda et al., hep-ex/0503008. 14. S. Eidelman et al, Phys. Lett. B 592, 1 (2004).

T O P PHYSICS RESULTS AT C D F

TREVOR VICKEY* University of Illinois at Urbana-Champaign Department of Physics 1110 West Green Street Urbana, IL 61801-3080, USA E-mail: Trevor. [email protected]

The most recent results on top quark physics at CDF are reported. Measurements of cross-section and mass are presented, and the status of single top quark production searches are discussed. The results obtained from probing various top quark properties are also presented.

1. Introduction Recently discovered1 by the CDF and DO Collaborations, the top quark is the least well understood fundamental particle. As a consequence of its enormous mass, around 175 GeV/c 2 , this hefty particle has a lifetime shorter than the hadronization timescale. With the top mass close to the scale of electroweak symmetry breaking there are hints of an intimate relationship between top and this mechanismHiggs is most strongly coupled to the top quark. By studying top we are testing electroweak theory, as this quark may be sensitive to physics beyond the standard model (SM). 2. Top Quark Production and Decay Modes At the Tevatron, a pp collider with a center of mass energy of y/s = 1.96 TeV, top is predominantly pair produced via qq -» ti 85% of the time with the remaining fraction generated via gg —> ti. The cross-section for ti production at the Tevatron, assuming mt = 175 GeV/c 2 , is 2 6.7ig'9 pb. By comparison, the total cross-section for producing top singly via electroweak processes is smaller by about a factor of two. "On behalf of the CDF Collaboration.

310

311

CDF II preliminary D • • • • • • ED •

160E 140L,

mistags Wbb Wcc non-W Wo WW,W.Z,Z~m Single top Totbkgd±1o Data (162 pb"1)

."S22ISS2SS ••«•• -- > ! i

t-

';•?!) U

-- •

Number of jets in W+jels

S 4

Figure 1. The top quark signal region of the lepton-plus-jets sample occupies the 3 and > 4 jet bins.

Top decays to aW boson and a b quark nearly 100% of the time due to unitarity constraints on the CKM matrix. The experimental signature of a it event includes two b quark jets, the presence of multiple light-quark jets and/or a single high-pr charged lepton accompanied by significant missing transverse energy ($x) from an undetected neutrino. Top candidate events are frequently classified by the W boson decays. The "dilepton" mode occurs when each of the two Ws decay leptonically. Both Ws decaying hadronically produce the "all-hadronic" mode; events with a mixture of leptonic and hadronic decays are dubbed "lepton-plus-jets" events. 3. Top Quark Cross-section Measurements Conducting a top quark production cross-section measurement validates our top-enriched samples and could yield the first signs of new physics in the top quark sector. The dilepton analyses use event selections of either two identified charged leptons (e or fj,), at least two jets and large ftp or a single charged lepton in addition to a well isolated track. Analyses in the lepton-plus-jets channel have a larger initial data sample than dilepton analyses, albeit one which contains a larger amount of background contamination. Tagging 6-jets is a technique used to increase the fraction of top in the lepton-plus-jets sample. The tagger used by CDF is sensitive to displaced secondary vertices due to the relatively long-lived

312

b quarks, in addition to semi-leptonic decays of the b. The signal region for tagged lepton-plus-jets events is shown in Fig. 1. The b tagging is also used by the all-hadronic analysis in addition to a trigger which requires four high pr jets and a large total transverse energy in the event. Results of CDF's most recent cross-section measurements are summarized in Table 1. All results obtained thus far are consistent with the SM.3 4. Top Quark Mass Measurements Through the correlation with other SM parameters, a measurement of the top mass puts constraints on the Higgs. A precise top mass measurement is difficult due to the level of understanding necessary concerning jet energies and the relationship between parton-level objects and detector observables. This measurement is also hampered by our ability to correctly assign jets to the parton-level objects in top decays. Several methods are used by CDF to measure the top mass in the dilepton and lepton-plus-jets channels. Most of the analysis techniques use templates generated from Monte Carlo events in conjunction with likelihood fitting. The Dynamical Likelihood Method (DLM), however, takes into account all possible jet combinations in an event and the likelihood is multiplied event-by-event to derive the top quark mass using a maximum likelihood method. The advantage of the DLM method over the canonical template methods lies in the fact that the cross-section is used as a posterior probability whereas in the template methods it is used as a prior Table 1.

Top quark pair-production cross-section measurements. JCdtlpb-1}


7-°tl'l

(stat.) t\\l

Dilepton: Jfr, Num. jets

8

(stat.) ± 1.1 (syst.)

Lepton + Jets: Kinematic

4.7 ± 1.6 (stat.) ± 1.8 (syst.)

193

Lepton + Jets: Kinematic NN

6.7 ± 1.1 (stat.) ± 1.6 (syst.)

193

-^-IA

(syst.)

200 200

Lepton + Jets: Vertex Tag + Kinematic

6.0 ± 1.6 (stat.) ± 1.2 (syst.)

162

Lepton + Jets: Vertex Tag

5 6

162

- - l ' . i (stat.) t%% (syst.)

Lepton + Jets: Double Vertex Tag

5-°-l'.g (stat.) j j j ' i (syst.)

162

Lepton + Jets: Jet Probability Tag

5 8

162

Lepton + Jets: Soft Muon Tag

5 2

All Hadronic: Vertex Tag

7.8 ± 2.5 (stat.) ti'l

- - i " . | (stat.) ± 1.3 (syst.) - t i ' . i (stat.) t\\l

(syst.) (syst.)

193 165

313 Table 2.

Top quark mass measurements. mt

[GeV/c 2 ]

fCdt

[pb- 1 ]

Dilepton:
170.0 ± 16.6 (stat.) ± 7.4 (syst.)

