NSTAR
2004
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editors
Jean-Paul Bocquet Laboratoire de Physique Subatomique et de Cosrnologie, France
Via t ch esl av Ku zn etsov Institutefor Nuclear Research, Russia
Dominique Rebreyen d Laboratoire de Physique Subatomique et de Cosrnologie, France
Proceedings o f the Workshop on the
Physics o f Excited Nucleons
NSTAR 2004 24 - 27 March 2004
Grenoble. France
1; World Scientific -
N E W JERSEY * L O N D O N * S I N G A P O R E
BElJlNG
SHANGHAI
*
HONG KONG
-
TAIPEI * C H E N N A I
Published by World Scientific Publishing Co. Re. Ltd. 5 Toh Tuck Link, Singapore 596224 USA ofice: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK ofJice: 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.
NSTAR 2004 Proceedings of the Workshop on the Physics of Excited Nucleons Copyright 0 2004 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereoj 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 permissionfrom the Publisher.
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ISBN 981-256-090-4
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NSTAR 2004 Workshop on the Physics of Excited Nucleons March 24-27, 2004 Laboratoire de Physique Subatomique et de Cosmologie GRENOBLE - FRANCE
Organization Conference Chairman Dominique Rebreyend
Organizing Committee J.P. Bocquet (Grenoble), V. Burkert (JLab), B. Desplanques (Grenoble), D. Drechsel (Mainz), V. Kuznetzov (Moscow), B. Saghai (Saclay), B. Silvestre-Brac (Grenoble)
Advisory Committee R. Beck (Mainz), C. Benhold (GWU), S. Capstick (Florida State), S. Dytman (Pittsburgh), M. Giannini (Genova), H. Lee (Argonne), M. Manley (Kent), B. Mecking (JLab), D. Menze (Bonn), R. Minehart (Virginia), T. Nakano (Osaka), Y. Oh (Yonsel), W. Plessas (Graz), A. Ramos (Barcelona), D. Richards (JLab), J.M. Richard (Grenoble), M. Ripani (Genova), A. Sandorfi (BNL), M. Soyeur (Saclay), H. Stroeher (Julich), E. Swanson (Pittsburgh), L. Tiator (Mainz), A. Titov (Dubna), H. Toki (Osaka), A. Thomas (Adelaide), V. Vento (Valencia), R. Workman (GWU), B.S. Zou (Beijing)
vii
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FOREWORD This volume contains the invited and contributed talks of the 9th workshop on The Physics of Excited Nucleons which was hosted by the Laboratoire de Physique Subatomique et de Cosmologie in Grenoble, France from March 24-27, 2004. This conference was the latest of a series which started at Florida State University in 1994, followed by Jefferson Lab (1995), INT in Seattle (1996), George Washington University (1997), ECT’ in Trento (1998), Jefferson Lab (2000), Mainz (2001) and Pittsburg (2002). Contributions of the Baryon Resonance Analysis Group premeeting, held on March 23, are also included. The workshop was attended by about 80 physicists from 12 countries. Despite the bad weather conditions, the mood of the participants were relaxed, creating a pleasant atmosphere during the whole conference. After a tour in the nearby Chartreuse mountains under winter conditions, all participants could appreciate the warming virtue of local liquors. As usual, the aim of this meeting was to bring together experimental and theoretical specialists of baryon spectroscopy. New high quality experimental results, produced a t facilities all around the world such as BES, BNL, ELSA, GRAAL, JLab, MAMI and LEPS, were presented in several review talks. For this issue, special emphasis was given to omega and strangeness production where data on double-polarization observables start to become available. On the theory side, related activities from resonance parameters extraction to the description of nucleon excited states on the Lattice were extensively covered: partial wave analysis, coupled-channel calculation, l/Nc expansions, chiral symmetry, QCD-inspired models etc. Furthermore, a likeIy focus session was devoted to the various implementations of relativity in hadron structure. After 30 years of unsuccessful search, the first observation of a pentaquark state has been reported by the LEPS collaboration in Summer 2003. Since then, this discovery has been confirmed by several other experiments, creating a new challenge in the field of hadron spectroscopy, generating an enormous activity. To cover this hot topic, an entire day was devoted to a comprehensive review of both experimental evidences and theoretical interpretations. All speakers are greatly acknowledged for their valuable contributions to make the workshop as success. We wish to thank all institutional sponsors: Thomas Jefferson National Accelerator Facility, Commissariat B 1’Energie Atomique, Institut National de Physique Nucleaire et de Physique des Particules, Universitk Joseph Fourier de Grenoble, Grenoble city, Conseil Gknkral de l’Iskre, Rkgion Rh6ne-Alpes, and the Laboratoaire de Physique Subatomique et de Cosmologie for hosting the meeting and providing personnels. ix
X
We are grateful for the advice provided by the International Advisory Committee and also the help of the members of the Organizing Committee. We would like t o address special thanks to Jocelyne Riffault who managed all organizing issues and tirelessly provided smiling and efficient assistance to participants, and to Anne Wolfers for her appreciated contribution before and during the meeting. August, 2004 Jean-Paul Bocquet, Viatcheslav Kuznetsov, Dominique Rebreyend
xi
CONTENTS NStar2004-photo
V
Organization
vii
Foreword
ix
P l e n a r y Talks Experiment Review on Exotic Baryons T. Nakano
3
Search for Pentaquark States with CLAS at Jefferson Lab V. Burkert, R. De V i t a , S. Niccolai and the CLAS collaboration
9
K N Scattering Data and the Exotic O+ Baryon 1.1. Strakovsky, R.A. Arndt, R.L. Workman, W.J. Briscoe
27
Notes on Exotic Anti-Decuplet of Baryons M.V. Polyakov
31
Quark Model Perspective on Pentaquark Exotics K. Maltman
39
The Status of Pentaquark Spectroscopy on the Lattice F. Csikor, Z. Fodor, S.D. Katz, T.G. Kovhcs
51
Study of the Exotic O+ in Polarized Photoproduction Reactions Q. Zhao
63
On the Determination of the @+Quantum Numbers and other Topics on Exotic Baryons E. Oset et al.
71
Mass Spectrum and Magnetic Moments of Pentaquark States R. Bijker, M.M. Giannini, E. S a n t o p i n t o
82
Pentaquark Spectra in the Diquark Picture C . Semay, B. Sivestre-Brac, I.M. Narodetskii
90
Pentaquarks and Radially Excited Baryons
96
H. Weigel
xii
Models of Meson-Baryon Reactions in the Nucleon Resonance Region T.-S.H. Lee, A. Matsuyama, T . Sato
104
Review on Kaon-Hyperon Electromagnetic Production on the Nucleon in the Resonance Region K.-H. Glander
116
Role of the Baryon Resonances in the 17 and K+ Photoproduction Process on the Proton B. Saghai
126
Resonances in T and 17 Channels S. Kamalov et al.
137
Experimental Review on w Production F.J. Klein, P.L. Cole
146
The GDH-experiment at MAMI - Recent Results and Future Plans H.-J. Arends for the GDH- and A2-Collaborations
155
Double-Polarization Experiments with Polarized HD at LEGS A. Sandorfi et al. (The LEGS Collaboration)
164
CLAS Results from the First and Second Resonance Regions L.C. Smith et al., for the CLAS Collaboration
169
Experimental Review of Double Pion electromagnetic Production M. Ripani
178
A Partial Wave Decomposition of ~p + PT+TM. Bellis for the CLAS Collaboration
189
77 Photoproduction off the Neutron at GRAAL: Evidence for a Resonance Structure at W = 1.67 GeV.
197
V. Kouznetsov for the GRAAL Collaboration Excited Baryons and Pentaquarks on the Lattice F.X. Lee
204
N* Properties from the l/Nc Expansion (An Update) C. Schat
219
xiii
Dynamical Baryon Resonances from Chiral Unitarity A. Ramos e t al. Form Factors of Hadronic Systems in various Forms of Relativistic Quantum Mechanics B. Desplanques
228
239
Hadron Structure from the Salpeter Equation B. Metsch
246
Point-Form Approach to Baryon Structure W. Plessas
252
Generalized Parton Distributions in the Light-Front Constituant Quark Model S. Simula
264
Baryon Resonances from J/P Decays B.S. Zou for the BES Collaboration
271
New Trends in Hadron Spectroscopy (Conference Summary) V. Vento
280
Parallel Talks q and no Photoproduction on the Deuteron: Beam Asymmetries A. Fantini et al. (the GRAAL Collaboration)
289
Photoproduction of no and 77 Mesons off Protons at CB-ELSA 0. Bartolomy for the CB-ELSA Collaboration
293
Target and Double-Spin Asymmetries for A. Biselli
Z$-+e’pn’
298
Compton Scattering of Polarized Photons on the Proton at GRAAL 0. Bartalini et al. (A. Guisa)
303
Total Photoabsorption off the Proton and Deuteron at Intermediate Energies V. Nedorezov, N. Rudnev for the GRAAL Collaboration
309
Study of Nucleon Resonances in (7,n ) N Coupled-Channel Lagrangian Model V.V. Shklyar, G. Penner, U. Mosel
+ cpX’ within a 313
xiv Helicity-Dependent Angular Distributions in Double-Charged-Pion Photoproduction S. Strauch for the CLAS Collaboration
317
Baryon States in Double Charged Pion Photo- and Electroproduction 321 V.I. Mokeev et al. Double 7ro Photoproduction and the Second Resonance Region M. Kotulla for the TAPS and A2 Collaborations
325
N* Photoproduction from Nuclei S. Schadmand
329
Multi Resonance Contribution to the Eta Production in Proton-Proton Scattering S. Ceci, A. Svarc, B. Zauner
333
Nucleon Resonances and Processes Involving Strange Particles S. Ceci, A. Svarc, B. Zauner
337
Multichannel F N Scattering and Hyperon Resonances M. Manley, J. Tulpan
341
New Evidence for the Breathing Mode of the Nucleon from High-Energy Proton-Proton Scattering H.-P. Morsch, P. Zupranski
345
Generalized Sum Rules of the Nucleon in the Constituent Quark Model M. Gorshtein, M.M. Giannini, E. Santopinto
351
Strong Decay of N and A Resonances in the Point-Form Formalism T. Melde, W. Plessas, R.F. Wagenbrunn
355
Chiral Dynamics of the two A(1405) States D. Jido et al.
359
Baryon Form Factors in the Three Forms of Relativistic Kinematics B. Julib-Diaz, D.O. Riska, F. Coester
363
Electromagnetic Form Factors of Hyperons in a Relativistic Quark Models T. Van Cauteren et al.
367
xv
Baryon Resonance Analysis Group Premeeting Talks Presence of Extra PI1 Resonances in Zagreb Analysis since 1995 S. Ceci, A. Svarc, B. Zauner
373
Electromagnetic Multipoles - Theory Issues
377
M.M. Giannini PI1
and
S11
Resonances in Multichannel 7rN Scattering
382
D.M. Manley Model Dependence of Nucleon Resonance Parameters L. Tiator, S. Kamalov
385
Scientific Program
393
List of Participants
399
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PLENARY TALKS
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Experimental Review on Exotic Baryons T . NAKANO RCNP, Osaka University 10-1 Mihogaoka, Ibaraki, Osaka, 567-0047, Japan E-mail:
[email protected] I report the recent experimental evidences and counter evidences for pentaquark baryons whose quark configuration is qqqqq. A very preliminary result from the LEPS deuterium data is also reported.
1. Introduction
There were no clear experimental evidence for existence of a hadron with a quark configuration rather than three quarks or a quark-antiquark pair although QCD does not forbid the existence of other combination such as qqqqq or qqqq. The absence of the baryon state with more than three quarks was one of the big mysteries in particle physics for decades. In fact, the summary of the search for baryon resonances with the strangeness quantum number S=+l, that cannot be formed by three quarks, has been dropped from the Particle Data Group (PDG) listings although the possible exotic resonances were noted in the 1986 baryon listings Recently Diakonov, Petrov and Polyakov calculated masses and widths of an anti-decuplet baryons by using chiral quark soliton model. The lightest member of the anti-decuplet is the @+ which is an exotic 5-quark state with a quark configuration of uuddS that subsequently decays into a K+ and a neutron. The model predicts the mass of the O+ to be 1530 MeV with a narrow width of 15 MeV. This narrow width was very attractive for experimentalists because the search could be done without a partial wave analysis with a wide detector acceptance.
'.
-
N
2. First evidence for the O+
The first evidence for the O+ was reported by the LEPS collaboration at Spring-8 '. The experiment was carried out by using a laser-electron
3
4
photon (LEP) beam which was generated by Backward-Compton scattering of laser photons with the 8-GeV electrons.
Figure 1. The LEPS detector setup.
Figure 1shows a schematic drawing of the LEPS detector. The detailed information about the detector can be found elsewhere The most important detector component for the the present analysis was a 0.5-cm thick plastic scintillator (SC) located 9.5 cm downstream from the 5-cm thick liquid-hydrogen (LH2) target. The events from the SC is turned out to be very useful to study events generated from neutrons in carbon nuclei at the sc. In the analysis, we selected K+K- pair events produced in the SC, which accounted for about half of the K+K--pair events. The missing mass MM7K+K- of the N(y, K+K-)X reaction was calculated by assuming that the target nucleon (proton or neutron) has the mean nucleon mass and zero momentum. Subsequently, events with the MM?K+K- to be con-
5 sistent with the nucleon mass were selected. The main physics background events due t o the photo-production of the 4 meson were eliminated by removing the events with the invariant K+K- mass from 1.00 GeV/c2 to 1.04 GeV/c2. In order to eliminate photo-nuclear reactions of yp + K+K-p on protons in the SC, the recoiled protons were detected by a vertex counter. In case of reactions on nucleons in nuclei, the Fermi motion has to be taken into account to obtain appropriate missing-mass spectra. The missing mass corrected for the Fermi motion, M M y K * , is deduced as
MMyK* = M M 7 ~ *- MM-,K+K- + M N ,
(1)
where M N is the nucleon mass. The corrected K+ missing-mass distribution for the events that satisfy all the selection conditions is compared with that for the events for which a coincident proton hit was detected in the SSD. In the latter case, a clear peak due t o the y p + K+A(1520) + K+K-p reaction is observed while the A(1520) peak does not exist in the signal sample. This indicates that the signal sample is dominated by events produced by reactions on neutrons. Fig. 2 shows the corrected K- missing mass distribution of the signal sample. A prominent peak at 1.54 GeV/c2 is found. We assumed the broad background centered around 1.6 GeV/c2 is due to non-resonant K+K- production and it can be fitted by a distribution of events from the LH2.The estimated number of the events above the background level is 19.0, which corresponds t o a Gaussian significance of 4.6 u. This narrow peak indicates the existence of an 5’ = +l resonance which may be attributed to the exotic 5-quark baryon proposed as the O+.
+
3. Confirmation of O+ Soon after a preliminary result on the was announced by the LEPS collaboration at the international conference PANIC in October 2002, the CLAS collaboration at Jefferson Lab re-analyzed photo-reaction data which were collected in 1999 by using a liquid deuterium target. They observed a peak at 1542 MeV in the n K + invariant mass spectrum of the reaction yd + K+K-pn, where all charged particles in the final state were detected lo. Since the momentum of the final neutron was fully determined by using total momentum conservation law, their result was not affected by a Fermi motion of the initial neutron. The CLAS collaboration also announced an evidence for the @+ by analyzing the reaction yp + K + K - r + n in a different data set.
6
15
. 0 0
10
Y
v)
C
a, > W
5
n "
1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 MM>- (GeV/c2)
Figure 2. The M I W K T spectrum for the signal sample (solid histogram) and for events from the LH2 (dotted histogram) normalized by a fit in the region above 1.59 GeV.
Prior to the CLAS reports, the DIANA collaboration at the Institute of Theoretical and Experimental Physics (ITEP) in Russia reexamined lowenergy K+ Xe collision events in the Xenon bubble chamber, which were taken in 1986. They found a 4.4 u peak at 1539 MeV with a very narrow width of < 9 MeV in the invariant pKo invariant mass spectrum of the charge-exchange reaction K+Xe' -+ KOpXe' '. Since the production crosssection is proportional to the decay width, it can be estimated to be 0.9 MeV assuming the background under the peak is due to the charge exchange reaction of K+n + Kop outside of the resonance region '. This narrow width is consistent with the K N phase shift analysis of the old data *. Most recently, the COSY-TOF collaboration found a O+ peak at 1530 MeV with a width less than 18 MeV in the reaction p p + KopC+ g . The production cross-section was estimated t o be 0.4 f0.1 f0.1 pb. It suggests the parity of the O+ is positive if one assumes the width of the O is 5 MeV or less and a model calculation by Nam and others lo is correct. In addition to these experiments, many experiments found an evidence
7
for the O+ by mainly analyzing old data. Positive results for the O+ are summarized in Table 2. Table 1. Summary of positive experimental results for the O+.