Dilepton: pz it

176.5J:Jg;o (stat.) ± 6.9 (syst.)

193

Dilepton: v weighting

168.1 tgf

200

Lepton + Jets: Multivariate

179 6

Lepton + Jets: Mreco

177.2tl\j

Lepton + Jets: DLM

(stat.) ± 8.6 (syst.)

- te'.3 ( stat -)

193

± 6 8

- ( s y st -)

162

(stat.) ± 6.6 (syst.)

162

1 7 7 . 8 1 ^ (stat.) ± 6.2 (syst.)

162

probability. Results of the most recent top mass measurements are summarized in Table 2. 5. Single Top Quark Searches Investigating single top production is a great opportunity to study the charged-current weak interaction and to search for new physics thought to be exclusive to these channels. Single top production cross-sections are proportional to the CKM matrix element Vtb', a measurement of the crosssection provides a direct measurement of this quantity. CDF has searched for the s and i-channel single top production modes which have theoretical cross-sections of 0.88 and 1.98 pb, respectively.4 The strategy for single top analyses is to search for W decay products plus two or three jets. Two analyses were conducted in 162 p b - 1 of data to search for single top. A combined search using the scalar sum of the event transverse energy (HT distribution) was used for single top discovery and to measure |Vtf,|. Separate s and i-channel searches using the Q x rj distribution*1 were carried out to reveal any new physics. The combined search sets a limit of < 17.8 pb @ 95% CL. Limits from the s and i-channel searches are < 13.6 pb @ 95% CL and < 10.1 pb @ 95% CL, respectively.5 6. Measurements of Top Quark Properties Now that sizable samples of top quark candidate events have been accumulated, we can proceed to measure various top quark properties. a

Q is the charge of the lepton and JJ of the light-quark jet.

314 The fraction of right-handed W bosons from top decay is heavily suppressed in the SM. The charged-lepton px and angular distributions for each of the three W helicity states are very distinct-a feature exploited to make a helicity measurement using templates in likelihood fits to the CDF data. CDF uses both the charged-lepton pr and lepton angular distributions for extracting the fraction of longitudinal Ws. The lepton pr analysis carries out a measurement in both the dilepton and lepton-plus-jets datasets measuring F0 = 0.27io'.2i (stat.) ± 0.17 (syst.), the angular distribution method uses the lepton-plus-jets dataset measuring F0 = 0.89+^34 ( s t a t -) ± ° - 1 7 (syst.). CDF has recently revisited the Run I data to make a measurement of the right-handed fraction,6 F+ < 0.18 @ 95% CL. An analysis of top decay kinematics 7 yields results consistent with the SM. CDF has measured several ratios of branching fractions: BR(t —>• Tub)/BRSM(t -> rvb) < 5.0 @ 95% CL and BR(t - • WB)/BR(t ->• Wq) > 0.62 @ 95% CL. We have also measured the ratio of the crosssections (Tdilepton/^lepton+jets = 1.45lo'.55(stat. + Syst.). 7. Outlook Experimentally, top quark physics is still in its infancy. While no unexpected results have been observed thus far, many opportunities for discovery still exist at CDF. As CDF continues the trend of doubling its dataset each year, statistical and systematic uncertainties will be reduced greatly improving the current measurements. References 1. F. Abe et aZ., Phys. Rev. D50, 2966 (1994); Phys. Rev. Lett. 74, 2626 (1995) S. Abachi et al, Phys. Rev. Lett. 74, 2632 (1995). 2. R. Bonciani et al, Nucl. Phys. B529, 424 (1998) N. Kidonakis and R. Vogt, Phys. Rev. D68, 114014 (2003); Eur. Phys. J. C33, s466 (2004). 3. D. Acosta et al, Phys. Rev. Lett. 93, 142001 (2004); Phys. Rev. D71, 052003 (2005); Phys. Rev. D71, 072005 (2005). 4. B.W. Harris et al, Phys. Rev.T>66, 054024 (2002) Z. Sullivan hep-ph/0408049. 5. D. Acosta et al., Phys Rev. D71, 012005 (2005). 6. D. Acosta et al, Phys. Rev. D71, 031101(R) (2005); erratum ibidD71, 059901 (2005). 7. D. Acosta et al., hep-ex/0412042, submitted to Phys. Rev. Lett.

INCLUSIVE B R A N C H I N G F R A C T I O N OF D ^

vX

MICHAEL L. WEINBERGER Wilson Lab Cornell University, Ithaca, New York 14853 E-mail: [email protected] This analysis will use the extremely clean event environment of CLEO-c to select D —> i/X decays without identifying the charged lepton. The analysis will be fully inclusive with respect to lepton flavor and semileptonic decay mode. This will be the first measurement of BR(D -> vX).

1. Introduction This analysis is an alternative and independent method of making inclusive D semileptonic measurements. The data is taken with a beam center of mass energy at the ^(3770) resonance, just above threshold for DD production, therefore ^(3770) -> DD only, and no extra particles enter the event. Using the neutrino reconstruction method of summing the visible momentum and energy, the missing 4-momentum of the neutrino can be calculated. 1 Non-neutrino events can then be eliminated by cuts on event properties. 2. CLEO-c and CESR-c CESR-c is a symmetric e+e~ accelerator on the campus of Cornell University. For the CLEO-c datasets the machine was run at the V(3770) resonance, with plans to run on other energies in the future. CLEO-c is nearly identical to the CLEO III detector. 2 The most important property of the detector for the reconstruction of the neutrino's 4-momentum is the hermeticity, covering a solid angle of 93%. Another important feature is the particle ID for charged tracks which is calculated by the wire drift chambers and a RICH detector. Information about the dE/dx is obtained from the drift chambers. The drift chamber has very good momentum resolution of ^ = 0.6%. 315