1
Where LEPS DIANA CLAS SAPHIR ITEP
Mass
Width
Significance
yc-t K+K-x
1540f10
<25
4.6
2
K f X e t KopX
1539f2
<9
4.4
6
yd t K + K - p ( n )
1542f5
<21
5.2
10
1540f6
<25
4.8
2
<20
6.7
13
<26
7.8
5
yp
+K + K O ( ~ )
u A t KopX
CLAS
1533415
y p -t T + K - ~ + ( n )1555f10
HERMES ZEUS
e+d
+ KopX
e + p t e'KopX
COSY-TOF
Ref.
Reaction
pp
-+
KopC+
1528f3
13f9
N5
12
1522f3
8f4
N5
14
1530f5
<18
4-6
9
4. Observation of other pentaquarks and counter evidences
The NA49 collaboration announced the observation of the cascade particles at 1.86 GeV 15. Among them the doubly-negative cascade 2-- is a genuine pentaquark state which cannot be explained with a 3-quark configuration. Although no theoretical model could not predict its mass before the observation, the observation supports the existence of the anti-decuplet if the state is established. Recently, HERA-B collaboration searched for both O+ and B-- in proton-induced reactions on C with a 920 GeV/c beam hera-b. They found no signal of the pentaquarks although the A(1520) and E-- peaks were clearly seen in the invariant mass spectra. The upper limit of relative yield ratios were (Theta+)/(A(1520)) < 0.02, (E--)/(B(l530)') < 0.077, (?+)/(E(1530)') < 0.058. at the 95 % confidence level. At the time of writing this manuscript, there are several other experimental groups which have reported negative results for the pentaquarks Those experiments were carried out at very high energy, and some of the experiments give very stringent upper limits on the production rate of the pentaquarks with high statistics. If the pentaquarks exist, their production at high energy must be heavily sippressed with respect t o normal baryons. 17718,19,20721.
8
5. New result from LEPS The LEPS collaboration performed a new experimental search for the O+ using a 15cm-long liquid deuterium target. A preliminary analysis with cuts similar to the previous analysis reproduced the O+ peak in the K missing mass spectrum with higher statistics. Therefore, the observed peak is not likely due t o statistical fluctuations. Further analysis is in progress t o confirm if the peak is not generated artificially by the cuts, detector acceptances, or kinematical reflections. As stated in Ref. “The standards of proof must simply be much more severe here than in a channel in which many resonances are already known to exist.”
References 1. 2. 3. 4. 5.
Particle Data Group, Phys. Lett. 170B,289 (1986). T. Nakano et al. (LEPS Collaboration), Phys. Rev. Lett. 91,012002 (2003). D. Diakonov, V. Petrov, and M. Polyakov, 2. Phys. A359,305 (1997). S. Stepanyan et al. (CLAS Collaboration), Phys. Rev. Lett. 91, 252001 (2003). V. Kubarovsky et al. (CLAS Collaboration), Phys. Rev. Lett. 92, 032001 (2004). 6. V.V. Barmin et al. (DIANA Collaboration), Phys. At. Nucl. 66,1715 (2003). 7. R.N. Cahn and R.L. Trilling, Phys. Rev. D 69, 011501(2004). 8. S. Nussinov, arXiv:hep-ph/0307357; R.A. Arndt, 1.1. Strakovsky, and R.L. Workman, Phys. Rev. C 68, 042201 (2003). 9. M. Abdel-Bary et al. (COSY-TOF Collaboration), arXiv:hep-ex/0403051. 10. S.I. Nam, A. Hosaka, and H.C. Kim, arXiv:hep-ph/0401074. 11. J. Barth et al. (SAPHIR Collaboration), Phys. Lett. B 572, 127(2003). 12. A. Airapetian et al. (HERMES Collaboration), Phys. Lett. B 585, 213(2004). 13. A.E. Asratyan, A.G. Dolgolenko, M.A. Kubantsev, arXiv:hep-ex/0309042. 14. S. Chekanov et al. (ZEUS Collaboration), arXiv:hep-ex/0403051 15. C. Alt et al. (NA49 Collaboration), arXiv:hep-ex/0310014. 16. K.T. Knopfle, M. Zavertyaev, and T. Zivko (HERA-B Collaboration), arXiv:hep-ex/0403020. 17. J.Z. Bai et al. (BES Collaboration), arXiv:hep-ex/0402012. 18. C. Pinkenburg (for the PHENIX Collaboration), arXiv:nucl-ex/0404001. 19. M. Longo (Hyper-CP Collaboration), Talk at the QNP2004 (May 27, 2004, Bloomington). 20. D. Christian (FNAL-E690 Collaboration), Talk at the QNP2004 (May 27, 2004, Bloomington). 21. M.J. Wang (CDF Collaboration), Talk at the QNP2004 (May 27, 2004, Bloomington).
Search for Pentaquark States with CLAS at Jefferson Lab V. D. BURKERT Jefferson Lab, 12000 Jefferson Avenue, Newport News VA 23606, USA E-mail:
[email protected] R. DE VITA Istituto Nazionale di Fisica Nucleare via Dodecaneso 33, 16146 Genova, Italy E-mail:
[email protected]
S. NICCOLAI IPN Orsay, 15 rue Georges Clemenceau, 91406 Orsay France E-mail:
[email protected] AND THE CLAS COLLABORATION We discuss the experimental program to search for baryon states with exotic flavor quantum numbers using CLAS at Jefferson Lab
1. Physics Motivation
The existence of baryons with quantum numbers that cannot be obtained with only 3 valence quarks qqq, but require a minimum quark content qqqqq, has excited the hadron community since the first public announcements of such a state were made in the year 2003. The observed state is now called the O+(1540). It appears t o have a mass in the range 1525 MeV to 1550 MeV, and strangeness S = + l l . While pentaquark states with such quantum numbers have been discussed for years, specific predictions for both a mass of 1530 MeV and a narrow width of < 15 MeV were made in a paper by Diakonov et al. in 1997 based on the Chiral Soliton Model ( x S M ) . In this model, the O+ is an isosinglet member of a J = anti-decuplet of ten states with a minimum quark content of 5 quarks (“pentaquarks”), three of the states have exotic flavor quantum numbers, the O+, and the
++
9
10
two baryons EF- and E$. The other non-exotic members are three C5, and two N; states. The width appears t o be much more narrow than the experimental resolutions, and may be as narrow as 1 MeV3i475. Following the first experimental announcements, an avalanche of theoretical papers have appeared trying t o understand its low mass and narrow width, as well as to make predictions on production mechanism and possible excited states of the O+ 6 . Lattice QCD is currently not providing fully satisfactory predictions for the O+. One group finds no signal, three groups find a signal a t about the right mass, two at negative parity, one at positive parity7. Evidence for the state has been claimed in more than 10 published works from medium energy t o very high energy experiments. There are a number of experiments, mostly a t high energies, that report null results. Most of the results, if not all, come from the analysis of data that were taken for other purposes. This fact may explain the relatively low significance of all positive results, which range from about 4a t o 717 for individual experiments. Experimentally, the O+ has been observed in either nK+, or pKo final states. Reported masses in some cases vary by more than the uncertainties given for the individual experiments, with the masses obtained from processes involving nK+ in the initial or final states giving on average 10-15 MeV higher masses. The discrepancy in mass determination needs to be resolved, but may not solely be an experimental problem. For example, could the mass difference be explained by different initial or final state interactions involved in nK+ and pKo channels, or could different interference effects be involved that depend on the kinematics where the signal is observed? In this case theoretical input will be needed t o resolve the discrepancy. Finding a definite answer to the question of existence or non-existence of the O+ and of the other 5-quark baryons is, of course, of overriding importance and urgency. It will tell us much about how QCD works at the hadron scale, and can only be answered experimentally. In this contribution we report on the results from Jefferson Lab using the CLAS detector, and on the current program of second generation experiments aimed at improving the statistical accuracy of the measurements by at least one order of magnitude. We also need to better understand the systematics involved and obtain some insight into production mechanisms. In section 2 we report the experimental apparatus t o the degree it is relevant for the physics at hand. In section 3 we discuss the already published results. Section 4 describes ongoing analyses, and in section 5 we report on the status of two second generation measurements, and then outline planned experiments to further study the systematics of pentaquark states.
11
Main Tarus Coils
Figure 1. The CLAS detector. Left: Longitudinal cut along the beam line shows the 3 drift chamber regions, the Cherenkov counters at forward angles for electron and pion separation, the time-of-flight system, and the electromagnetic calorimeters for the detection of photons and neutrons. Right: Transverse cut through CLAS. The superconducting torus coils provide a six sector structure, each sector being instrumented with independent detectors.
2. CLAS and CEBAF - unique capabilities for baryon spectroscopy
The continuous electron beam provided by the CEBAF accelerator is converted into a bremsstrahlung photon beam at CLAS using a gold radiator located 20 meters upstream of a liquid hydrogen or deuterium target. The photon energy is measured by detecting the scattered the electrons that generated the photons in the energy range from 20% t o 95% of the incident electron energy. Typical photon beam rates range from a few times lo6 to lo7 per second. The CLAS detector is shown in Fig. 1. At its core is a superconducting toroidal magnet, providing momentum analysis of charged particles in six sectors. The magnetic field produced by the six-coil toroidal magnet is oriented in such a way as t o maintain a constant azimuthal angle of the scattered particles while changing only their polar angle. Tracking is provided with three regions of drift chambers with a total of 34 layers of drift cells arranged radially from the target. The total number of drift cells in CLAS is about 35,000 providing a highly redundant tracking information. Charged tracks are reconstructed in polar angles from about 10 to 140 degrees. 288 plastic scintillator paddles provide time-of-flight information used for particle identification. For experiments with a bremsstrahlung
12
photon beam, a segmented scintillation counter is arranged around the target for triggering and to provide improved start time information. CLAS is optimized for the selection of exclusive processes in a large kinematic range and with good resolution. The large acceptance of CLAS allows simultaneous measurement of several processes. Often, as is also the case in the study of the O+, the missing mass technique is used to identify final states with one unmeasured particle, usually a neutron or a neutral meson. At intermediate energies all kinematic regions can play important roles, and may be sensitive to different production mechanisms, e.g. in s-channel, t-channel, and u-channel processes. With its large coverage CLAS can explore baryon excitation processes in all of these regions. These capabilities are unique to CLAS and, as long as the major production mechanisms are unknown, are crucial in the study of processes with small cross sections, such as the O+ or its possible excited states. For example, the small O+ signal may be completely swamped by background processes in t-channel kinematics. However, it may show up more prominently in u-channel kinematics through baryon exchange processes at large cms angles. The wide coverage of CLAS allows selection of all kinematics and reaction channels, and provides the utmost in sensitivity.
Table 1. Runs completed in Hall B at Jefferson Lab with the CLAS detector using photon beams. The experimental conditions are summarized.
I Experiment I
Year
1
Beam Energy
I
Target
1
SL: (pb-l)
1
Since 1998, several experiments using photon beams and different targets have been completed: a summary is given in Table 1. In the last year, the existing CLAS data were reanalyzed to study possible evidence for pentaquark production. The CLAS collaboration has published two positive signals on the O+ using deuterium l 4 and hydrogen targets 15. We discuss these in the following section.
13
3. Discussion of published results 3.1. Production on deuterium The first evidence for the O+ was seen in experiments on nuclear targets l 2 > l 3 , l 4 .In CLAS, the fully exclusive process yD -+ K-pK+n was measured. The 4-momentum vectors of the photon, target nucleus, and all charged particles in the final state are known, the neutron can be identified by computing the missing mass of the remaining system as can be seen in Fig. 2. In this process the O+ would be produced on the neutron in the
Figure 2. Left: Missing mass M x of yd --t p K - K + X . A peak at the neutron mass is seen. The inset shows the results with more stringent vertex time cuts. Right: Possible diagram for the observed process.
deuteron, while the proton would be a spectator. However, in order t o be able t o detect the proton in CLAS, it must have a minimum momentum of about 200 MeV/c. This requires a complex final state interaction. The final state also contains 4 and A(1520) that are eliminated by cuts in the K+K- and p K - invariant mass spectra. A possible diagram is shown in Fig. 2. The final spectrum is shown in Figure 3. The nK+ invariant mass shows a significant peak at 1542 f 5 MeV. An analysis of these data using a different technique finds that the significance of the observed peak may not be as large as presented in the published work. We expect a definitive answer from a much larger statistics data set (g10) that is currently being analyzed. Could this peak be generated by a statistical fluctuation? If we consider this result isolated from the evidence seen by other independent ex-
14
Figure 3. Left: Invariant mms distribution M ( n K + ) for the final state p K - n K + . Right:M(nK-) for the same event as in the left graph. The lack of a narrow peak shows that kinematic reflections do not seem to generate narrow structures in n K - .
periments, there is a small probability that it could be a fluctuation. However, such an interpretation becomes extremely unlikely if the evidence from other independent experiments is considered. Other effects such as kinematical reflections have been studied. Here structures in (NK) mass spectra may be produced as kinematical reflections of high mass meson production with decays t o the K+K- final state. If the phase space for the reaction is limited, the invariant mass nK+ could show an enhancement in the 1.55 GeV mass range. Kinematical reflections are well-known effects in spectroscopy, and have been studied extensively. For the current analysis, broad enhancements or shoulders can indeed be produced this way as is shown in the right panel of Fig. 3, where the mass of the K - n is shown using the same events that are included in the left panel. The smooth shoulder near 1.55 GeV may indeed be due to such an effect. Clearly, the sharp O+ peak in the left panel has very different characteristics from a kinematical reflection.
3.2. Production on hydrogen Here the process y p -+ 7r+K+K-n is selected, using the g6a, g6b, and g6c data runs 15. Cuts are applied with the hypothesis that the O+ is produced via intermediate N * excitation. Possible contributions t o that channel are shown in Fig. 4. Events are selected with a forward angle 7 r + , and events with a forward angle K+ are ejected. The latter cut was used to reduce t-channel contributions to K+. The final mass spectrum is shown in Fig. 5.
15
A very significant peak is seen at a mass of 1.555f10 MeV. In this analysis background processes contributing t o the selected channel were subjected to a partial wave analysis. This allowed for a precise determination of the shape of the background contributions. If the reaction mechanism is indeed through excitation of an intermediate N * , then such a N* would presumably not be a usual 3-quark state but rather a 5-quark or even 7-quark state with strong sS components. Selecting events in the mass range around the peak, and plotting the invariant mass nK+K- in Fig. 5 we see indications of a structure near 2.4 GeV. While the results hint at a narrow structure near 2.4 GeV the statistics are too poor to allow drawing definite conclusions. Further studies with higher statistics are clearly needed. Y
x
+
----*-----
n
P
b)
n
+
P C)
p
n d)
Figure 4. Diagrams that may contribute to the process y p --t r+K-nK+. The left top diagram contributes to O+ production through intermediate N' excitation. The other diagrams represent background processes.
4. Ongoing analysis
In this section we describe analyses that have shown some promise in the search for the @+ and possible excited states, however they lack the statistics and significance to be fully convincing. The CLAS collaboration has decided to not publish these works but wait for the completion of the ongoing runs with much higher statistics. Although no final results are presented here, it may be instructive to describe the techniques used in preparation for the analysis of the new high statistics data.
16
12
10 n
P
: .
8
0
N
M(nK+K) (GeVlc')
6
Y
B
&
4
2
2
M(nK+) (GeV/c3)
23
2.4
1.6
2.8
3
:
2
M(nK+K) (GeV/c?
Figure 5 . Left: Invariant mass distribution of M ( n K + ) after all cuts. T h e inset shows the n K + mass distribution with only the cosO:+ > 0.8 cut applied. Right: Mass distribution M ( K - n K + ) for events selected in the peak region of the graph on the left. T h e inset shows the distribution for events outside of the O+ region.
4.1. Reactions o n protons
The g l c data set was used to study the reaction yp + K+Kon and y p + pK+K-, searching for evidence of S = f l resonances in the K+n and K+p invariant masses.
M(Ko) (GeV)
Figure 6. Final particle identification for the reaction yp + K + K 0 n . T h e left plot shows the K O mass spectrum reconstructed as invariant mass the 7r+a- system. T h e right plot shows the K+7r+7r- missing mass.
17
The first channel was selected by detecting the K+ and reconstructing the K O via the K , component decaying into T + T - . The final state was then identified using the missing mass technique. Figure 6 shows the quality of the channel identification: both K O and n are reconstructed within 1-2 MeV of the nominal mass value with small background. The corresponding event sample is dominated by the production of known hyperons decaying into the same final state. These include yp + KfA*(1520),"yp -+ K+C+T-, and yp -+ K+C-T+. Fig. 7 shows the A*(1520) and C+ peaks reconstructed as missing mass of K+ and the K+T- system. Events associated with these reactions are excluded by cutting on the corresponding masses. After such cuts, the nK+ invariant mass spectrum was constructed. After selecting events in which the K0 is emitted at backward angles, two structures with masses near 1525 and 1575 MeV were visible. However, the low statistics of the final event sample did not allow us to draw definitive conclusion on such structures.
-
B V
-
zB
800
300
V
250
700 600
200
500 150
400 300
100
200 50
100 9.4
1.5
1.6
1.7
1.8
1.9
2
MM(K*) (GeV)
9.1 1.12 1.14 1.16 1.18 1.2 1.22 1.24 1.26 1.28 1.3
MM(K+rr-)(GeV)
Figure 7. K+ and K+T- missing masses after the cuts on the K+ and K O , and n masses. The A'(1520) and C f peaks are clearly visible. The highlighted areas correspond to the events selected for further analysis.
The reaction "yp + pK+K- was selected by detecting two of the three charged particles in CLAS and using the missing mass technique allows us to identify the third one. Two different topologies, "yp -+ p K + ( K - ) and yp -+ ( p ) K + K - ,were analyzed while the topology with pK- detected was dropped due to the marginal statistics. One of the largest contributions to
18
this particular final state is due to the diffractive production of the 4( 1020) meson. This is shown in the left panel of Fig. 8. The associated events as well as the events coming from A*(1520) production (see the right panel of the same figure) are rejected by cutting on the corresponding masses. To further reduce the background contribution coming from other reactions and t o maximize the signal to background ratio, angular and energy regions were selected where Monte Carlo simulations showed maximum sensitivity t o the reactions of interest. After these additional cuts, the pK+ invariant mass spectrum showed a structure in the mass region around 1.58 MeV. However also in this case, the limited statistics did not allow us to reach definitive conclusions. In either case, the much higher statistics of the g l l experiment that will finish data taking by July 29, 2004, will allow more definite conclusions as t o the existence and significance of these possibly new narrow structures.
1600 1600 1400
1400 1200 1200
lo00 lo00 800
600
800
600
400
400
200
200
n
"
19
B h
1.4 1.425 1.45 1.475 1.5 1.525 1.55 1.575 1.6 sqrt(mZ-ek(1))
Figure 8. p and K+ missing masses showing the 4(1020) and A'(1520) contribution. The highlighted areas correspond to the events selected for further analysis.
4.2. Reactions on 3 H e
The g3c data set was analyzed searching for the reaction y3He+ PA@+. The advantage of this channel (see l6 for theoretical predictions of the cross section) is that it allows to identify the final state without the need of cutting on competing channels, while at the same time excluding kinematical reflections in the N K invariant mass spectrum. Moreover, thanks to the
19
presence of the A having strangeness S = -1, the pKo decay mode must have S = + l . The reaction threshold is E-, 21 800 MeV for a Of mass of 1.55 GeV/c2. The main reaction mechanism can be pictured as a two-step process (Fig. 9): the initial photon interacts with one of the protons of 3He and produces a h and a K+ ( ~ +p K+h). The A leaves the target nucleus, while the K+ reinteracts with the neutron in 3He to form a O+. In this process, one of the two protons of 3He can either be a spectator, as pictured in Fig. 9, or rescatter, and thus gain enough momentum t o be detected.
Figure 9. Production mechanism for A@+ in 3He. The decay modes A K o p and KO -+ n+.rr- are shown here.
4 pn-,
@+
4
The following decay channels are most suitable for detection in CLAS: h-+p.ir-,
Of KO
+ pKo and O+ + n K + , + 7r+7r-.
The final state therefore is p7r-p7r+n-p for the O+ + pKo decay mode, and pp7r-nK+ for the O+ + nK+ decay mode. Having many particles in the final state (6 for the O+ + pKo case, 5 for the O+ + nK+ case), many different topologies of detected particles in the final state are possible. The most promising three techniques are summarized in Table 1. Event selections in the 3 analyses are shown in Figs. 10, 11, 12. In all three cases the final state is well identified, without the need of applying cuts to remove background channels. The preliminary analysis reveals an enhancement in the N K invariant mass spectrum, near 1.55 GeV/c2. While the statistical significance of the peak is limited, this analysis shows that a search for the A@+ channel can contribute towards resolving the issue of the Of. The final state can be identified, unambigously, and no kinematical reflections can produce peaks
20 Table 2. Decay modes, combinations of detected particles in the final state and channel-identification techniques adopted for the analysis of the y 3 H e t pAO+ reaction. Decay modes
O+
+ p K o , A -+
pn-
Final-state particles ppn-.rr+X
ppn-
O+
+ nK+, A t p r -
T+7r
ppn-K+X
-x
Channel ID m x = mA m(n-n+) = mKo mx = m p m(pn-) = mA m(n-a+) = mKo mX = mn m(p7r-) = mA
1.5
I 14
1.3
1.2
1.1
Figure 10. Analysis of the pp7r+7r- topology. The cuts E, > 1 GeV and p , < 0.8 GeV/c have been applied in order to reduce the background under the A peak. Shown is here the missing mass of the pp7r+n- system as a function of the invariant mass of 7r+a-, the lines represent the cuts applied to select the A (horizontal lines) and the KO (vertical lines)
in the N K invariant mass distribution. An analysis of this reaction using the high-statistics photoproduction data on the deuteron (part of the g10 run) will give a more definite answer as t o the existence and the properties of the O+ exotic baryon.
21
Figure 11. Results of the analysis for the p p ~ - 7 r + 7 r - topology. Left: missing mass of the p p ~ - 7 r + 7 r - system, showing a peak a the proton mass; center: invariant mass of the p7r- system, peaking at the A mass; right: invariant mass of the n+n- system, the peak is at the KO mass. The vertical lines represent the selection cuts applied.
MM (GeVle')
Results of the analysis for the pp7r-K+ topology. Left: missing mass of the p7r-K+ system, showing a peak at the neutron mass; right: invariant mass of the p7r- system, peaking at the A mass. The vertical lines represent the selection cuts applied.
Figure 12.
5 . Perspectives
The analysis of existing data shows the capabilities of CLAS to select exclusive final states with high multiplicity. The reaction channels described above were cleanly identified with small background due t o misidentified particles. Concurrent reactions decaying to the same final states were seen and rejected from the final event sample. However the statistical accuracy of the preliminary data is not sufficient to exclude that the observed signals are due to statistical fluctuations, kinematic reflections, or some experimental artifact. The number of events in the Of peaks is rather small and does
22 not allow us to perform detailed checks of systematic dependencies.
1A
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.4
1.45
1.5
1.55
M (nK) (CeV)
1.6
1.65
1.7
1.75
1.8
M (pK") (GeV)
Figure 13. Expected statistical accuracy of the mass spectra for the reactions yp @+(@+*)KO,with El+(@+*) decaying into K + n (left) and p K o (right).
+
To obtain a definitive answer on the existence of pentaquark states, four dedicated experiments were recently approved for CLAS in Hall B at Jefferson Lab. The goals and experimental conditions of these experiments are summarized in Table 3. Table 3. states .
New experiments proposed in Hall B for the search of pentaquark
Run
Beam
Energy
Target
g10
7
3.8 GeV
LD2
yd
gll
y
4.0 GeV
LH2
yd -+ @+Ao yp-+ @+KO
Reaction
yp
eg3
e
5.7 GeV
LH2
g12
y
5.7 GeV
LH2
+O+K-p +@+Ira+
-_-X
^(vp -+ c
yp + z + x yp+ @+K-x+ yp + @ + K O yp +K + K - ~ -
Status Completed In progress December 2004 To be scheduled
5.1. Search f o r the @+ and excited states
The g10 experiment which has taken data during the spring of 2004, aims at studying the production channels yd -+ pK-O+, yd -+ p K o X , and
23 yd -+ A@+ with an order of magnitude improved statistics over the previous g2a run. The g l l experiment will study yp -+ @+KO and yp + O+K-n+, and two decay modes, O+ -+ nK+ and O+ -+ pKo, increasing by an order of magnitude the statistics of the previous data. Both experiments have similar experimental setups and beam condition as used in the g2a and glc runs, respectively. The g l l experiment l8 will use tagged photons produced from a 4 GeV primary electron beam impinging on a 40-cm long hydrogen target. Photons from 1.6 GeV up 3.8 GeV are tagged and the data acquisition is triggered by events with at least two tracks to maximize the efficiency for the reaction of interest. The total expected integrated luminosity is 75 pb-', i.e. approximately 20 times larger than in the previous run. If the O+ can be established with certainty, the new data will allow us to make progress on establishing the phenomenology of the O+ spectrum, e.g. determining in what production channels the O+ is seen and what higher mass states are excited. The expected statistical accuracy is shown in Fig. 13, where the background was estimated based on the existing data and the signal was simulated assuming a production cross section of 10 nb. If the existence of the O+ is confirmed or new states are seen, these data will provide accurate measurements of the mass position. In addition, the large acceptance of the CLAS detector will allow us t o measure both the production and decay angular distribution, providing information on the production mechanism and spin. Expected statistical accuracy for the measurement of the production and decay angular distributions are shown in Fig 14, for different assumptions on the production angular distribution and for the spin and parity of the pentaquark state. This measurement will provide a solid foundation for a long term plan for the investigation of the pentaquark spectrum and properties.
-
5.2. Search f o r
ZF- and
S; baryons
The anti-decuplet predicted by the x S M or quark-cluster models for 5-quark states also contains 5, states, two of them of exotic nature, the c5 and the 5;. Evidence for such states has so far been seen in only one experiment 23. The signal found by NA49 has a mass 100 to 200 MeV away from any prediction. This makes it urgent to confirm or refute these claims. Two new experiments with CLAS are in preparation to search for Es baryons. The eg3 experiment 22 will use an untagged electron beam of 5.75 GeV 19320
---
24
e= r
32s
-
$20
I
t
1.4
1.2
27.5
I
I
15 12.5 10
+
*
0.8
+
0.6
7.5
0.4
5 0.2
2.5
n -1 -0.8 -0.6 -0.4 -0.2 0
0.2 0.4 0.6 0.8
-=(e)
1
0
- I 4.8 -0.6 -0.4 -0.2 0
0.2 0.4 0.6 0.8
.(w&
1
Figure 14. Expected statistical accuracy for the measurement of the production and decay angular distribution. A total cross section of 10 nb was assumed. The left plot shows the expected error bars for the production angular distribution in the assumption of a t-channel, s-channel, and u-channel production mechanism. The right plot shows the expected error bars for the decay angular distribution for different assumption on the spin and parity of the state and 100% polarization. N
impinging on a liquid-deuterium target. Electrons will interact with the neutrons in the deuterium through exchange of quasi-real photons. The process y*n -+ Z--X will be searched for by measuring the decay chain z -+ T - Z - -+ T - A + T-P. One proton and 3 T - emerging from three different vertices have to be reconstructed. The experiment is scheduled to take data in the winter 2004/2005. The second experiment 21 is part of g12. It uses the missing mass method to search for the Z- in the exclusive reaction yp + K + K + X . If the NA49 results are correct, the 2- would be seen in the missing mass spectrum as a peak at 1862 MeV. Excellent missing mass resolution is required for such a measurements. Figure 15 illustrates the method with data taken a t photon energies between 3.2 - 3.9 GeV. The E(1320) ground state is observed as a narrow spike. Limitations in beam energy and/or in the statistics did not allow us to observe higher mass 2 s in this measurement. 3--
6. Summary In conclusion, CLAS is currently pursuing high statistics searches for the O+ on hydrogen and deuterium, and in various final states. We are also searching for possible excited states of the @+. The experiments are con-
25 Photoproduction on Hydrogen 60
I ' " I " ' " ' ' l " ' l ' ' " ' " ~ ' ' '
Figure 15. Missing mass M x for the reaction y p + K+K+X for photon energies in the range 3.2 to 3.9 GeV. The narrow peak observed for the ground state 2(1320) illustrates the excellent mass resolution that can be obtained using this method 2 1 . For the pentaquark Ss search, higher energies and much higher statistics are needed.
ducted under similar kinematical conditions as previous measurements. The much higher statistics will allow more definite conclusions as t o the existence of the O+ in the exclusive channel yd + K-pK+(n). In addition, the existence of a possible excited state with mass about 50 MeV above the O+ will be clarified. Moreover, an experiment is in preparation t o search for the ZF- in the mass range where the NA49 experiment at CERN claimed evidence for the observation of the 55(1862) in various charge channels. If evidence for the pentaquark states remains and is considerably strengthened, another high statistics experiment (g12) will be able t o study the spectroscopy of pentaquark states.
7. Acknowledgments This work was supported by the Italian Istituto Nazionale di Fisica Nucleare, the French Centre National de la Research Scientifique, the French Commissariat B 1'Energie Atomique, the U.S. Department of Energy, the U.S. National Science Foundation, and the Korean Science and Engineering Foundation. The Southeastern Universities Research Association (SURA) operates the Thomas Jefferson National Accelerator Facility for the United States Department of Energy under contract DE-AC05-84ER40150.
26
References For recent experimental overviews see: T. Nakano, these proceedings. D. Diakonov, V. Petrov, and M. Polyakov, Z. Phys. A359, 305 (1997). R. Arndt et al., Phys. Rev. C68, 42201 (2003). C. Cahn and G. Trilling, Phys. Rev. D69, 011501 (2004). W. Gibbs, nucl-th/0405024 (2004). For a theoretical overview see: F. Stancu, hep-ph/0408042. F. Csikor, Z. Fodor, S.D. Katz, T.G. Kovacs, hep-lat/0407033; T.G. Kovacs, these proceedings. 8. K. Hicks, hep-ph/0408001. 9. J. Dudek and F. Close, Phys. Lett. B583, 278 (2004). 10. D. Borisyuk et al., hep-ph/0307370 (2003). 11. B. Mecking et al., Nucl. Instr. and Meth. A503, 513 (2003). 12. T. Nakano et al., Phys. Rev. Lett. 91, 012002 (2003). 13. Dolgolenko et al., Phys. Atom. Nucl. 66, 1715 (2003). 14. S. Stepanyan et al. (CLAS collaboration), Phys. Rev. Lett. 91, 252001 (2003). 15. V. Koubarovsky et al., Phys.Rev.Lett. 92, 032001 (2004). 16. V. Guzay, hep-ph/0402060 (2004). 17. K. Hicks, S. Stepanyan, et al. (CLAS), Jlab experiment E-03-113. 18. M. Battaglieri, R. De Vita, V. Koubarovsky, et al. (CLAS), JLab experiment E-04-021. 19. R. JaEe and F. Wilczek, Phys. Rev. Lett. 91, 232003 (2003). 20. M. Karliner and H. Lipkin, Phys. Lett. B575, 249 (2003). 21. J. Price, D. Weygand, et al. (CLAS), Jlab experiment E-04-017. 22. E. Smith, R. Gothe, S. Stepanyan, et al. (CLAS), JLab experiment E-04-010. 23. C. Alt et al. (NA49 collaboration), Phys. Rev. Lett. 92, 042003 (2004).
1. 2. 3. 4. 5. 6. 7.
K N Scattering Data and the Exotic O$ Baryon 1.1. STRAKOVSKY, R.A. ARNDT, R.L. WORKMAN, W.J. BRISCOE Center for Nuclear Studies, Department of Physics, The George Washington University, Washington, D. C. 20052 We review the recent history and pre-history of the exotic S = +1 O+ resonance. While seen in many recent experiments, evidence for this state is conspicuously absent in older kaon-induced reaction data. We concentrate on these older data and the constraints they imply for the O+ resonance.