316 Outside of the drift chamber is the electro-magnetic calorimeter which is used to detect photons and to eliminate KL for this analysis. Beyond the calorimeter is the 1 Tesla superconducting solenoid magnet. 3. Method One of the D mesons decays into a simple hadronic mode, is tagged, and is then eliminated from the neutrino reconstruction. This elimination of the tag is not necessary, but is used to simplify the reconstruction. The cleanest tagged modes, D° —»• Kn, KTTK°, Kmrir, and D+ —> Ksir, KTTTT are used. On the signal side, the 4-momenta of the tracks and showers are summed. The dE/dx and RICH information, when available, is used to make the identification. The particle identification is done by a conditional tree. The track is first tested to see if it is identified as an electron, then as a kaon, otherwise it is defaulted to a pion. Given that there is no muon id available, unless a muon is misidentified as an electron or kaon, which is very rare, it will be treated as a pion. Showers caused by a charged tracks have already been counted in the reconstruction and should not be included in the shower sum. Code has been developed to eliminate all showers produced by tracks. The remaining showers are then added to the track 4-momentum sum. The missing momentum and energy can now be calculated. The sum of the tracks, showers, and the momentum of the tagged D is then subtracted from the 4-momentum of the beam-beam system. If there is a neutrino in the event, the missing energy will be the energy of the neutrino and the other main variable Mass2Miss = £ ^ j g s — PmiSs-> should be equal to zero within resolution. 3.1.

Cuts

The first set of cuts ensures a good D tag. There is a cut on the AE and on the beam constrained mass. Due to mis-identification of daughter particles there may be more than one tag for an event. In these infrequent cases the event is eliminated. The next set of cuts ensures that the reconstruction is clean. If something, for example, a track failing the loose quality cuts, will cause the reconstruction to be incorrect, the event is not used. If a track does not pass the cuts it will not be used for the reconstruction and this event is eliminated. The next cut eliminates events where the code used to remove

317 showers from charged particles in the reconstruction, passes showers that it should not. The last cut eliminates events with one track that is not a lepton. Since muons are identified as pions, this cut eliminates only single track kaon events.

3.2. EMUS

VS Mass%r-

and

V

cut

A highly instructive plot for this analysis is the plot of EM, vs. Mass2Miss [Figure 1, left side] which shows most of the important features of this analysis. The most important feature is the vertical clustering of events near zero composed of correctly reconstructed neutrino events. The missing energy is that of the neutrino and it is grouped around Mass2Miss = 0. A large grouping of fully reconstructed hadronic events is clustered at the zero energy bottom of this line, which can smear up in to the signal region. The next noticeable feature is the cut-off curved line on the right of the plot. Since Mass2Miss = E ^ - P^iss, at a fixed energy, the maximum Mass2Miss occurs when the missing momentum is equal to zero. This cutoff condition is simply a plot of EvsE2. The last feature is the vertical clustering of events, to the right of the neutrino line, consisting of KL events that do not interact in the detector. They have Mass2Miss of the mass of the KL squared. A V-shaped cut is used in place of a simple Mass2Miss = 0 to eliminate the remaining events without neutrinos. The error on the Mass2Miss is dominated by the error on the energy so this cut is a constant cut on the fractional error on the Mass2Miss.

Figure 1. L E F T : Plot of EMiss vs. Mass2Miss in MC; RIGHT: Plot of cos Weinberger angle - (dashed = events containing a neutrino, solid = events with a KL and no neutrino).

318

3.3. KL Suppression

Cuts

There is no hadronic calorimeter in the CLEO-c detector, so it it not possible to fully reconstruct KL events. However, the crystal calorimeter is about one nuclear interaction length, so approximately half of the KL will interact and leave a shower. The half of the KL particles that do not interact in the detector can be eliminated by the V-cut as their Mass2Miss will be at the mass2 of the KL • Those that do interact leave some fraction of their energy in the electromagnetic calorimeter, which can be used to cut out these events. The angle between the missing momentum vector and the closest unmatched shower is used to eliminate these interacting KLS. A vector that represents a neutrino will be randomly distributed with respect to the showers. However, if the missing vector is from a partially interacting KL, then the vector will point near the shower produced. The cos of the angle is shown in the right side plot in Figure 1. The events with KL in them peak at cossh6 — 1, with the missing momentum vector pointing towards the shower, thus making it possible to eliminate a large number of the KL events. 4. Plots of

EMXSB

and Data vs. Monte Carlo

The missing energy for D° and D+ is plotted in Figure 2. The background has been highly suppressed and is mostly flat. The background starts to peak as it gets to lower energy due to the start of inclusion of the fully reconstructed hadronic events at zero EMISS and Mass2Migs. Another noteworthy feature is the rise in events at high energy in the D+ plot, around 1 GeV. This is caused by the two body decay, D -» fiu. As this is a two body decay, the neutrinos are monoenergetic, with one half of the energy of the D meson. Figure 3 contains plots of the data vs. MC, with the points in the plots representing the data, and the line representing the MC spectrum scaled down by the ratio of the luminosities. There is no fit performed. There is very good agreement between the data and the Monte Carlo, which shows that the MC accurately reflects the data, and that the numbers obtained from the MC are trustworthy. 5. Conclusion Using the cleanliness of the events in CLEO-c, this measurement of the inclusive branching ratio of D -)• vX can be done for the first time. It is

319

Figure 2. MC plots of EMiss, D° left and D+ right

\f\ 4 i

•J

'W.

Figure 3. Data vs. MC, D° left and D+ right fully inclusive as t o lepton flavor and the decay mode of the D meson. This analysis is orthogonal t o other semileptonic decay measurements and can be used as a check for branching ratios and form factors.