The subject of S = +1 Z+ resonances, once occupying a section of the PDG review, remained dormant for many years until a number of photoinduced reactions gave evidence for a narrow structure in their final-state K+n and Kop mass distributions. A (by now incomplete) summary of recent mass and width determinations is given in Table 1. While a number of resonance-like structures were found earlier in partial-wave analyses of K+N and K+-deuteron scattering data, these were eventually dropped from the PDG review, as their existence required a higher standard of proof than ordinary non-exotic resonances and could be qualitatively explained in terms of pseudo-resonance dynamics. The recently discovered @+(1540), predicted by the chiral soliton model' , is different in that its mass is far below any of the structures found in previous fits to K+N scattering data17 and its width is much smaller, though it has yet to be directly measured. A list of resonance-like structures from the 1992 VPI KN analysis is given in Table 2. Width determinations for the new W(1540) state have so far provided only upper limits - the DIANA CXS experiment giving the tightest constraint of r < 9 MeV3. A number of groups have reexamined the existing KN scattering data in order to deduce significantly reduced values for this width limit. Nussinov was the first to examine total cross section data for this purpose13. Improved versions of this technique, applied to the older scattering data have yielded width limits of 1-2 MeV16i1s. A modified PWA of older K+N and K+-deuteron scattering data is also consistent with this c o n c l ~ s i o n ~ ~ . Capstick, Page, and Roberts suggested the narrow width was due to an isospin-violating decay, and further predicted the existence of a Of+
27
28 Table 1. Comparison of O+ properties. Collaboration
Mass
Width
Ref
LEPS DIANA CLASIyn CLASI7P SAPHIR I TEP /v CLASlYP HERMES SVD COSY-TOF ZEUS USC GWU Jiilich LBNL
1540f10 1539f2 1542&5 1540f10 1540rt4f.2 1533&5 1555f10 1528f2.6f2.1 1526&2.6&2.1 1530f5 1521.5&1.5+2.8-1.7 1543 1540-1550 1545 1540
<25
2
<9
3
<21 <32 <25 <20 <26 <24 <24 <18 <15 <6
7
lo
13
51
14
<5 0.9f0.3
l5 l6
statelg. Thus far, this additional exotic resonance has not been confirmed. No evidence for peaks in K+p mass distributions was found20. Searches for @++ states, using a standard K N PWA, suggest poles in PI3 and Ol5 wavesL7,but too far above the @+ to be its isospin partner. Given the higher quality of existing K + p scattering data, even more stringent limits on a @++ width can be obtained21.
3
2
I
I
I
Q = +1
1 o -1
-1 -2
-3
I
I
I
-
@+( 1540)
(Suudd)
t
n o -2
I
Antidecuplet
N(1650 ? )
4 \
-
\
&+-4 \
C( 1755 ? )
- \
\-
(s s d d u ) I
\
I
- 3 - 2 - 1 0
\
\-
I
-
.
-
1862 ? )
\
-
(SSUUIT)
I
1
I
I
2
3
I
4
I 5
13
Figure 1. Tentative unitary anti-decuplet with O+ . Isotopic multiplet and constant values of the charge are shown respectively by solid and dashed lines.
29 Table 2.
KN PWA finding^'^.
Amplitude
ReW (MeV)
-1mW (MeV)
Po1 DO3
1831 1788 1811 2074
95 170 118 253
p13
D15
A different approach to this problem involves a search for further states which would presumeably populate a multiplet associated with the @+ (see Fig. 1). According t o the Gell-Mann-Okubo rule, the antidecuplet mass difference, based on the @+ and E3/223masses, is about 107 MeV. The soliton calculation of this mass difference depends on the value of the 0term. Its value, taken from a recent analysis23, gives about 110 MeV24.
It is expected that associated antidecuplet states would also be quite narrow25. In searching for N* states of this type, we have found possible candidates near 1680 and 1730 MeV25. These would necessarily have a very small value for r T N and should be more easily found in other reactions. (A search of this kind was reported at this and Trento meetings by Kouznetsov for the GRAAL Collaboration and at the Jamaica workshop by Kabana for the STAR C ~ l l a b o r a t i o n ~ ~A) .state of similar mass, the N(1710), is already listed by the PDG, but has a width estimate in line with ‘normal’ N* resonances ( L e . a width of order 100 MeV). Acknowledgments This work was supported in part by U.S. Department of Energy grant No. DE-FG02-99ER41110. The authors acknowledge partial support from Jefferson Lab, through the Southeastern Universities Research Association under the Department of Energy contract No. DE-AC05-84ER40150.
References 1. D. Diakonov, V. Petrov, and M. Polyakov, 2. Phys. A , 359, 305 (1997). 2. T. Nakano et al. Phys. Rev. Lett. 91, 012002 (2003). 3. V.V. Barmin et al. Phys. Atom. Nuclei, 66, 1715 (2003). 4. S. Stepanyan et al. Phys. Rev. Lett. 91, 252001 (2003). 5. V. Koubarovsky and S. Stepanyan, in Proceedings of “Conference on the Intersections of Particle and Nuclear Physics (CIPANP2003), New York, NY, USA, May 2003” [hep-ex/0307088].
30 6. J. Barth et al. Phys. Lett. B572, 127 (2003). 7. A.E. Asratyan et al. Phys. Atom. Nuclei, 67,682 (2004). 8. V. Koubarovsky et al. Phys. Rev. Lett. 92,032001 (2004). 9. A. Airapetian et al. Phys. Lett. B585, 213 (2004). 10. A. Aleev et al. hep-ex/0309042. 11. M. Abdel-Bary et al. hep-ex/040311. 12. S . Chekanov et al. hep-ex/0403051. 13. S . Nussinov, hep-ph/0307357. 14. R.A. Arndt, 1.1. Strakovsky, and R.L. Workman, Phys. Rev. C 68,042201 (2003). 15. J. Haidenbauer and G. Krein, Phys. Rev. C 65, 052201 (2003). 16. R.N. Cahn and G.H. Trilling, Phys. Rev. D 69,011501 (2004). 17. J.S. Hyslop, R.A. Arndt, L.D. Roper, and R.L. Workman, Phys. Rev. D 46, 961 (1992). 18. R.A. Arndt, 1.1. Strakovsky, and R.L. Workman, nucl-th/0311030. 19. S. Capstick, P.R. Page, and W. Roberts, Phys. Lett. B570, 185 (2003). 20. J. Barth et al. Phys. Lett. B572, 127 (2003); V.Kubarovsky et al. Phys. Rev. Lett. 92, 032001 (2004); A. Airapetian et al. Phys. Lett. B585, 213 (2004); H.G. Juengst et al. nucl-ex/0312019; S . Chekanov et al. hep-ex/0403051. 21. R.A. Arndt, Ya.1. Azimov, 1.1. Strakovsky, and R.L. Workman, to be submitted. 22. C. Alt et al. Phys. Rev. Lett. 92,042003 (2004). 23. M.M. Pavan, R.A. Arndt, 1.1. Strakovsky, and R.L. Workman, in Proceedings of 9th International Symposium on Meson-Nucleon Physics and the Structure of the Nucleon (MENU2OOl), Washington, DC, USA, July 2001, edited by H. Haberzettl and W.J. Briscoe, TN Newslett. 16,110 (2002) [hepph/0111066]. 24. D. Diakonov and V. Petrov, Phys. Rev. D 69,094011, (2004). 25. R.A. Arndt, Ya.1. Azimov, M.V. Polyakov, 1.1. Strakovsky, and R.L. Workman, Phys. Rev. C69,035208 (2004). 26. V. Kouznetsov et al. these Proceedings; V. Kouznetsov et al. Pentaquark states: structure and properties, Feb. 2004, Rento, Italy. http://www.tp2.ruhr-uni-bochum.de/talks/trento04/index.html 27. S . Kabana et al. Proceedings of 20th Winter Workshop on Nuclear Dynamics Jamaica, March 2004.
Notes On Exotic Anti-Decuplet Of Baryons M.V. POLYAKOV Innstitut de Physique, Universite' de Liege, B-4000 Liege 1, Belgium We emphasize an importance of identification of non-exotic S U f l ( 3 ) partners of O+ pentaquark and indicate possible ways to do this. Also we use the soliton picture of baryons to relate reggeon couplings of various baryons. These relations are used to estimate O+ production cross section in high energy processes. It is demonstrated that the corresponding cross sections are sizably suppressed relative to production cross sections of usual baryons.
1. Introduction The first independent evidences for the exotic baryon O+ with strangeness +1 in y 12C and K+Xe reactions, which followed by important confirmation in about ten experiments by spring 2004 urge us to take a fresh look at baryon spectroscopy. We still know rather little about properties of exotic O+, even its the very existence is not yet firmly established, see negative experimental results l l . In my contribution I am going t o give neither review of ideas which lead us12 t o prediction of O+ nor account of various theoretical ideas about possible nature of exotic pentaquarks. For former I would recommend t o the reader talk by D. Diakonov at APS meeting documented in 13. For review of other theoretical ideas see contribution t o this conference by K. Maltman 1 4 . Here I plan just t o stress an importance t o search for non-exotic (cryptoexotic) flavour partners of O+ pentaquark. As original contribution I decided to include here my notes written in year 1997 which appeared as the result of the discussion with J. Bjorken and J. Napolitano of the possibility to search for O+ in LASS data15. Probably today these calculations can be useful to explain why production of O+ is suppressed in some of high energy experiments. Very important point is that a discovery of a baryon with positive strangeness would imply an existence of a new flavour multiplet of baryons, beyond familiar octets and decuplets. An exotic baryon should be always accompanied by its large family. A minimal SUfl(3) multiplet containing pentaquarks is an anti-decuplet of baryons. A multiplet containing pen2671375,5,798,9310,
31
32 taquarks should also contain baryons with non-exotic ( “ 3 - q ~ a r k ~ quan~) tum numbers. In the case of the anti-decuplet these are: isodoublet of nonstrange l‘nucleonsl’ and isotriplet of S = -1 C’s. Are they already known baryons or we should look for new states? How to reveal their hidden exoticness? In our view it is very important for understanding of nature of O+ pentaquark t o identify its non-exotic partners. To do this one can employ 1) symmetry rules dictated by flavour S U ( 3 ) 2) dynamical picture of the anti-decuplet baryons. Surprisingly, this topic has been discussed in the literature rather little. The reader can consult details of such studies in e.g. One of amazing properties of nucleons from the antidecuplet is that they can be excited by electromagnetic probe much stronger from the neuteron target than from the proton one 16. Evidence for the nucleon resonance with such properties and in the expected mass range has been reported at this conference by V. Kouznetsov 2 2 . Further evidence for this state has been reported by the STAR collaboration 2 3 . It could be that during many many years we have been overlooking narrow nucleon resonance with the mass of around 1700 MeV! This could be possible due to unusual properties of this resonance inherited from its anti-decuplet origin. It is expected12Jg that the nucleon from the anti-decuplet has rather small coupling to 7rN channel, with preferred decay channel such us T T N ,qN and K A . I think the problem of existence of such nucleon resonance can be clarified rather easily with such machines as CEBAF, MAMI, ELSA, etc. Concerning the C’s from the anti-decuplet, they are also expected to be relatively narrow, as it follows from SUjl(3) rules. Such states can be searched in high energy collisions, although the corresponding production cross section can be rather strongly suppressed, see next section. 16117318719120,17.
18719
2. Reggeon couplings from chiral soliton
Here we derive relations between reggeon couplings to various baryons, including exotic pentaquark O+. Such kind of relations are useful for estimations of production cross sections of baryons in high energy processes. We apply these relations t o estimate the O+ production cross section in reaction K+p -+ rffaSt@+ + 7rf+,,,K+nat = 11.5 Gev/c. Corresponding data were collected by the LASS collaboration, see e.g. Ref. 1 5 . We restrict ourselves to the spin-flip dominated production reactions: 7r-p -+ Ton, 7r+p --t 7roA++, 7r+p K+C’+(1385),
-+
33
K - p -+7r-C*+(1385), K+p -+ 7r+O+ , Other spin-flip dominated reactions can be related to these by the (broken) SU(3) relations for reggeon couplings, which is known to work well (see 24). In the chiral quark soliton model the low-lying baryons are different rotational excitations of the same object. This enables us t o derive relations between spin-flip reggeon couplings in the above list of reactions. We shall check the relations between reggeon coupling from the chiral soliton confronting them with data on measured reactions in the above list. On other hand these relations can be used to estimate the production cross section of the exotic Of baryon, say, in the reaction K+p -+ ~ ' f + , ~ ~ @ +-+ ~ ' f + , ~ ~ 15
We consider here only the spin-flip dominated reactions, because our objective is to estimate the production cross section of exotic O+ baryon in the reaction K+p + 7r+O+ which is obviously spin-flip dominated (spin nonflip part is zero for transitions between baryons from different SU(3) multiplets, this was confirmed by experiment: the spin nonflip part of the amplitude of say 7r"p + K+C*+(1385) and 7r+p + ,'A++ is negligently small). The smallness of the spin nonflip part of the amplitude of reaction x - p -+ .ironis related to large isovector magnetic moment of the nucleon. The soliton-reggeon coupling can be written in terms of rotational coordinates R of the baryon as (for notations see Ref. 1 2 )
here a ( t ) is the corresponding Regge trajectory and index m denotes the flavour of the leading meson on the corresponding trajectory ( p , K * ) . In the next to leading order we have to add to eq. (1)collective operators depending on the angular momentum J,. The corresponding operators have a form : -i3W2
- -.
6
1
Tr(RtXmRXg)53
5
where dabc is a SU(3) invariant symmetric tensor, a,/? = 4,5,6,7 and J, are generators of infinitesimal SU(3) rotations.
34
Sandwiching eqs. (1,2) between the rotational wave functions of initial and final baryons (explicit expressions for the corresponding wave functions can be found in Appendix A of ref. 1 2 ) , one gets expressions for the B1 + Bz +Reggeon vertices in reactions listed above (we do not write kinematical factors):
m
-i3Gg-
7.\/2 , 30
(3)
1
m,
43Gm-
here we introduced the following coupling constants: 1 1 Gg = wo - -WI - - ~ 2 , 2 14 1 Glo = wo - - 2 ~ 1 , 2 1 Gm = wo 201 -wg. 2 The constants wi can be estimated using measured high energy processes. Here we shall be interested in ratios of various cross sections, therefore for us here only ratios of these constants are relevant. The structure of collective operators eqs. (1,2) is the same as in the case of axial and vector currents. Analysis of corresponding axial and magnetic constants areo negative. Model calculations 26 con25y26indicatethat ratios w ~ , ~ / w firm the negative sign of w1,2/wo and give the following values:
+ +
= -0.35f0.1 WO
w2 = -0.25 WO
f 0.1 ,
(7)
35 where the errors are added by hands simply on the basis of our working experience with this model. It should be mentioned that the non-relativistic quark model (which, t o some extent, can be used as a guiding line) predicts w1/wo = -415 and W ~ / W O= -215, which is in a qualitative agreement with a more realistic calculation in the quark soliton model. Amazingly] though, these ratios produce exactly zero Gm. At the moment we are unable to point out the deep reason for such a cancellation. Using the equations derived above we can obtain the relations between different spin-flip dominated reaction cross sections (the list is given at the beginning of the section). Doing this we shall assume that these reactions are dominated by the one reggeon exchange ( p and K*-trajectories). The first group of relations is simply SU(3)fl relations which is known 24 t o be well reproduced by experimental data. Given this fact we shall not discuss this group of relation. The nontrivial prediction of the chiral quark-soliton model is the relations between high energy reactions which involve baryons from different SU(3) multiplets. These are (for the same incident plab):
+ +
a(K+p + 7r+O+) 3 (wo w1 i W 2 ) 2 -_. a ( K - p + 7r-C*+) 4 (wo- +w1)2 ' (9) all other relations can be obtained with a help of (broken) SU(3) relations and hence they are trivial. The eq. (8) can be confronted with experiment, whereas the eq. (9) is a prediction. Let us note that the first equality in eq. (9) is a consequence of assumed exchange degeneracy of Regge trajectories. The exchange degeneracy is in general violated] although not very strongly] for rough estimate of the O+ production cross section it is sufficient to assume the exchange degeneracy. Using the estimates for w1,2 eq. (7) we get: a(K+p + 7r+O+)
a(7r+p + K+C*+(1385))
-
we see that this number is not sensitive t o uncertainties in determination of w1,2. Let us compare this prediction with data, ref. 27 gives:
i-0'5+ dt
da(7r-p dt
TO.)