References 1. L. K. Gibbons, "Measurement of the CKM matrix element Vu(, and exclusive B ->• ntv and B -* ptv decays," Annu. Rev. Nucl. Part. Sci. 48, 121 (1998). 2. Y. Kubota et al., Nucl. Instrum. Meth., A320, 66 (1992); G. Vi'ehhauser et al., Nucl. Instrum. Meth. A462, 146 (2001); D. Peterson et al, Nucl. Instrum. Meth., A478, 142 (2002); M. Artuso et al., Nucl. Instrum. Meth., A502, 91 (2002); CLEO-c/CLEO-c Taskforces & CLEO-c Collaboration, Cornell LEPP preprint CLNS 01/1742 (2001).

I N T E G R A L FLUXES, DAY-NIGHT, A N D S P E C T R U M RESULTS F R O M SNO'S 391-DAY SALT P H A S E

JURGEN WENDLAND University of British Columbia for t h e S N O Collaboration The Sudbury Neutrino Observatory is a 10001 heavy water Cherenkov detector observing neutrinos from the Sun and other astrophysical sources. Measurements of the integral solar neutrino fluxes of charged current, neutral current and elastic scattering events are reported for 391 days of live data from the salt phase of SNO operation. In this phase 21 of salt were dissolved in the heavy water, which enhanced and differentiated the detection of neutral current events. Day-night asymmetries in these fluxes were also determined. The measured electron spectrum from the charged-current channel is compatible with the undistorted spectrum of the solar 8 B neutrino flux.

1. Solar Neutrinos Solar neutrinos are produced in nuclear fusion processes in the center of the Sun, predominantly from the so-called pp cycle. These neutrinos have energies up to about 19 MeV. The flux of solar neutrinos arriving at Earth was measured prior to 2001 by a variety of experiments sensitive to various ranges in the neutrino energy spectrum. These experiments were exclusively or primarily sensitive to electron neutrinos and included radiochemical measurements using CI or Ga and measurements of elastic scattering off electrons in light water Cherenkov detectors. The observed solar neutrino fluxes were two to three times smaller than those predicted by solar models 1,2 ' 3 . This discrepancy may be explained by the oscillation of massive neutrinos giving rise to flavor change in neutrinos. The formalism for this process was introduced by Maki, Nakagawa, Sakata, and Pontecorvo (MNSP) 4 ' 5 and was expanded to include matter-enhanced oscillations in the Earth or the Sun by Mikheyev, Smirnov, and Wolfenstein (MSW) 6,7 . In a two neutrino flavor model the mixing of the two neutrino flavor eigenstates ve and v^ is described by the mixing angle 8 with respect to the neutrino mass eigenstates v\ and v^ and the difference of the squared neutrino masses 320

321

Am 2 = m 2 — m\. The survival probability for an electron neutrino in vacuum is then P(ve -> ve) = 1 - sin2 20sin 2 (1.27Am 2 L/.E), where L is the distance traveled in km and E the neutrino energy in MeV. In matter the mixing angle depends on the electron density Ne of the medium, t a n 2 0 M = tan0/(1 - 2y/2EGFNe/(Am2 cos26)). The hypothesis of solar neutrino flavor transformation was first directly verified with measurements by the Sudbury Neutrino Observatory (SNO), which included a measurement of the total flux of solar 8 B neutrinos via the neutral current reaction in pure heavy water 9,10 ' 11 ' 12 . 2. The Sudbury Neutrino Observatory SNO is a 10001 pure heavy water Cherenkov detector located 2039 m (~ 6000 mwe) underground in the Inco Creighton Mine near Sudbury, Ontario, Canada 8 . The heavy water is contained in a 12 m diameter acrylic vessel which is surrounded by ~ 7,0001 of light water. 9,456 photomultiplier tubes (PMTs) that provide a photocathode coverage of 54 % are used to observe neutrino induced Cherenkov events. SNO detects neutrinos via elastic scattering from electrons (ES, vx + e~ ->• vx + e~), and via the charged current (CC, ve + d - > p + p + e" ) and neutral current reactions (NC, vx+d —> n +p + vx) on the deuteron. The ES reaction is sensitive to all neutrino flavors, but the electron neutrino sensitivity is higher than the others by a factor of about 6.5. The CC reaction is exclusively sensitive to electron neutrinos, whereas the NC reaction is equally sensitive to all active neutrino flavors. The detection of the neutron is critical for the identification of the NC reaction. During SNO's first of three phases of operation the neutron was detected in pure heavy water via photon emission induced by neutron capture on deuterons. In the second phase, the addition of 2t of salt to the heavy water enhanced the neutron detection via capture on chlorine and enabled a statistical separation of the NC and CC events through measurement of the isotropy of events on the phototubes. For the ongoing third phase, a discrete array of 40 3He-filled proportional counters for individual neutron detection was deployed in the heavy water. 3. The SNO Salt Phase Neutron capture on 35C1 in the salt increases the neutron detection efficiency by about a factor three compared to pure heavy water. In the subsequent de-excitation of 36C1 a cascade of photons with a total energy