= 87 f 4 pbarn ,
36 at plab = 5.9 Gev/c. The A++ production experiment
29
gives:
da(7r+p + 7roA++) = 133 f 13 pbarn , dt dt
1-0,5
(12)
a t plab = 5.45 Gev/c. This cross section can be rescaled to plab = 5.9 Gev/c using a(7r+p t 7r0A++) pl,i.59 29. Eventually we get: N
a(7r+p -+ 7roA++) = 1.35 f0.15 a(7r-p -+ T o n )
(expt. at plab = 5.9 Gev/c) ,
(13)
in a good agreement with our prediction eq. (lo)! The agreement is even better for experiments at higher energies. The value of a(7r+p t 7roA++) = 44.83~7pbarn measured at plab = 13.1 Gev/c being divided by a ( ~ - p+ ran) = 36 f 2 pbarn measured at plab = 13.3 Gev/c 27 gives: a(7r+p -+ 7roA++) = 1.2 & 0.1 a(7r-p Ton)
+
(expt. at plab
M
13 Gev/c) .
(14)
We see that the chiral soliton model successfully predicts non-trivial relations between reggeon couplings to baryons from different multiplets. Given this success we turn now t o estimation of a(K+p + 7r+O+). From eq. (9) and estimates of w1,2 (7) we get:
a(K+p + 7r+O+) a(K+p + 7r+O+) = 0.05 + 0.25, a ( r + p + K+C*+(1385)) a ( K - p t 7r-C*+)
(15)
we see that in this case the result is very sensitive to uncertainties of w1,2 due to deep cancellation of these constants. With present state of the art we can not say precisely how deep is this cancellation, but in any case we can conclude that the suppression is rather sizable. In order to estimate the absolute value of a(K+p t 7r+Of) at plab = 11.5 Gev/c l 5 we need the value of a(7r+p -+ K+C*+(1385)) or a ( K - p -+ 7r-c*+) at the same plab. Fortunately the latter cross sections were measured exactly at plab = 11.5 Gev/c with the results 30: a(7r+p t K+C*+(1385)) M 8 pbarn,
and
31
a ( K - p -+ 7r-C*+) x 10.1 f 1.1 pbarn,
37 slight difference of the above two cross sections is related to the violation of exchange degeneracy of the K’ and K** trajectories. From the above data and with the help of eq. (15) we get an estimate:
a(K+p += .ir+O+) M 0.5 + 2.5 pbarn.
(16)
We see that the O+ production cross section is rather small. Let us note that the above estimate of the O+ production cross section should be considered as an order of magnitude estimate (up t o factor of 2). In course of derivation we neglect: 0
0
The violation of the exchange degeneracy of the Regge trajectories. This could give uncertainty about 20-30%. The produced particle mass dependence of the reggeon parameters, e.g. we take the scale parameters (so, parameter in reggeon residue, etc.) t o be universal (= a’) following Veneziano model pattern. This could give uncertainty about 30-40%.
References 1. T. Nakano (LEPS Collaboration), Talk at the PANIC 2002 (Oct. 7, 2002, Osaka); T. Nakano et al., Phys. Rev. Lett. 91,012002 (2003), [ hep-ex/0301020]. 2. V.A. Shebanov (DIANA Collaboration), Talk at the Session of the Nuclear Physics Division of the Russian Academy of Sciences (Dec. 3, 2002, Moscow); V.V. Barmin, A.G. Dolgolenko et al., Phys. Atom. Nucl. 66, 1715 (2003) [Yad. Fiz. 66,1763 (2003)], [hep-ex/0304040]. 3. S. Stepanyan, K. Hicks et al. (CLAS Collaboration), Phys. Rev. Lett. 91, 252001 (2003); V. Kubarovsky et al. (CLAS Collaboration), Phys. Rev. Lett. 92,032001 (2004), [hep-ex/0311046]. 4. J. Barth et al. (SAPHIR Collaboration), Phys. Lett B 572,127 (2003), [hepex/0307083]. 5 . A. E. Asratyan, A. G. Dolgolenko and M. A. Kubantsev, Phys. Atom. Nucl. 67 (2004) 682 [Yad. Fiz. 67 (2004) 7041 [arXiv:hep-ex/0309042]. 6. A. Airapetian et al. (HERMES Collaboration), Phys. Lett. B 5 8 5 , 213 (2004), [hep-ex/0312044]. 7. A. Aleev et al. (SVD Collaboration), [hep-ex/0401024]. 8. M. Abdel-Bary et al. (COSY-TOF Collaboration), [hep-ex/0403011]. 9. P.Zh. Aslanyan, V.N. Emelyanenko, G.G. Rikhkvitzkaya, [hep-ex/0403044]. 10. S. Chekanov et al. (ZEUS Collaboration), [hep-ex/0403051]. 11. J. 2. Bai et al. [BES Collaboration], hep-ex/0402012. K. T. Knoepfle, M. Zavertyaev, and T. Zivko [HERA-B Collaboration], contribution to Quark Matter 2004; hep-ex/0403020. C. Pinkenburg [PHENIX Collaboration], contribution to the 17th Intern.
38
12.
13. 14.
15. 16. 17. 18. 19. 20. 21. 22.
23. 24. 25. 26. 27. 28. 29. 30.
31.
Conf. on Ultra-Relativistic Nucleus-Nucleus Collisions, Jan.2004; nuclex/0404001. D. Diakonov, V. Petrov and M. Polyakov, Z. Phys. A 359, 305 (1997), [hepph/9703373]. D. Diakonov, arXiv:hep-ph/0406043. K. Maltman, contribution to this conference; see also: B. K. Jennings and K. Maltman, Phys. Rev. D 69 (2004) 094020 [arXiv:hep-ph/0308286]. J. Napolitano, J . Cummings and M. Witkowski, “Baryon ezcitation in K * p reactions,” PIN Newslett. 13 (1997) 276. M. V. Polyakov and A. Rathke, Eur. Phys. J. A 18 (2003) 691 [arXiv:hepph/0303138]. R. L. JafTe and F. Wilczek, Phys. Rev. Lett. 9 1 (2003) 232003 [arXiv:hepph/0307341]. D. Diakonov and V. Petrov, Phys. Rev. D 69 (2004) 094011 [arXiv:hepph/0310212]. R. A. Arndt, Y. I. Azimov, M. V. Polyakov, I. I. Strakovsky and R. L. Workman, Phys. Rev. C 6 9 (2004) 035208 [arXiv:nucl-th/0312126]. T. D. Cohen, arXiv:hep-ph/0402056. L. Y. Glozman, arXiv:hep-ph/0309092. V. Kouznetsov [for the GRAAL collaboration], contribution to this conference; see also: V. Kouznetsov, talk at international workshop Pentaquark states: structure and properties, February 10 - February 12, 2004, Trento, Italy. http://www.tp2.rub.de/talks/trento04/index.html S. Kabana [STAR Collaboration], arXiv:hep-ex/0406032. A. C. Irving and R. P. Worden, Phys. Rept. 34 (1977) 117. H. C. Kim, M. Praszalowicz and K. Goeke, Phys. Rev. D 6 1 (2000) 114006 [arXiv:hep-ph/9910282]. H. C. Kim, M. Praszalowicz, M. V. Polyakov and K. Goeke, Phys. Rev. D 58 (1998) 114027 [arXiv:hep-ph/9801295]. Stirling, et al., Phys. Rev. Lett.14 (1965) 763. J.H. Scharenguivel, et al., Nucl. Phys. B36(1972) 363. I.J. Bloodworth et al., Nucl. Phys. B81 (1974) 231. P.A. Baker, J.S. Chima, P.J. Dornan, D.J. Gibbs, G. Hall, D.B. Miller, T.S. Virdee, A.P. White, Nucl.Phys. B166 (1980) 207; J . Ballam, J. Bouchez, et al., AMPLITUDE ANALYSIS OF Y * (1385) PRODUCTION IN THE LINE REVERSED REACTIONS: PI+ P-+ K+ Y * (1385) AND K- P + PI- Y * (1385) A T r-GEV/C AND 11.5-GEV/C., SLAC-PUB-2175, Aug 1978. 18pp. Contributed paper to 19th Int. Conf. on High Energy Physics, Tokyo, Japan, Aug 23-30, 1978. J. Ballow et al., Phys. Rev. Lett.41 (1978) 676.
Quark Model Perspectives on Pentaquark Exotics K. MALTMAN Dept. Math. and Stats., York Univ., 4700 Keele St. Toronto, O N C A N A D A M3J 1P3 E-mail:
[email protected] CSSM, University of Adelaide, Adelaide, S A 5005 A U S T R A L I A I discuss the expectations and predictions for pentaquark exotics based on the quark model perspective. Recent quark model scenarios, and calculations performed in different realizations of the quark model approach, up to the end of March 2004, are also discussed.
1. Introduction
A large number of experiments now appear to confirm the existence of the exotic, strangeness +l 6 baryon'. The I = 3/2 exotic E312 signal observed by NA49 remains t o be confirmed (it is not seen by HERA-B, and its compatibility with earlier high statistics Z production experiments has also been questioned)2. Recently, H1 reported evidence for an anti-charmed exotic, though this state was not seen by ZEUS3. Whether or not the NA49 and H1 signals are confirmed by subsequent experiments, the existence of the 6 makes a rethinking of our understanding of the excited baryon spectrum inevitable. If the B has I = 0, and lies in a multiplet, for example, exotic pentaquark partners having N and C quantum numbers necessarily also exist. These should sit in the same region as the 39 radial excitations of the N and C ground states and, unavoidably, mix with thema. This immediately calls into question past quark model treatments of the excited, positive parity baryon spectrum which included only 3q configurations. It also undercuts one of the main phenomenological motivations for the effective Goldstone boson (GB) exchange model of the
m~
aMixing between non-exotic radial excitations and the corresponding states in the exotic 1 0 and ~ 2 7 multiplets ~ is also significant in the chiral soliton model4. In the quark model, where additional non-exotic pentaquark states are expected, the mixing will be even more complicated. Phenomenologically, a more complicated mixing pattern than just ideal mixing between 1 0 and ~ 8~ pentaquark multiplets6 is likely required to account for the N(1440) and N(1710) masses and decay patterns5.
39
40
baryon spectrum’, i.e., the failure of the 3q Isgur-Karl (effective colormagnetic (CM) exchange) approach t o successfully reproduce the low-lying P = Roper-like resonances. The existence of the 6 does not, of course, invalidate the GB model, but does suggest that any differences between GB and CM model predictions in the exotic sector become of heightened phenomenological interest. Below, we discuss recent scenarios, and some qualitative features of pentaquark states expected in the quark model (QM) framework. Comparisons to the results of the chiral soliton model (CSM) a p p r o a ~ h ~ whose prediction of a low-lying, narrow 8’ was a primary motivation for the initial LEPS search, will also be made.
+
2. The 8 Parity and Other Discrete Quantum Numbers
The CSM approach unambiguously predicts that the lowest lying S = +1 exotic state should lie in the 1 0 multiplet ~ and have I = 0, J p = 1/2+. It has sometimes been stated that the naive quark model “predicts” P = for the lowest lying exotic baryon state. This statement is incorrect and has led to some confusion in the literature. It should actually be rephrased t o state that the quark model “might naively be guessed to produce P = -” for the lowest-lying exotic state. Whether or not this guess is correct is a dynamical question. In fact, it turns out that a competition exists between the additional orbital excitation needed for the P = + sector and the decreased spin-dependent (generically, “hyperfine”) expectation available in this sector. The following qualitative argument, given by Jaffe and Wilczek (JW)6,12,shows why the P = + sector might be favored. The F = 3, J = 0, C = 3 qq configuration is known to be very attractive in QCD. It is also the most attractive qq correlation in a number of QCD-inspired models (the GB and CM models, as well as models based on instantoninduced effective interactions). Assuming pentaquark states are dominated by optimal two-quark correlations, one expects a state with two such pairs to be particularly low-lying. Such a state is Pauli forbidden unless the two pairs are in an odd relative orbital state6. To take advantage of this optimal qq pairing, one must thus go t o the P = sector. The lowest-lying exotic configuration is then necessarily the S = I = 0 member of a OF, J p = 1/2+ multiplet, as in the CSM picture. A qualitative understanding of why the hyperfine energy might be significantly lowered in the P = + sector, and hence win out over the orbital
+ +,
41
excitation, can can also be arrived a t using the “schematic approximation” to the GB and CM models, in which the spatial dependence of the spindependent operators is neglectedb. In this approximation, the expectations of the flavor-spin (FS) (GB case) or color-spin (CS) (CM case) dependent interactions can be worked out by group-theoretic methods, even in the P = sector. In both models, higher FS or CS symmetries produce more attractive hyperfine expectations. For the GB case, the highest FS symmetry for the spatially-unexcited [ 4 ] orbital ~ q4 configuration is [31]~s, while for the [ 3 1 ] ~ configuration it is [ ~ ] F s Similarly, . for the multiplets containing exotic states in the CM case, the highest CS symmetries are [ 2 2 ] ~ s for the [ 4 ]and ~ [31]cs for the [ 3 1 ] configuration. ~ In both cases one thus expects a significant gain in hyperfine energy in going from the P = - to the P = sector. Explict dynamical model calculations bear this out14. Dynamically, it need not be the case that qq correlations are dominant. Indeed, in the CM model, as pointed out by Karliner and Lipkin (KL)15, a more complicated correlation, consisting of one F = 3, C = 3, J = 0 pair (as in the J W scenario) and one F = 3, C = 3 pair with the qq spin flipped to J = 1 and anti-aligned to the ii spin, yields a lower hyperfine energy for the 8 than does the J W correlation. (Such a configuration is also favored in a model with effective instanton-induced interations16.) Mixing between the J W and KL correlations in the CM model, induced by the same qS interactions responsible for favoring the KL qqS correlation, actually leads to an even lower-lying state, which is nearly an equal mixture of the J W and KL correlation^'^. It should be stressed that, while in the J W and KL scenarios it has been argued that intercluster interactions and antisymmetrization effects will be suppressed by the relative pwave between the clusters, it is only in particular dynamical models that these effects can be explicitly calculated. Such a calculation was performed for the GB and CM models in Ref. [14]. In such calculations, one can directly compare the hyperfine expectations in the P = - and P = sectors. As shown in Ref. [14], at least for the GB and CM models, the increase in hyperfine attraction in the optimal (CSM quantum numbers) P = channel, as compared to that in the optimal non-fall-apart P = - channel, is such that, with expectations for the orbital excitation energy based on experience from the baryon sector15,
+
+
+
+
bThe approximation has also been employed quantitatively in a number of recent cal~ulations’~.However, although it successfully identifies optimally attractive channels, it turns out to be quantitatively unreliable (see Ref. [14] for more details).
42
+
the lowest-lying exotic state is expected to have P = and NOT P = -, with other quantum numbers also agreeing with the CSM predictionc. Two important qualitative differences do exist between the CSM and QM pictures. The first difference concerns “flavor partners”. In the QM picture, in the absence of flavor-dependent qij interactions, the exotic flavor multiplets come accompanied by non-exotic flavor partners with which they are degenerate in the s u ( 3 ) F limit. For example, the 4q flavor configuration in the multiplet is [ 2 2 ] ~Combining . this with the [ l l ]i j ~ configuration yields
rn~
[ 2 2 ]8 ~ [ l l ]= ~
mi^ @ 8~ ,
(1)
m~
i.e., the pentaquark multiplet containing the 8 is accompanied by an 8 F pentaquark multipletd. When s u ( 3 ) F breaking is turned on, the N and C partners of the 8, the members of the pentaquark 8 ~and , the radially excited 3q configurations will all mix. Thus, if the 6 is, indeed, real, the P = + excited baryon sector becomes very complicated in the QM picture. The second difference between the QM and CSM pictures is that P = pentaquarks in the QM approach are accompanied by spin-orbit partners not present in the CSM. For the 0, for example, the intrinsic spin of 1/2, coupled t o the L = 1 of the orbital excitation in the P = sector, leads t o both J p = 1/2+ and 3/2+ S = +, I = 0 states. While a low-lying S = +, J p = 3/2+ state is predicted in the CSM approach, it lies in a 2 7 ~and , has I = 1, not I = 0. An estimate of the expected splitting of the J p = 3/2+ partner of the 0 in the CM model suggests it should be rather small, several 10’s of MeV, with a conservative maximum of 150 MeV1’. Such observations make the importance of searches for excitations of the 6 obvious.
+
+
N
3. Masses of Exotic States The CSM approach naturally predicts a low-lying S = + exotic with a mass in the region of the observed experimental 0 signal (see Ref. [ll] for a detailed discussion of this point). In contrast, simple extensions of constituent quark model calculations from the non-exotic 3q baryon sector CAneven stronger statement is true in the CM model. There, even if one argues that the approach used in Ref. [15]might mis-estimate the orbital excitation energy, the model allows no phenomenologically acceptable P = - assignment for the e l 4 . dThe exotic 2 7 pentaquark ~ multiplet similarly comes accompanied by a 1 0 and ~ an 8 ~ the , 3 5 pentaquark ~ multiplet by a 1 0 ~ .