322

of 8.6 MeV is released. In comparison to the pure heavy water phase where neutron capture resulted in a 6.25 MeV photon, the energy profile of the radiative capture photopeak is thus moved further above the analysis threshold. In addition the multi-photon signature of neutron capture on chlorine is more isotropic than the single-ring Cherenkov events from the CC and ES interactions. Event light isotropy thus provides an additional means of distinguishing these event classes. To obtain the rate of the CC, ES, and NC reactions and the energy spectrum of the CC events an extended maximum likelihood fit was applied to 4722 neutrino candidate events from the 391-day salt phase data set 13 . Probability density functions for each of the reactions and for an external neutron background were generated by a detailed Monte Carlo simulation of the detector in terms of the following parameters: event energy (Teff), event direction (cos0 0 ), volume weighted radius (p — (R/RAV)3, RAV — 600.5 cm), and event isotropy (/3i4). The inclusion of event isotropy allowed a fit to the energy spectrum of the CC events that was not constrained to the spectral shape of solar 8 B neutrinos. Systematic uncertainties on the detector response were measured by comparing data from the Monte Carlo simulation with data from calibration sources. By propagating these uncertainties through the signal extraction process their effects on the fit parameters were determined. The fluxes of the CC, ES, and NC channels obtained in this fit are respectively in units of 1 0 6 c m _ 2 s _ 1 : (j>cc = 1.68 ± 0.06 (stat)* 0 0 8 (sys), Nc = 4.94±0.21 (stat)*^® (sys). These fluxes are the equivalent fluxes of 8 B electron neutrinos above an energy threshold of zero assuming an undistorted spectral shape. The main sources of systematic uncertainties are the isotropy measurement, the energy scale and bias, the event reconstruction biases, the neutron detection efficiency (NC flux only) and the angular resolution (ES flux only). The ratio of the CC and NC flux is (fcc/^NC = 0.340 ± 0.023(stat)+o°^(sys), providing clear evidence that solar electron neutrinos change flavor in transit to the Earth. The energy spectrum of the solar CC flux is shown in the left hand panel of Fig. 1. The expected shapes for an undistorted 8 B solar neutrino flux and for the best fit MSW model, see below, are also shown. For certain ranges of mixing parameters the MSW effect predicts a regeneration of solar electron neutrinos when they pass through the Earth. The regeneration could be measurable as an asymmetry ADN = 2 (D)/(4>N + 4>D) of the solar neutrino flux jv measured at SNO

323

7t„(MeV)

7"cff(MeV)

Figure 1. Left: The energy spectrum of the solar neutrino CC flux. The error bars are the statistical uncertainties. The band on the undistorted 8 B model shape represent the detector systematic uncertainties. Note that the data points are statistically and systematically correlated. Right: The day-night asymmetry of the charged current solar neutrino flux as a function of energy. The errors bars show the statistical uncertainties, and the horizontal line shows the expectation for the best fit MSW parameters.

during the night and the flux measured during the day £>. The energyunconstrained analysis described above was carried out separately for the day and night neutrino candidate events. The resulting asymmetries in the CC, NC, and ES fluxes are ACc = -0.056±0.074(stat)±0.053(sys), ANC = 0.042±0.086(stat)±0.072(sys), and AES = 0.146±0.198(stat)±0.033(sys), respectively, where the systematics largely cancel in the asymmetry ratio. The day-night asymmetry of the CC flux as a function of electron energy is shown in the right hand panel of Fig. 1. Within the uncertainties the asymmetry is compatible with zero and with the best fit MSW solution, discussed in the following. In an MSW two-parameter fit the presented results were combined with the global solar neutrino data set from SNO's pure heavy water phase, the CI14 and Ga 15 ' 16 experiments and with the Super-Kamiokande zenith spectra 17 . Assuming CPT invariance the rates and spectra of the KamLAND experiment were also included to further restrict the allowed parameter space. The result of this neutrino oscillation analysis is shown in Fig. 2. The best fit point, Am 2 = 8.0+g'j-lO- 5 eV2 and 0 = ZZ$±t\i degrees, lies in the large mixing angle (LMA) region. In this fit the SNO data provide strong constraint of the mixing angle. 4. Summary The SNO collaboration has completed the salt phase data acquisition. Integral fluxes of the CC, NC, and ES reaction rates were extracted from

324

68% CL 95% CL 99.73% CL

tan26 Figure 2. Neutrino oscillation contours in MSW parameter space for two flavor mixing. The best fit point is indicated by the star. the full salt d a t a set. T h e electron energy spectrum of the solar electron neutrino flux was observed with the charged current reaction and the daynight solar neutrino flux asymmetries were measured. T h e spectrum and t h e day-night asymmetries are consistent with the no-oscillation hypothesis and with the prediction by the best fit M S W LMA solution, which was determined in an M S W fit t o global solar plus K a m L A N D d a t a .

References 1. J. N. Bahcall and M. H. Pinsonneault, Phys. Rev. Lett. 92, 121301 (2004). 2. J. N. Bahcall, A. M. Serenelli and S. Basu, Astrophys. J. 621, L85 (2005). 3. S. Turck-Chieze et al, Phys. Rev. Lett. 93, 211102 (2004). 4. Z. Maki, M. Nakagawa and S. Sakata, Prog. Theor. Phys. 28, 870 (1962). 5. V. N. Gribov and B. Pontecorvo, Phys. Lett. B 28, 493 (1969). 6. S. P. Mikheev and A. Y. Smirnov, Sov. J. Nucl. Phys. 42, 913 (1985). 7. L. Wolfenstein, Phys. Rev. D 17, 2369 (1978). 8. J. Boger et al. [SNO], Nucl. Instrum. Meth. A 449, 172 (2000). 9. Q. R. Ahmad et al. [SNO], Phys. Rev. Lett. 87, 071301 (2001). 10. Q. R. Ahmad et al. [SNO], Phys. Rev. Lett. 89, 011301 (2002). 11. Q. R. Ahmad et al. [SNO], Phys. Rev. Lett. 89, 011302 (2002). 12. S. N. Ahmed et al. [SNO], Phys. Rev. Lett. 92, 181301 (2004). 13. B. Aharmim et al. [SNO], arXiv:nucl-ex/0502021. 14. B. T. Cleveland et al., Astrophys. J. 496, 505 (1998). 15. V. N. Gavrin [SAGE], Nucl. Phys. Proc. Suppl. 138, 87 (2005). 16. M. Altmann et al. [GNO], Phys. Lett. B 490, 16 (2000). 17. S. Fukuda et al. [Super-Kamiokande], Phys. Lett. B 539, 179 (2002).

JETS A N D H I G H - P T (DI-HADRON) CORRELATIONS I N PHENIX

DAVID L. WINTER FOR THE PHENIX COLLABORATION

1

Columbia University 538 West 120th St. New York, NY 10027, USA E-mail: winterQnevis. Columbia, edu

The method of azimuthal correlations has proven to be an extremely useful tool to study jet observables at RHIC. We present an overview of the method of azimuthal correlations as used in the measuring jet structure in the PHENIX experiment. We also report on recent results in jet studies of p + p , d + A u , and A u + A u collisions at y/s^ = 200 GeV.

1. Introduction The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory has provided a rich data set of heavy ion interactions at extremely high energy (,/iJviv = 200 GeV) 3 . The PHENIX experiment 2 is one of four at RHIC, and consists of two central arms for measuring rare hadronic and leptonic probes at midrapidity and two forward arms for measuring muons. An important result to emerge from the RHIC physics program is the behavior of spectra at high pr, especially suppression of produced particles in Au+Au collisions (compared to p+p) and the apparent disappearance of the away-side jet production in Au+Au collisions. The cold or hot nuclear environment can affect the partons involved in jet formation, and changes in the structure of the di-jet production can shed important insight into the properties of the nuclear medium. The two-particle azimuthal correlation technique provides an alternative method of accessing the properties of jets in the high-multiplicity environment of a heavy-ion collision, where traditional jet reconstruction is impossible. An important observable for studying the physics of the nuclear medium is the Nuclear Modification Factor. It has a number of similar definitions, but essentially represents a comparison of particle yields from nuclear col325

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lisions to that from p + p collisions (scaled by the number of effective interactions). Our first example is RCP, the ratio of yields in central collisions (scaled to the number of binary collisions taking place in the collisions) to that in peripheral collisions: RCP

=

Yield (central), scaled Yield (peripheral), scaled

(1)

The RCP for d+Au collisions is shown in Figure 1. If the physics of a d+Au reaction were simply a superposition of p + p interactions, we would expect RCP to be one. Instead, we see an enhancement in the PT range of 3 — 5 GeV/c. This peak is typically called the "Cronin Enhancement" and is usually attributed to multiple scattering in the medium. In contrast, one can calculate RAA f° r a given centrality, RAA

=

Yield (centrality bin), scaled Yield (p+p), scaled

(2)

The RAA for Au+Au collisions at 200 GeV is also shown in Figure 1. Again, if a nucleus-nucleus collision were a simple collection of p + p collisions, a ratio of one would be expected. For peripheral collisions, RAA is close to unity. However, in central collisions we observe a strong suppression of pion production. The source of the suppression is an area of active

327

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Figure 2. Azimuthal Correlation Kinematics. On the left is the near-side jet kinematics and on the right the the far-side.

study, and is thought to be dominated by medium-induced energy loss. The observed RCP and RAA are clearly exciting, but we would like to go beyond what single-particle observables can tell us about the nuclear medium. In other words, what can jet observables tell us about the underlying dynamics of the nucleus?

2. Correlations and Jet Structure A heavy-ion collision can produce particle multiplicities in the thousands, so it is clear that modern jet reconstruction techniques are extremely difficult to use in analyzing such collisions. The method of azimuthal correlations provides an alternative to full jet reconstruction. The basic idea is that one constructs a A<£ distribution, where A(f> is the angle between the highest pT (leading) particle and each of the other (associated) particles in the event. A correlation function can then be constructed by dividing the distribution of pairs from the same event by pairs from mixed events:

°m

=

Nmixed{W)

(3)

Any resulting peaks would reflect the angular correlation between pairs of particles. The kinematics important to the azimuthal correlation function are shown in Figure 2. For the near-side correlations, the leading or highest PT particle is called the "trigger" particle, and is considered an estimator of the jet axis. When we measure the A0 distribution between trigger and "associated" particles in the event, we expect the pairs to be correlated in a peak around A(fr = 0. Assuming pr,trig » 3TV, we can derive simple relations between characteristics of the correlation function and jet structure

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variables, for instance:

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(5)

where ztrig = PT,trig/pr,jet, while CTJV and <JF are the near- and far-side peak widths. Again, there are small corrections. The results of the correlation measurements for p+p, d+Au, and Au+Au collisions can be seen in Figure 3. It is striking to note that there are no significant differences between the correlation functions in p + p collisions compared to d+Au. This implies that the initial nuclear state of the Au nucleus has little effect on the jet evolution. In contrast, there is significant broadening of the di-jet in Au+Au collisions, even suggesting that the away-side peak is disappearing in some centralities. If we want to further quantify the similarity between the di-jet behavior of the p + p and d+Au correlations, we can compare the RMS of kx,yzTrig as a function of px, as

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shown in Figure 4. We expect the mean kT in AA collisions to factorize approximately as {kT)AA = (kT)vac + {kT)Init + (k^)Final, thereby providing a handle on the vacuum-, initial-, and final-state effects via the comparison of kx in p+p, p(d)+Au, and Au+Au interactions, respectively. Based on the results of Figure 4, we calculate A(kT ) between p + p and d+Au to be —0.25 ± 0.68(stat) ± 0.27(sys), consistent with zero. The disappearance of the di-jet complicates the comparison with Au+Au correlations. 3. Summary To make jet studies possible in the heavy-ion collisions in PHENIX, we use the method of azimuthal correlations. The angular correlations between particles make it possible to statistically measure the average value of the jet variables JT and kx- These observables allow for separation of vacuum-, initial-, and final-state nuclear effects. Currently we have measured these variables in p+p, d+Au, and Au+Au collisions at yijviv = 200 GeV. One of the most striking results is that there is little difference between the correlations as seen in p + p and d+Au, yet there is significant broadening of the di-jet peak in Au+Au collisions. References 1. 2. 3. 4.