43 to the exotic sector will produce a mass for the lowest such exotic which is too high. It is important t o bear in mind that, although it is not unreasonable to attempt such calculations as an exploratory first stage, there are good reasons for expecting them to be physically unreliable, even if the underlying models on which they are based are reasonable. The reason is that the models typically lack a representation of physical effects which one expects to be present and to, potentially, have a significant impact on the values of one-body energies. An example of such effects is provided by the bag model. In going from the 3q to 6q sector, for example, the equilibrium bag radius increases, reducing the quark kinetic energies. This effect is counterbalanced by the change in the phenenological Z I R term, meant t o represent the effects of zero point motion and corrections for CM motion in the bag. It turns out that each of these changes is large (- 400 - 450 MeV) on the scale of baryon splittings, and that the level of cancellation between them is a very sensitive function of the bag parameter El1*. Such effects are almost certainly present physically, and in need of representation if one wants to generalize calculations from the 3q to the 4qq sector. They are not, however, represented at all in constituent quark model approaches such as those of the GM and CM models. As a result, one would not generally expect the one-body energies, calculated in those versions of the models calibrated in the 3q sector, to be reliable in the pentaquark sector. It thus appears fair t o say both that the 8 mass has not been predicted, and that it most likely cannot be sensibly predicted, in the QM framework. This does not mean that the various quark models cannot make any predictions in the pentaquark sector, only that, realistically, they lack the features required to allow them to have a chance of successfuly predicting the splitting between (exotic) pentaquark and (non-exotic) 3q states. For example, one of the assumptions of the models is that the spin-dependent interactions can, to a good approximation, be treated perturbatively. If this is the case, then the splittings between different spin-flavor channels, all within the pentaquark sector, should still be predictable by the models. Failure of experiment to reproduce these splittings would then allow one to rule out a given model, or models. The minimal model-dependence for such predicted splittings occurs for 444 states where all of the four quarks are u and/or d. When there are both u (or d ) and s quarks among the four quarks, there can be a modeldependent interplay between the flavor-breaking in the hyperfine expectations and the lowering of orbital excitation energies for relative coordinates
44
involving the heavier s quark(s). One of the interesting predictions, of the minimally-model-dependent type, is that, as in the CSM, a rather lowlying I = 1, S = excitation, &, of the 6 should exist in both the GB and CM models. In the GB model there is actually a degenerate pair with ( I , J r ) = (1,1/2+) and (1,3/2+), where Jq is the total quark spin (still t o be combined with the orbital L = 1 to produce the total spin). In the CM model, the lowest excitation of the 8 has (I,J:) = (1,1/2+). Using non-exotic baryon values of the pair hyperfine matrix elements to estimate the hyperfine energies one finds14
+
msl - ms cz 60 - 90 MeV (CM) msl - ms
N
140 MeV (GB)
,
(2)
to be compared t o N 55 - 85 MeV in the rigid rotor version of the CSM approachlO>ll. Estimates for the splitting between the 8 and its I = 3/2 E3I2 1OF partner have been made in both the J W and KL scenarios. Both the original version of the J W estimate and the KL estimate, which yielded m ~ ~N , ,1750 MeV and N 1720 MeV, respectively, were based on the assumption that the pair matrix elements for the spin-dependent interactions, and the cost of the replacement d tt s , could be estimated using the analogous quantities from the non-exotic baryon sector. The J W estimate can be raised t o 1850, more in line with the NA49 observation, if one allows significant deviations from the non-exotic baryon sector parameter valueslg. One should again bear in mind that cross-cluster interaction and antisymmetrization effects, where novel flavor-breaking contributions might be generated, are implicitly neglected in these estimates. More detailed dynamical model estimates will be subject to the model-dependence noted above, associated with the need to estimate flavor-breaking effects on the one-body energies. One such dynamical calculation has been performed, for the GB model, in Ref. [20], with the result mz:3,2N 1960 MeV. Note, however, that, while the actual calculation is non-schematic, the wavefunction is restricted to the single component which lies lowest in the schematic approximation. While, for technical reasons having to do with the explicit form of the flavor-spin interactions employed in the model, this approximation is a good one for the S = sector (where all four quarks have equal mass), there are reasons to expect much more significant mixing in the Z3I2sector once the schematic approximation is relaxed. Allowing additional components in the wavefunction will lower the mass. The size of this effect is not known at present.
-
-+
45
+
The lowest I = 2 S = exotics, using non-exotic baryon values for the two-body spin-dependent matrix elements, are predicted to lie around 1980 MeV in both the GB and CM models, similar to the values obtained in the CSM approach. Both experiment and theory, therefore, strongly disfavor an I = 2 interpretation of the 8.
-
4. The 0 Width
One of the striking predictions of the CSM calculation of Ref. [9] was that the 8 should be naturally narrow (- a few lo’s of MeV or less) in the CSM picture, as subsequently observed experimentally. Some initial speculations, based on the observed widths of known, non-exotic baryons a comparable distance above their own two-body decay thresholds, suggested that the 8 should be relatively broad in the QM picture. Such arguments, however, are necessarily unreliable since the decay mechanism for the non-exotic 39 and exotic pentaquark baryons in the quark model cannot be the same. Indeed, for two-body decays of a 39 baryon, a pair creation is required whereas, for the decay of a pentaquark state, the number of constituents is the same in the initial and final states. If one considers K N scattering, and the possibility of forming an S = exotic resonance as a result of the residual short-range interaction among the fixed number of constituents, one realizes that an above-threshold resonance can only be formed in a pwave or higher. The reason, as stressed in Ref. [6], is that a single-range residual s-wave interaction insufficiently strong to bind produces no resonance behavior, only positive phase motion. In contrast, for pwave (and higher) scattering, a residual short-range attraction can play off against the peripheral centrifugal barrier to produce resonance behavior. One can make a rough estimate for the width of such a resonance as follows. It is straightforward t o verify that the intrinsic width for a K N resonance at the observed mass of the 0 produced by an attractive K N square-well potential of hadronic size is 200 MeV‘. Thus, if one has a pentaquark configuration with overlap f t o the short-range K N configuration, one expects a width, for a pwave resonance, of order
+
-
rs
-
200 f 2 MeV .
(3)
Whether or not the small widths compatible with experimental observations are natural in the QM picture is then a matter of how large or small the overlap factor f is. It turns out that, for the JW correlation, the isospin-spin-color part of the overlap factor is rather small, = 1/2414. A similar value,
[f;&l2
46
[fsg]’
21 1/25, is obtained for the optimized combination of the JW and KL correlations in the CM model14. Since these results do not include any further reduction associated with the mismatch between the spatial configurations (which can be numerically quite significant2’) , the natural width of the 0 in the QM picture is, in fact, quite small. Indeed, a width greater than 10 MeV would be very difficult to accommodate. S U ( 3 ) arguments then require the width of the E3/2 partner of the 8 t o also be smaW9. It is obvious that the above width estimate is at best semi-quantitative. Unfortunately, it seems unlikely that significant improvements can be made to ite. The most natural improvement one could envisage, in the GB and CM models, would be t o use the non-relativistic constituent QM framework, where CM motion can be cleanly separated, and do a scattering calculation of the resonating group type. The obvious difficulty with this approach is that the one-body operators enter such a calculation in a non-trivial fashion. The existence of problems with the one-body energies in such models thus means that resonance widths obtained in such a calculation could not be treated as reliable. Finally, it should be mentioned that a common coupling of nearby states t o the same decay channel can lead, through mixing, t o one of the mixed states having a width much narrower than the natural width of either state22. To produce a significant narrowing, the mechanism requires the two states, before mixing, t o be relatively close together. For the GB and CM models, the next excitation with 8 quantum numbers lies 330 MeV (GB) and 230 MeV (CM) above the e l 4 . In these models, therefore, the mixing mechanism is unlikely to play a significant role in generating the narrow 0 width. This does not, of course, preclude the possibility that the mixing mechanism might be important in other realizations of the QM approach.
-
-
N
5 . Heavy Quark Analogues of the 8
Interest in heavy pentaquarks (Qq4, where q = u,d, s and Q = C, b), was initially aroused by the observation that the Qs13 ( l = u,d ) states with I = eThe discussion of Ref. [ll] shows that, because of cancellations between nominally leading-order contributions to the widths of the states, it is similarly difficult to provide a quantitatively reliable prediction for these widths in the CSM approach. Such cancellations can also amplify the impact of higher order SU(3)~-breakingeffects on the relation between the 0 and Z 3 l 2 widths.
m~
47
1/2, J p = 1/2- have strong hyperfine attraction relative to that of their two-body decay thresholds, ND,, N B , , in the CM model, in the m9 + 00 limit23. Subsequent work, however, showed that decreased binding from s U ( 3 ) breaking, ~ kinetic energy, confinement and ma # 00 effects was likely sufficient t o make all of these states unbound24. Predictions turned out to be very different in the GB model, with the P = - states lying several 100 MeV above threshold25. Only the Qt4 P = +, ( I ,J,’) = (0,1/2+) states were found to be bound, with binding energies of 75 - 95 MeV26. An experimental search for the predicted anticharmed, strange state, covering the mass range 2.75 - 2.91 GeV, was performed by the E791 Collaboration, with negative results27. Interest in heavy pentaquark states has been greatly revived by the discovery of the 8. If, as is now generally assumed, the parity of the 8 is indeed positive, then the same mechanism which makes the 8 narrow is expected to also make its heavy quark analogues narrow, even if they lie above the relevant nucleon-plus-heavy-pseudoscalardecay threshold. The situation for the P = - heavy pentaquarks is less clear. Models, as well as a JW-like scenario for the Qse3 states28, suggest that the lowest-lying of these states should have J = 1/2. Unless such a state is bound, it will have an s-wave fall-apart decay and hence almost certainly be non-resonant. A number of recent estimates exist for the P = heavy pentaquark These are typically produced by extensions of the scenarios MASSES for the 8 based on the assumption that a reasonable approximation to the splitting between the 8 and its I = 0, J p = 1/2+ analogue, OC or 8 b , should be obtainable using the LLcorresponding”splitting between the A and Ac or At,, supplemented by an estimate for the change (if any) in the spindependent quark-antiquark interactions in going from the 8 to the heavy quark system. Since, in the J W scenario, the diquarks are assumed to have spin zero and be tightly bound, there is no such quark-antiquark interaction, and hence no spin-dependent correction to be made. The resulting estimates are6
+
meb N 6050 MeV , (4) N 100 and 170 MeV below the relevant strong decay thresholds. If one assumes that the same diquark-triquark clustering postulated in the KL scenario for the 8 persists for heavy systems, one obtains, after taking into account the reduced strength of the Qe, relative to 8, hyperfine interaction,
me, N 2710 MeV;
me, N 2985 MeV;
meb 21 6400 MeV ,
(5)
48
now N 180 MeV above the relevant strong decay thresholds. The estimate of Ref. [28] for the low-lying Q d 3 P , = - states is based on the JW scenario, and the J W estimate for the P = states. Estimates for the reduction in mass associated with the absence of a n orbital excitation, and the increase in mass associated with changing one of the u, d quarks of the 8, to an s, both are taken from analogous splittings in the ordinary charmed and charm-strange baryon spectrum. While the neglect of cross-cluster interactions and antisymmetrization effects is more questionable when the diquark clusters are in a relative s-wave, the resulting estimate is of interest since it puts the Qst3 states not only below strong decay thresholds (at 2580 and 5920 MeV for Q = c , b, respectively) but also below the lower edge of the E791 search window in the Q = c case. It should be pointed out that the KL assumption that the same diquarktriquark clustering is present in both the heavy quark and 8 systems requires some deviation from the strict CM model picture. The reason is that the constituent charm quark mass is sufficiently heavy that, already in the charm system, the KL correlation has become less attractive than the JW correlation. The strict CM picture would thus predict different structures for the 8 and its heavy quark analogues. This does n o t mean that the CM picture would yield the J W mass estimates given in Eq. (4). Indeed, the J W correlation, which would dominate the heavy quark system, produces only a portion of the hyperfine attraction in the 8 for CM interactions. Thus, in the CM model, a correction for the reduction in the hyperfine expectation in the heavy quark system would need to be added to the JW estimates. This correction t o the JW value moves the estimated BC mass to N 20 MeV above the strong decay threshold. This effect, if present, would also impact the estimates of Ref. [28] for the P = -, Qse3 states. Interesting predictions of the minimally-model-dependent type can be made for the P = Qt4 states in the GB and CM models. The low-lying spin-flavor excitations for the two models are shown in the table below. Numerical values for the splittings from the ground-state pentaquark configuration have been obtained by fully diagonalizing in the space of all Pauli-allowed, fully antisymmetrized states for each channel, and using the pair matrix elements from the baryon spectrum t o estimate the overall scale31. One sees that a rather dense spectrum of excitations is predicted, especially in the CM model, and that the pattern of excitations is very different for the two models. It also turns out that the overlaps to the nucleon-plus-heavy-pseudoscalar decay channel are roughly comparable for all states listed (with the exception of one channel for the CM interactions
+
+,
49
where the overlap is strongly suppressed). Since the relative strengths of the couplings to the decay products are expected to be given by the ratio of the corresponding overlap factors32, one expects a rich spectrum of experimentally observable excited states. Such predictions should be rather easy to confirm or rule out, assuming any of the predicted states can be found experimentally. Table 1. Low-lying positive parity excitations of the 6Q in the GB and CM models, in the ma --f co limit. E,, is the excitation energy in MeV.
Acknowledgments
The ongoing support of the Natural Sciences and Research Engineering Council of Canada is gratefully acknowledged. There are many topics and recent papers I have been unable t o discuss due to space restrictions. Apologies in advance to the authors of those works. References 1. T. Nakano, et al., Phys. Rev. Lett. 91, 012002 (2003) 012002; V. Barmin, et al., Phys. At. Nucl. 66, 1715 (2003); S. Stepanyan, et al., (The CLAS Collaboration), Phys. Rev. Lett. 91, 252001 (2003); J. Barth, et al., (The SAPHIR Collaboration), Phys. Lett. B572, 127 (2003); A.E. Asratyan, A.G. Dolgolenko and M.A. Kubantsev, Phys. Atom. Nucl. 67, 682 (2004); V. Kubarovsky et al., Phys. Rev. Lett. 92, 032001 (2004) (Erratum ibid. 92, 049902 (2004)); H.G. Juengst et al., nucl-ex/0312019; A. Airapetian et al., Phys. Lett. B585, 213 (2004); A. Aleev et al., hep-ex/0401024; M. Abdel-Bary et al., hep-ex/0403011; P.Z. Aslanyan, V.N. Emelyanenko and G.G. Rikhkvitzkaya, hep-ex/0403044; S. Chekanov et al., hep-ex/0403051; T . Nakano, presentation at NSTAR 2004, Grenoble, France, Mar. 24-27, 2004 (http://lpsc.in2p3.fr/congres/nstar2004/talks/nakano.pdf) 2. C. Alt et al., Phys. Rev. Lett. 92, 042003 (2004); K.T. Knopfle et al., hepex/0403020; H.G. Fischer and S. Wenig, hep-ex/0401014. 3. A. Aktas et al., hep-ex/0403017; K. Lipka et al., hep-ex/0405051.
50 4. 5. 6. 7. 8.
H. Weigel, hep-ph/0404173. T. Cohen, hep-ph/0402056; S. Pakvasa and M. Suzuki, hep-ph/0402079. R. JafFe and F. Wilczek, Phys. Rev. Lett. 91,232003 (2003). L. Ya. Glozman and D. 0. Riska, Phys. Rep. 268,263 (1996). A.V. Manohar, Nucl. Phys. B248, 19 (1984); M. Chemtob, Nucl. Phys. B256, 600 (1985); M. Praszalowicz, Phys. Lett. B575, 234 (2003). 9. D. Diakonov, V. Petrov, and M. Polyakov, Z. Phys. A359, 305 (1997). 10. H. Weigel, Eur. Phys. J. A2, 391 (1998); H. Weigel, Proc. Intersections of Particle and Nuclear Physics, hep-ph/0006191; H .Walliser and V.B. Kopeliovich, hep-ph/0304058; V.B. Kopeliovich, hep-ph/0310071; D. Borisyuk, M. Faber, A. Kobushkin, hep-ph/0307370 and hep-ph/0312213; D. Diakonov and V. Petrov, Phys. Rev. D69, 094011 (2004); B. Wu and B.Q. Ma, Phys. Rev. D69, 077501 (2004) and Phys. Lett. B586, 62 (2004). 11. J. Ellis, M. Karliner and M. Praszalowicz, JHEP 0405,002 (2004). 12. S. Nussinov, hep-ph/0307357. 13. K. Cheung, hep-ph/0308176; F. Stancu and D.O. Riska, Phys. Lett. B575, 242 (2003); C.E. Carlson et al., Phys. Lett. B579, 52 (2004). 14. B. Jennings and K. Maltman, hep-ph/0308286, in press Phys. Rev. D. 15. M. Karliner and H.J. Lipkin, Phys. Lett. B575, 249 (2003) and hepph/0307243. 16. N.I. Kochelev, H.J. Lee and V. Vento, hep-ph/0404065. 17. J.J. Dudek and F.E. Close, Phys. Lett. B583, 278 (2004). 18. K. Maltman, Phys. Lett. B291, 371 (1992). 19. R. Jaf€e and F. Wilczek, hep-ph/0312369. 20. F. Stancu, hep-ph/0402044. 21. C.E. Carlson e t al., hep-ph/0312325. 22. N. Auerbach and V. Zelevinsky, nucl-th/0310029; M. Karliner and H. Lipkin, Phys. Lett. B586, 303 (2004). 23. C. Gignoux, B. Silvestre-Brac and J.M. Richard, Phys. Lett. B193, 323 (1987); H.J. Lipkin, Phys. Lett. B195,484(1987); J. Leandri and B. SilvestreBrac, Phys. Rev. D40, 2340 (1989). 24. S. Fleck, C. Gignoux, J.M. Richard and B. Silvestre-Brac, Phys. Lett. B220, 616 (1989); S. Zouzou and J.M. Richard, Few-Gody Syst. 16,1 (1994). 25. M. Genovese et al., Phys. Lett. B425, 171 (1998). 26. F. Stancu, Phys. Rev. D58, 111501 (1998). 27. E.M. Aitala et al., Phys. Lett. B448, 303 (1999). 28. I.W. Stewart, M.E. Wessling and M.B. Wise, hep-ph/0402076. 29. M. Karliner and H.J. Lipkin, hep-ph/0307343. 30. K. Cheung, hep-ph/0308176; P.Z. Huang et al., hep-ph/0401191. 31. K. Maltman, YU-PP-I/E-04-KM-l1 2004, in preparation. 32. F.E. Close and Q. Zhao, hep-ph/0403159.
The Status of Pentaquark Spectroscopy on the Lattice F. CSIKOR~,z. F O D O R ~ )s. ~ ,D. K A T Z ~ T. ~ , G. KOVACSC ADepartment of Theoretical Physics, Eotvos Lora'nd University, H-1117 Budapest, Pa'zma'ny Pe'ter se'ta'ny l / a BDepartment of Physics, Bergische Unaversitat Wuppertal, Gaussstr. 20 D-42119 Germany CDepartment of Physics, University of Pe'cs, H-7624 Pe'cs, Ifj6sC;g u. 6 Hungary The present work is a summary of the status of lattice pentaquark calculations. After a pedagogic introduction to the basics of lattice hadron spectroscopy we give a critical comparison of results presently available in the literature. Special emphasis is put on presenting some of the possible pitfalls of these calculations. In particular we discuss at length the choice of the hadronic operators and the separation of genuine five-quark states from meson-baryon scattering states.
1. Introduction
The recent experimental searches for and the of the previously theoretically predicted5 exotic hadrons has sparked considerable activity and gave rise to diverse speculations regarding their structure, unexpectedly small width, parity, isospin and spin. The only presently available technique for computing low energy hadronic observables starting from first principles (i.e. QCD) within systematically controllable approach is lattice QCD. All this said, it might seem surprising that of the more than 200 papers devoted to the subject of exotic baryons in the past year, there were only four lattice papers. Besides critically reviewing the currently available lattice results, in the present work we also try to resolve this apparent paradox =On leave from Eotvos L o r h d University, Budapest, Hungary.
51
52 by discussing some of the difficulties and pitfalls of the lattice approach. The presentation is aimed for the general particle and nuclear physics community. For this reason, in Section 2 we start with an introduction t o lattice hadron spectroscopy and also address two points that are usually not discussed in great detail in lattice papers, but are essential for the correct interpretation of lattice pentaquark results. In our opinion the biggest challenge lattice pentaquark calculations face is how to choose the baryonic operators. Not only the errors, but also the very possibility to identify certain states depends crucially on the choice of operators. Unfortunately there is very little guidance here and many technical restrictions. Subsection 2.1 is devoted t o this issue. Since the five-quark bound states we want t o study can be close to threshold, it is essential in any lattice spectroscopy calculation to reliably distinguish between genuine five-quark bound states and meson-baryon scattering states. In Subsection 2.2 we discuss how this can be done. Having set the stage, in Section 3 we give a critical review of the currently available lattice results and interpret them. In Section 4 we conclude by summarising the status of lattice calculations and stressing what is needed to be done for a final consolidation of the lattice results.
2. Hadron spectroscopy on the lattice 2.1. The choice of operators
In the framework of lattice QCD the role of the regulator is played by a space-time lattice that replaces continuous space-time. As a result, in a finite spatial volume the infinite dimensional functional integral turns into a mathematically well defined finite dimensional integral. The lattice also opens the way to the explicit numerical computation of hadronic observables by Euclidean Monte Carlo techniques. In hadron spectroscopy one would like to identify hadronic states with given quantum numbers. Practically this means the following. We compute the vacuum expectation value of the Euclidean correlation function (OlO(t)0t(O)lO)of some composite hadronic operator 0. The operator 0 is built out of quark creation and annihilation operators. In physical terms the correlator is the amplitude of the “process7’of creating a complicated hadronic state described by 0 at time 0 and destroying it at time t . After inserting a complete set of eigenstates li) of the full QCD Hamil-
53 tonian the correlation function can be written as
(o~o(~)o+(o)~o) = C I (ilot(0)10)e-(Ei-Eo)t,
(1)
i
where
~ ( t=)e-Ht O(O)eHt
(2)
and Ei are the energy eigenvalues of the Hamiltonian. Note that since we work in Euclidean space-time (the real time coordinate t is replaced with -it), the correlators do not oscillate, they rather die out exponentially in imaginary time. In particular, after long enough time only the lowest (few) state(s) created by 0 give contribution t o the correlator. The energy eigenvalues corresponding t o those states can be extracted from exponential fits to the large t behaviour of the correlator. In the simplest cases one is typically interested in hadron masses. A trivial but most important requirement in the choice of 0 is that it should have the quantum numbers of the state we intend t o study. Otherwise the overlap (iIOt(0)(0) would be zero and the corresponding exponent could not be extracted. In order t o have optimal overlap with only one state li), 0t(0)10) should be as t o li) as possible. A hadron mass is the ground state energy in a sector with given internal quantum numbers and zero momentum. Projection t o the zero momentum sector is achieved by summing a local operator over all of three-space as
2
5
One of the most important experimentally still unknown quantum numbers of pentaquark states is their parity. Thus, we also briefly touch upon the parity assignment on the lattice. The simplest baryonic operators do not create parity eigenstates, rather they couple to both parity channels. Projection to the +/- parity eigenstates can be performed as 1 0* = -(0 2 f PoP-1).
(4)
For the simplest operators the parity operator P acts on 0 as
where 7 = f l is the internal parity of the operator 0. For more complicated operators, in particular for non-pointlike ones, this might become more involved. If the parity of a state is not known, it can be determined
54 by computing the correlator in both parity channels and deciding which channel produces a mass closer to the experimentally observed one. All quantum numbers fixed, there is still considerable freedom in the choice of 0. This freedom has to be exploited to ensure maximal overlap of 0+(0)10)with the desired state and minimal overlap with close-by competing, but unwanted states. This is essential not only for smaller errors. With the wrong choice of 0 the desired state might be practically undetectably lost in the noise. Unfortunately, beyond the quantum numbers there is usually little if any guidance in the choice of 0 and herein lies the biggest challenge of lattice pentaquark spectroscopy. It is almost impossible t o disprove the existence of a given state. If one cannot detect it with a given operator 0 , it might just mean that 0 has too small overlap with the desired state and the signal is lost in the noise. If the wave function of the quarks in the given hadronic state were known, that would dictate the form of the operator to be used. In the case of pentaquarks there are several suggestions in the literature and in principle it would be interesting to try operators corresponding to at least some of them. There are, however, two serious restrictions lattice calculations face in this respect. The first one concerns the spatial structure of the wave function, the second one its index structure. In the remainder of this section we discuss these. Concerning the spatial structure of the wave function, we have to note that the correlation function in Eq. (I) is computed on the lattice by decomposing it in terms of single quark correlators (Olqa(x)qL(y)lO). Those in turn are simply the matrix elements D-l (z, a ;y, /3) of the inverse of the lattice Dirac operator. If 0 were to be based on an arbitrary five-quark wave function, the brute force computation of the correlator of 0 would in general require quark propagators D - l ( x , a ;y , /3) from any space-time point x to any other point y. On currently used lattice sizes this would require the computation and storage of order matrix elements, taking up about 100 Terabytes and requiring hundreds of Teraflops of CPU power. This is clearly out of reach for presently available computers. The only way around is to fix a quark wave function $ p ( f ) and store only the matrix elements
This choice drastically cuts down the computing requirements. Unfortunately, at the same time it also restricts c3 to be built as a product of single
55
quark wave functions with the single quarks being in some state $J. One needs t o perform as many Dirac operator inversions as the number of different quark wave functions contained in 0. Since Dirac operator inversion is usually the most expensive part of these computations, one typically settles with using only two different quark sources, one for the light quarks and one for the strange quark. In fact, all four lattice pentaquark studies have used this simplest choice. Besides the spatial structure of 0 the single quark spin, colour and flavour indices also have to be arranged properly for 0 to have the desired quantum numbers. Even then the arrangement of indices is also not unique. An additional difficulty one faces here compared to conventional three quark hadron spectroscopy is that index summation becomes exponentially more expensive if we increase the number of quarks. While with three quarks this part of the calculation is usually negligible] even for the simplest five quark operators it takes up around 50% of the CPU time. This circumstance restricted the choice of pentaquark operators so far to the simplest ones. To illustrate how these issues appear in practice we now discuss a few specific examples of 0 that have already been used. In the first lattice study4 0 had the same Dirac structure as that of nucleon plus kaon system, but colour indices were contracted differently, as5
where I = 0/1 and the two alternative signs correspond to the isospin singlet and triplet channel respectively. Another possible way to contract the quark indices in 0 is according to the diquark-diquark-antiquarkpicture of Jaffe and Wilczek6. They proposed t o insert the two diquarks in
in a relative P-wave. In general, in a diquark-diquark-antiquark wave function of the form (8) the two diquarks must be in different quantum statesb. On the lattice, that would require the computation of several quark propagators. Instead, Sasaki avoided the diquark-diquark symmetry by omitting a 7 5 from one of the diquarks7. The operator he, and subsequently Chiu & Hsiehs conbotherwise the operator identically vanishes due to its symmetry with respect to the interchange of the diquarks
56
sidered, was
In summary, both in terms of spatial and index structure there are many more possibilities for 0 ,but on the lattice they all require considerably more CPU time than the ones explored so far. However, we expect that several other possibilities will be tried in the near future. 2 . 2 . Separating two particle states
Pentaquark spectroscopy is further complicated by the presence of twoparticle scattering states lying close to the pentaquark state. Lattice calculations are always performed in a finite spatial volume, therefore these scattering states do not form a continuum. They occur at discrete energy values dictated by the discrete momenta pk = 2 k n / L , k = 0,1, ..., allowed in a box of linear size L . In lattice pentaquark computations it is absolutely essential to be able to distinguish between these two-particle nucleon-meson scattering states and genuine five quark bound states. In fact, the first experimentally found exotic baryon state, the Of(1540) lies just about 100 MeV above the nucleon-kaon threshold. This implies that for large enough time separation the correlation function is bound to be dominated by the nucleon-kaon state. However, the mass difference between the two states is quite small and the mass of the O+ might still be reliably extracted in an intermediate time window, provided that 1 ( ~ + 1 ~ 1 0> )> l I(N+ Kl0lO)l.
(10)
Even then, identifying the O+ is still a non-trivial matter since the O+ ground state is embedded in an infinite tower of nucleon kaon scattering states with relative momenta allowed by the finite spatial box. Since the parity of the 0' is unknown, we have to consider both parity channels. The situation is qualitatively different in the two channels. If the O+ had positive parity, its lattice identification would be somewhat simpler. This is because due to the negative internal parity of the kaon it is only the scattering states with odd angular momentum that produce positive parity. The scattering state with zero relative linear momentum does not couple to these and consequently it does not appear in the positive parity channel. Therefore, the lowest scattering state here has relative momentum p = 2 r / L and it is above the O+, provided the linear size of the spatial box is smaller than 4.5 fm. The box can thus be chosen small
57 enough to ensure that the O+ is the lowest state with positive parity and also to leave a large enough energy gap for its safe identification. The situation is much less favourable in the negative parity channel. Using a similar argument one can show that here it is always the prel = 0 scattering state that is the lowest. The best we can do is that with the proper choice of the spatial volume the O+ ground state can be the second lowest state. Due care must be taken t o ensure that O+ is between the first two scattering states, well separated from both of them. This is essential because the reliable identification of higher lying states is much more difficult. Finally, for a convincing confirmation of the pentaquark state in either parity channel, one also has to identify the competing scattering states observing the volume dependence dictated by the allowed smallest momentum. This would clearly require a finite volume analysis combined with a reliable method t o extract severd low lying states from the spectrum. There are essentially two possible ways of identifying more than one low lying state from correlators. Firstly, if there is a time interval where more than one state has an appreciable contribution to the correlator, a sum of exponentials can also be fitted as
(olo(t)o+(0)10) = Cle-EOt + C2epElt + ...
(11)
For this method to yield reliable energy estimates for higher states, one usually needs extremely good quality data. The other possibility is to make use of several different operators, compute all possible cross-correlators and diagonalise the Hamiltonian in the subspace spanned by the states created by those operators lo. This is a very powerful method to identify excited states and it can also be combined with the first possibility. 2.3. Extrapolations, sources of errors and uncertainties
The lattice spectroscopy of hadrons built out of light quarks involves two extrapolations. Firstly, simulations at the physical u / d quark masses would presently be prohibitively expensive, therefore one has t o do several calculations with heavier quarks and then extrapolate to the physical quark masses. A set of typical chiral extrapolations are shown in Fig. 1. The lightest quarks used in presently available pentaquark studies correspond t o pion masses in the range 180-650 MeV (see Table 1). Secondly, the space-time lattice is not a physical entity, it is just a regulator that has to be eventually removed to recover continuous space-time.
58
Figure 1. Chiral extrapolation of the masses different five quark states from Ref.7
Table 1. Lattice spacing and smallest pion mass of lattice pentaquark calculations. Csikor et al. Sasaki Liu et al. Chiu 8~ Hsieh
action Wilson Wilson chiral chiral
a (fm) 0.17-0.09 0.07 0.20 0.09
smallest m, (MeV) 420 650 180 400
This implies that physical quantities have t o be computed on lattices of different mesh sizes and extrapolated to the zero lattice spacing (continuum) limit. Lattice simulations can differ from one another in many technical details and it is only the continuum limit of physical quantities that is meaningful to compare among different simulations. In the remainder of this Subsection we briefly summarise the sources of errors and uncertainties in lattice simulations indicating also how t o handle them.
59 Statistical errors are well understood and can be kept at bay by increasing the statistics. Extrapolations in quark mass and lattice spacing are another source of uncertainty. Fortunately mass ratios of hadrons are usually quite insensitive in the present range of parameters. Quenching, i.e. neglecting the fermion determinant (omitting quark loops) is still a necessary compromise we have to live with in most of the lattice calculations. Fortunately experience tells us that stable hadron mass ratios have only a few per cent quenching error. Finite volume effects constitute another potential source of error. There are different sources of volume dependence that can be properly accounted for and even be used to distinguish between bound states and two particle scattering states. As we have already discussed the desired state can be contaminated from other nearby states, but this can be taken care of by a combination of the cross correlator technique and a careful finite volume analysis. Finally there is a theoretical uncertainty originating in the lack of any guidance in the choice of operators and the inability to choose 0 optimally. This can result in larger statistical errors or even in a complete failure to identify an existing state. For this reason it is almost impossible to rule out the existence of a state with given energy and quantum numbers. 3. Results Having set the stage we can now present the lattice results along with our interpretation. Four independent lattice pentaquark studies have been presented. Their main results can be summarised as follows.
Csikor, Fodor, K a t z and Kovacs4 identified a state in the Ip = 0channel with a mass consistent with the experimental @+ and the lowest mass found in the opposite parity I p = O+ channel was significantly higher. Using 2 x 2 cross correlators an attempt was also made t o separate the @+ and the lowest nucleon kaon state. Sasaki7 using a different operator and double exponential fits, subsequently also found a state consistent with the @+ also in the Ip = 0- channel. He also managed t o identify the charmed analogue of the @+ 640 MeV above the D N threshold. (The experimentally found anticharmed pentaquark lies only about 300 MeV
60
0
0
above the threshold.) Liu et aZ.l3 reported that they could not see any state compatible with the O+ in either parity isosinglet channel. Although their smallest pion mass was the closest to the physical one, they used the nucleonxkaon operator along with single exponential fits and rather coarse lattices. Finally Chiu & Hsiehg, in disagreement with the first two studies, saw a positive parity isosinglet state compatible to the @+, whereas the lowest state they found in the negative parity state was much higher. In a subsequent paperg they also identified states claimed to be charmed counterparts of the @+.