For a complete list of PHENIX collaborators, see . K. Adcox, et al, Nucl. Instr. Meth. A499 469 (2003) K. Adcox, et al, Nucl. Phys. A757, 184 (2005) J. Jia, J. Phys. G31 S521 (2005).

R E S O N A N C E P R O D U C T I O N AT STAR

HAIBIN ZHANG for the STAR Collaboration* Physics Department, Building 510A Brookhaven National Laboratory Upton, NY, 11973 USA E-mail: [email protected]

We report the measurements of the transverse mass spectra of K* (892)° —• 7r K+, 4>(1020) -> K+K-, p(770)° -> 7T+7T-, A(1520)* -»• pK~ and £(1385)** -> Avr* in Au+Au and p+p collisions at ^/s]^ = 200 GeV using the STAR TPC at RHIC. These resonances provide sensitive probes to examine the evolution dynamics in the hadronic medium through their decay and regeneration processes. The particle ratios of K* /K, 4>/K, p/n, A*/A and 2*/A and the dependence of these quantities on centrality provide evidence of dynamical interaction and rescattering between hadrons close to the kinetic freeze-out.

1. Introduction Lattice QCD calculations 1 predict a phase transition from hadronic matter to quark gluon plasma (QGP) at high temperatures and/or high densities. Matter under such extreme conditions can be studied in the laboratory by colliding heavy nuclei at very high energies. Resonance measurements in the presence of a dense medium can be significantly affected by two competing effects. Resonances that decay before kinetic freeze-out may not be reconstructed due to the rescattering of the daughter particles. In this case, the lost signal efficiency in the reconstruction of the parent resonance is relevant and depends on the time between chemical and kinetic freezeouts, the source size, the resonance phase space distribution, the resonance daughters' hadronic interaction cross-sections, etc. On the other hand, after chemical freeze-out, pseudo-elastic interactions 2 among hadrons in the medium may increase the resonance population. This resonance regeneration depends on the cross-section of the interacting hadrons in the medium. 'http://www.star.bnl.gov/

330

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Thus, the study of resonances can provide an important probe of the time evolution of the source from chemical to kinetic freeze-outs and detailed information on hadronic interactions in the final stage. 2. Experiments The data used in this analysis were taken in the second RHIC run (20012002) using the Solenoidal Tracker at RHIC (STAR) with Au+Au and p+p collisions at y'sjvjv = 200 GeV. The primary tracking device of the STAR detector is the time projection chamber (TPC) which is a 4.2 meter long cylinder for tracking with complete azimuthal coverage3. In Au+Au collisions, a minimum bias trigger was defined by requiring coincidences between two zero degree calorimeters (ZDCs) which are located in the beam directions and measure the spectator neutrons. In order to study the centrality dependence of the resonance production, the events from minimum bias Au+Au collisions were divided into several centrality bins from the most central to the most peripheral collisions according to the fraction of the charged hadron reference multiplicity distribution in all events 4 . A central trigger corresponding to the top 10% of the inelastic hadronic Au+Au cross-section was defined using both the ZDCs and the scintillating central trigger barrel, which surrounds the outer cylinder of the TPC and triggers on charged particles. In p + p collisions, the minimum bias trigger was defined using coincidences between two beam-beam counters that measure the charged particle multiplicity in forward pseudorapidities. 3. Analysis Through the ionization energy loss (dE/dx) in the TPC, charged pions and kaons are identified with momentum up to about 0.75 GeV/c, protons and anti-protons are identified with momentum up to about 1.1 GeV/c. The K(892)*°, K+ir~, (f> —> K+K~, A* -+ pK~ and Y,*± -¥ A ^ , respectively. The A signals used in the S* reconstruction are measured from a decay topology method 9 via A —> pn~. The p(770)° resonance 10 invariant mass spectra are reconstructed using the like-sign technique 10 via the decay channel p° —> n+ir~. From the reconstructed resonances invariant mass spectra, a BreitWigner function5 is used to fit with the resonance signals and the reso-

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nances raw yields can be extracted at mid-rapidity \y\ < 0.5 (< 1 for A*) for each transverse momentum (pr) bin in p + p and various centralities in Au+Au collisions. After efficiency and acceptance correction, the above resonances invariant yield spectra as a function of transverse mass (mr) can be achieved. Figure 1 shows the mr spectra for (a) K*°, (b) (j>, (c) p°, (d) A* and S* resonances in p + p and various centralities in Au+Au collisions. The mr spectra are fit with an exponential function5 to obtain the mid-rapidity yield (dN/dy), except the spectra of (j) and p in p+p collisions are fit with a power-law function5. Although the mr spectra of A* are not present in Au+Au collisions, A* signals were also observed from one single PT bin in each collision centrality and thus the A* mid-rapidity yields were obtained for Au+Au collisions by assuming the same mr spectrum shape

333

as in p + p collisions. Figure 2 shows the K*/K, <j>/K, p/n, A*/A and S*/A yield ratios as a function of dN/drj at y^ijvw = 200 GeV. All yield ratios have been normalized to the corresponding yield ratios measured in minimum p + p collisions at the same S/SNN and indicated by the dashed line in Figure 2. In this figure, one can observe that the K*/K and A*/A yield ratios for central Au+Au collisions are significantly lower than the minimum bias p + p measurements. The

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4. Discussions The measured K*/K yield ratio for central Au+Au collisions is significantly lower than the minimum bias p + p measurement. In addition, statistical model prediction 11 ' 12 ' 13 oiK*/K is considerably larger (in a 2
334

the K* decay product. Same arguments may also be applied to the lower ratio of A*/A in central Au+Au than in p + p. Due to the relatively long lifetime of the <> / meson and the negligible OKK , the rescattering of the cf> decay products and the regeneration should be negligible. The statistical model calculations 12 ' 13 also successfully predict the /K yield ratios in Au+Au. The p lifetime is even shorter than the K* and both its regeneration and rescattering effects might be strong since both effects are determined by aV7r which is relatively large. This could be a possible explanation that the observed p/n yield ratio in Au+Au is comparable to that in p + p. 5. Conclusions The K*, , p, A* and E* resonances and their m j spectra were measured in both Au+Au and p + p collisions at ^/SNN = 200 GeV at STAR. The yield ratios of K*/K and A*/A in Au+Au are significantly lower than their corresponding yield ratios in p + p. The p/ir and cj>/K yield ratios in Au+Au are comparable to p + p. The S*/A yield ratio in Au+Au is slightly larger than in p + p. These different behavior of the yield ratios for different resonances could be explained by the different hadronic interaction processes in the hot dense medium between chemical and kinetic freeze-outs and thus provides evidence of dynamical interactions and time evolution of the source in the final stage. References 1. 2. 3. 4. 5.

T. Blum et al, Phys. Rev. D 51, 5153 (1995). M. Bleicher et al., Phys. Lett. B 530, 81 (2002). M. Anderson et al., Nucl. Instrum. Meth. A 499, 659 (2003). C. Adler et al., Phys. Rev. Lett. 87, 112303 (2001). J. Adams et al., STAR Collaboration, nucl-ex/0412019, to be published in Phys. Rev. C. 6. J. Adams et al., Phys. Lett. B 612, 181-189 (2005). 7. C. Markert for the STAR Collaboration, J. Phys. G 30, S1313-S1316 (2004). 8. S. Salur for the STAR Collaboration, J. Phys. G 31, S179-S185 (2005). 9. C. Adler et al., Phys. Rev. Lett. 89, 092301 (2002). 10. J. Adams et al, Phys. Rev. Lett. 92, 092301 (2004). 11. R. Rapp, Nucl.Phys. A 725, 254 (2003). 12. W. Broniowski et al., Phys. Rev. C 68, 034911 (2003). 13. P. Braun-Munzinger et al, Phys. Lett. B 518, 41 (2001); 14. S.D. Protopopescu et al, Phys. Rev. D 7, 1279 (1973). 15. M.J. Matison et al., Phys. Rev. D 9, 1872 (1974).

LIST OF PARTICIPANTS N. E. Adam T. Allmendinger L. Arruda A. Astbury P. Azzurri J. Balewski A. Bellerive A. E. Bernardini D. Best J. Bolmont J. Brooke J. Burke B. Campbell G. Carosi J. Cat more C. A. Chavez M. Csanad A. Czarnecki J. C. Davies J. Dragic J. Drohan M. Eads P. Fleischmann R. Fleisher R. Frazier D. Gillberg R. Gran T. Gribuks H. Hara U. Harbach D. Hardtke A. Hart H. Hiejima R. Holman S. Kagawa D. Kcira R. Keeler F. Khanna E.-J. Kim A. Kiyomichi R. Kolb A. C. Kraan A. Lath

Cornell University Ohio State University LIP/IST TRIUMF INFN Pisa Indiana University Cyclotron Facility Carleton University State University of Campinas University of California, Irvine Universite Montpellier II University of Bristol University of Bristol Carleton University MIT Lancaster University University of Liverpool Eotvos Lorand University University of Alberta University of Sheffield BELLE/KEK University College London Northern Illinois University DESY CERN Bristol University Simon Fraser University University of Washington University of Alberta IPNS/KEK Johann Wolfgang Goethe-Universitat University of California, Berkeley University of Birmingham Brookhaven National Laboratory Carnegie Mellon University University of Tokyo/KEK University of Wisconsin/DESY University of Victoria University of Alberta University of Kansas RIKEN Fermilab National Laboratory University of Pennsylvania Rutgers University 335

336 M. Lefebvre V. Lemaitre V. Lendermann Z. Liu S. Lowette J. M. C. Malbouisson G. Marchiori D. Maybury M. Metlitski S. Metson N. Meyer A. K. Mohapatra A. Montanari R. Moore J. Moss O. Norniella M. Nozar B. Olivier A. Pak J. Perkin L. Piilonen M.-A. Pleier P. Podesta K. Rajagopal J. Rani Y. Rozen E. S. Santos A. Shotter A. Sidoti L. Somerville G. Sprouse J. Stelzer J. Storey S. Torre W. Trischuk Y. Ushiroda B. Vachon T. Vickey M. Vincter M. L. Weinberger J. Wendland D. L. Winter A. Yurkewicz H. Zhang

University of Victoria University of Louvain University of Heidelberg Simon Fraser University Vrije Universiteit Brussel - IIHE University of Alberta INFN University of Alberta University of British Columbia Bristol University DESY/University of Iowa SLAC INFN Bologna University of Alberta College of William and Mary Institut de Fisica d'Atles Engergies TRIUMF University of Birmingham University of Alberta University of Sheffield Virginia Tech University of Rochester Cinvestav MIT Tata Institute of Fundamental Research Technion Israel Institute of Technology University of Alberta TRIUMF Laboratoire de Physique Nucleaire et de Hautes Energies CERN/University of Oxford SUNY at Stony Brook SLAC Cambridge University Universita di degli Studi di Sienna University of Toronto KEK McGill University University of Illinois at Urbana-Champaign Carleton University Cornell University University of British Columbia Columbia University SUNY Brookhaven National Laboratory

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Fundamental Interactions

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This proceedings volume contains pedagogical lectures on theoretical and experimental particle physics, cosmology and atomic trap physics. It also includes additional contributions that provide up-to-date information on new experimental results from accelerators, underground laboratories, and nuclear astrophysics. This combination of pedagogical talks and topical short talks provides comprehensive information to researchers in the fields of particle physics, cosmology and atomic trap physics.

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