Our tentative interpretation of this somewhat controversial situation is as follows. Liu et al. used only one operator with exactly the same index structure as that of the nucleon kaon system. This might explain why they see only the expected scattering states. The three remaining studies could be interpreted to have found genuine pentaquark states. All three agree that the lowest masses in the two parity channels differ by about 50%, but they do not agree on the parity of the O+ state. While Csikor et al. and Sasaki suggest negative parity, Chiu & Hsieh claim positive parity. According to the interpretation of Chiu & Hsieh they found different parity because they used a quark action with better behaviour at small quark masses, albeit the same operator as Sasaki. The pion masses they use (2400 MeV) overlaps with those of Sasaki ( 2 650 MeV). In this region using the same hadron operator all other hadron masses in the literature obtained with these two quark actions agree (see e.g8>14).Thus it is extremely unlikely that the same operator with different lattice actions produces such vastly different masses. In our opinion a more likely resolution of this contradiction is that someone might have simply misidentified the parity. On the one hand, the results of Chiu & Hsieh and on the other hand, those of Sasaki (and Csikor et al.) would become compatible with each other if parities were flipped in one of them. A possible hint for a parity mismatch is provided by Chiu & Hsieh in their second paperg. They considered two operators with opposite internal parities, but otherwise having exactly the same quantum numbers. Contrary to physical expectations, their ordering of the lowest mass states in the two parity channels turned out to depend on the internal parity of the operator. This suggests that internal parity might not have been properly taken into account (see Eq. 5). Finally we would like to note
61
that at this stage we can merely offer these speculations and the issue has to be resolved by an independent study.
4. Conclusions In summary, lattice QCD is the only known systematic approach to calculate the features of the pentaquarks from first principles (i.e. QCD). There have been four independent exploratory lattice pentaquark studies SO far with somewhat different findings. One of them sees only the expected scattering state. Three analyses suggest mass states around the experimentally detected pentaquarks. In order to justify these signals as pentaquark states one should convincingly separate them from the existing nearby scattering states. None of the groups carried out this analysis. Furthermore, it should be realised that none of these analyses can be complete for the following reason. In such a complete analysis one should see the pentaquark in one parity channel and the lowest expected scattering state in the other. All of the three groups reported energy states coinciding with the pentaquark mass in one of the parity channels; however, in the other channel the energy state is much higher than the expected scattering state. Since both parities have been suggested by lattice works, at least one of the results will coincide with the parity to be found experimentally. Nevertheless, no convincing final answer from lattice QCD can be claimed unless the above program has been completed. More specifically, it cannot be ruled out that pentaquark states observed so far on the lattice turn out to be mixtures of nucleon-kaon scattering states. As we already emphasised, for a full picture one needs to systematically map out the lowest few states in all interesting channels. This will most likely be possible only with the use of non-trivial spatial quark wave functions, the study of several operators and the cross-correlator technique combined with a careful finite volume analysis. This is currently under way and we hope to be able to report new results in the near future.
Acknowledgments Partial support from OTKA Hungarian science grants under contract No. TO34980/TO37615/TSO44839/T046925 is acknowledged. T.G.K. was also supported through a Bolyai Fellowship.
62 References 1. T. Nakano e t al. [LEPS Collab.], Phys. Rev. Lett. 91, 012002 (2003); V. V. Barmin e t al. [DIANA Collab.], Phys. Atom. Nucl. 66, 1715 (2003) [Yad. Fiz. 66, 1763 (2003)]; S. Stepanyan e t al. [CLAS Collab.], Phys. Rev. Lett. 91, 252001 (2003); J. Barth et al. [SAPHIR Collab.], hep-ex/0307083; V. Kubarovsky and S. Stepanyan [CLAS Collab.], AIP Conf. Proc. 698,543 (2004); A. E. Asratyan, A. G. Dolgolenko and M. A. Kubantsev, Phys. Atom. Nucl. 67, 682 (2004) [Yad. Fiz. 67, 704 (2004)l; C. Alt et al. "A49 Collab.], Phys. Rev. Lett. 92, 042003 (2004); V. Kubarovsky e t al. [CLAS Collab.], Phys. Rev. Lett. 92,032001 (2004) [Erratum-ibid. 92,049902 (2004)]; A. Airapetian e t al. [HERMES Collab.], Phys. Lett. B 585, 213 (2004); A. Aleev e t al. [SVD Collab.], hep-ex/0401024; Y. Ohashi, hep-ex/0402005; J. Z. Bai e t al. [BES Collab.], hep-ex/0402012; M. Abdel-Bary et al. [COSYTOF Collab.], hep-ex/0403011; K. T. Knopfle, M. Zavertyaev and T. Zivko [HERA-B Collab.], hep-ex/0403020; P. Z. Aslanyan, V. N. Emelyanenko and G. G. Rikhkvitzkaya, hep-ex/0403044; S. Chekanov et al. [ZEUS Collab.], Phys. Lett. B 591, 7 (2004); Y. A. Troyan et al., hep-ex/0404003; S. V. Chekanov [ZEUS Collab.], hep-ex/0404007; S. Chekanov [ZEUS Collab.], hep-ex/0405013; [WA89 Collab.], hep-ex/0405042; S. Kabana, hepex/0406032. 2. A. Aktas et al. [Hl Collab.], hep-ex/0403017. 3. D. Diakonov, V. Petrov and M. V. Polyakov, Z. Phys. A 359,305 (1997). 4. F. Csikor, Z. Fodor, S. D. Katz and T. G. Kovacs, JHEP 0311,070 (2003). 5. S. L. Zhu, Phys. Rev. Lett. 91,232002 (2003). 6. R. L. Jaf€e and F. Wilczek, Phys. Rev. Lett. 91,232003 (2003). 7. S. Sasaki, hep-lat/0310014. 8. T. W. Chiu and T. H. Hsieh, hep-ph/0403020. 9. T. W. Chiu and T. H. Hsieh, hep-ph/0404007. 10. T. Burch et al., [Bern-Graz-Regensburg Collab.], hep-lat/0405006. 11. S. Sasaki, T. Blum and S. Ohta, Phys. Rev. D 65,074503 (2002). 12. M. Luscher and U. Wolff, Nucl. Phys. B 339,222 (1990). 13. K.-F. Liu, talk at the First Pentaquark Workshop, 2003; F. X. Lee, talk at the NSTAR Workshop, see the present volume. 14. S. Aoki e t al. [CP-PACS Collab.], Phys. Rev. D 67,034503 (2003).
Study of the Exotic O+ in Polarized Photoproduction Reactions QIANG ZHAO Department of Physics University of Surrey Guildford, Surrey GU.2 7XH, United Kingdom E-mail:
[email protected] We present an analysis of a Beam-Target double polarization asymmetry in y n -i O + K - . We show that this quantity can serve as a filter for the determination of the spin-parity assignment near threshold. It is highly selective between 1/2+ and 1/2- configurations due to dynamical reasons.
1. Introduction
The report of signals of a strangeness S = +l baryon @+ has stimulated a tremendous number of activities in both experiment and theory in the past 12 months. Baryon with strangeness S = f l and strongly coupled into K N implies that its minimum number of constituents should be at least five, i.e. a pentaquark state (uuddi?). With a rather-low mass of 1.54 GeV and a narrow width of less than 25 MeV, the existence of such a state (later another state Z-- was also reported 2, also initiates a tremedous number of questions about strong QCD dynamics in the low energy regime. Whether it is the chiral-soliton-model-predicted 10 multiplets 3 , or pentaquark 1 0 in the quark model such a state reveals some important new aspects of QCD, which have not been widely concerned before. The quantum numbers of the @+ are undoubtedly one of the key issues for answering some of those critical questions. So far, the spin and parin spite of ity of the @+ have not been well-determined in experiment that the absence of signals in yp + @++K- favors @+ to be an isopsin singlet (see e.g. SAPHIR results). Meanwhile, a series of theoretical approaches have been proposed to understand the nature of the @+. Due t o the limited space here, we will concentrate on the theoretical study of the @+ photoproduction on the nucleon. A number of phenomenological approaches have been proposed in the literature focussing on cross section 415,
617,
63
64
predictions However, due to the lack of knowledge about the underlying reaction mechanism] such studies of the reaction cross sections are strongly model-dependent. For instance] the total width of @+ still has large uncertainties and could be much narrower 1 0 ~ 1 1 J 2 and , the role played by K * exchange, as well as other s and u-channel processes are unknown. Also, in a phenomenological approach the energy dependence of the couplings is generally introduced into the model via empirical form factors, which will bring further uncertainties. Taking this into account, there are advantages with polarization observables (e.g. ambiguities arising from the unknown form factors can be partially avoided). In association with the cross section studies, supplementary information about the @+ can be obtained 1 3 , 1 4 , 1 5 , 1 6 , 1 7
2. A minimum phenomenology
The following effective Lagrangians are assumed for the O N K couplings with the spin-parity 1 / 2 + and 1 / 2 - for the @+, respectively: Lep,(1/2+)
= ~ Q N K O ~ ~ Y t~ h.c., P K N
Leff(1/2-)
= geNKONK
+ h.c.,
(1)
where 0, N and K denote the field of @+, neutron and K - . The coupling constant g Q N K is determined by the experimental data for the decay width of @+ + N K , which however is still very imprecise. In this work, the same set of parameters as Refs. l 3 > l 4is adopted by assuming r @ + + N K E 10 MeV. In Ref. 1 8 , a narrower width of 1 MeV is adopted, based on analyses of N - K scattering data l o . The change of such an overall factor will not change the behavior of polarization asymmetries for exclusive Born terms. The magnetic moment of O+ is estimated based on the phenomenology of diquark model of Ref. 4 , which is consistent with other models in the literature 19,9. We also include the K * exchange in this model as the leading contribution in association with the Born terms. The K * N @interaction is given by
and
65
where & N K * and K; denote the vector and LLanomalous moment" couplings, respectively. w e follow Refs. l 3 ? l 4t o adopt the values for g Q N K * and K ; . It should be note that Ig@NK*I = lg@NKI and K ; = 0 are widely adopted in the literature. In Ref. 18, g&,,K* (1/2+) = 3 g g N K and K ; = o are adopted in the calculation of cross sections for 1/2+ pentaquarks with the consideration of the "fall-apart" mechanism The change of parameters for the K* exchange does not change the behavior of the BT asymmetries for y n -+ @+K- near threshold due to the importance of the Born terms. The effective Lagrangian for the K * K y vertex is given by 2oi12,21,22.
where V 6 denotes the K* field. The coupling gK*OKOy = 1.13 is determined by rK*o+Kor = 117 keV 2 3 . In the photoproduction reaction: defining the z-axis as the photon momentum direction, and the reaction plane in x-z in the c.m. system of y-n, the transition amplitude for yn + K-@+ can be expressed as ~x~ ,x,xN
(@+, Ae, Pe; K - ,
qlpln,A N , pi;7, A, k),
~ 0 ,
(5)
where A, = f l , AN f 1/2, Xo = 0, and As are helicities of photon, neutron, K - , and @+, respectively.
3. Double polarization asymmetries We are interested in a Beam-Target (BT) double polarization asymmetry measured in y n + @+K-. In this reaction the photons are circularly polarized along the photon moment direction i and the neutrons transversely polarized along the 2-axis within the reaction plane. In terms of the density matrix elements for the @+ decays, the BT asymmetry can be expressed as, BT
P 2l ' 12.
D,, = -,
P'i2 ' 1 2
where the subscript xz denotes the polarization direction of the the initial neutron target along x-axis in the production plane and the incident photon along the z-axis, and the definition of the density matrix element is
where, N =
4 ~ x s , x , , x N I T A ~ , xis,the A ~normalization ~~ factor.
66
As follows, we express the transition amplitudes in terms of the CGLN amplitudes 24. This is useful for our understanding the behavior of the BT asymmetry near threshold. For 1/2+, we have (0'7 AS, PO; K-7 Ao, ql?'ln, A N , pi;7,A-,, k) = (As1-J . €-,IAN)
,
(8)
with
. .
The coefficients f1,2,3,4 are functions of energies, momenta, and scattering angle 8c.m., and contain information on dynamics. They provide an alternative expression for the BT asymmetry:
Dxz = sin~c.m.Re{fif,' - f2f;
+ cos~c.m.(fif; - f2.f;)).
(10)
-
We are interested in the energy region near threshold, namely, with the overall c.m. energy W 2.1 GeV. This is the region that the wellestablished contact term (Kroll-Ruderman term) dominates over all the other processes, and is the main component of f 1 . The term of f2 will have contributions from the s- and u-channel, while the terms of f3 and f4 from the t- and u-channel. Near threshold, it shows that the t-channel amplitudes have the least suppressions from the propagator l / ( t - M & ) in comparison with the s- and u-channel. Also, the terms contributing to f4 will be further suppressed near threshold due to the small momentum lql in the final state. Considering the products of f coefficients in Eq. (lo), we find the dominant contributions are from: 2 2 2 (11) f1f; - e O g @ N K m F c ( k 4 1 4 ( k4 ) , where Fc(k,q ) and F,(lc, q ) are form factors for the contact and t-channel, and are treated the same in this approach. This kinematic analysis leads to the robust prediction of the behaviour of D,, near threshold to be dominated by
Dxz c sinBC.,.Re{f1f;}.
(12)
Since the CGLN coefficients only depend weakly on OC,,. (via the Mandelstam variables), the dominance of the above term implies a sin@,.,. behavior of D,,, and the sign of D,, is determined by the product. In Fig. 1, the numerical results for the BT asymmetry at W = 2.1 GeV are presented. The solid curve denote results in the Born limit, while the
67 dashed and dotted curves represent results for including the K* exchange. Although the sign change of the K* exchange results in a quite significant change to the asymmetry values, in all the cases, a clear sin8,.,. behaviour appears in the BT asymmetry. In particular, it is the contact and t-channel kaon exchange in f1 and f 3 that control the sign of f1 f:, and produce the positive BT asymmetry near threshold 14. Also, note that it is natural that structures deviating from sin8,,,, may arise at higher energies, since other mechanisms could become important, and f l and f 3 will no longer be the leading terms. Such a feature can be seen through the asymmetries for different K* exchange phases at W = 2.5 GeV, where the interference of the C O S ~ , . , . fi ( ~ ~- fif:) term in Eq. (10) shows up indeed. Similar analysis can be applied t o the production of 1/2-. In general, the transition amplitudes can be arranged in a way similar to the CGLN amplitudes for 1/2+:
where coefficients C 1 , 2 , 3 , 4 are functions of energies, momenta and scattering angle, and contain dynamical information on the transitions. Restricted to the kinematics near threshold, a term proportional to q . e y u . (k x q) in the u-channel is neglected in the above expression, but included in the calculation. Such a term is the same order of C4. However, they are both relatively suppressed in comparison with other terms due to the small lql near threshold. As follows, we neglect the term of q . E,U . (k x q) and express the above in parallel t o the CGLN amplitudes. Since ( E , x k) = iXYey,one can replace vector (q, x k) with ~ X , E ~and , rewite the operator as
which has exactly the same form as Eq. (9) apart from an overall phase factor from the photon polarization iX,. It also leads to the same form of the BT asymmetry as that for 1/2+:
68
Quite remarkably, the behaviour of D,, due to these two different parities now becomes more transparent since the role played by the dynamics has been isolated out. Nevertheless, it also results in vanishing asymmetries at ec.m.= 0" and 180".
(b) W=2.5 GeV
0.5
o -0.5
p
j
o m __. ................... 45
I
.. ..
............... -lo
50
lo
Figure 1 . B T asymmetry for O+ of 1/2+ at W = 2.1 and 2.5 GeV. The solid curves are results in the Born limit, while the dashed and dotted curves denote results with the K' exchange included with different phases: ( g O N X * , K;) = (-2.8,-3.71) (dashed curves in (a) and (b)), (+2.8,+3.71) (dotted curves in (a) and (b)), (-2.8, $3.71) (dashed curves in (c) and (d)), and ($2.8,-3.71) (dotted curves in (c) and (d)).
.
150
-lo
( c ) w=2.1 GeV
0.5
-0.5
1w
50
..
I
'
1w
1M
(d) W=2.5 GeV
,. .......................
.
........... .... 50
100
...,.. 150
-10
50
100
150
Figure 2. B T asymmetry for Q+ of 1/2at W = 2.1 and 2.5 GeV. The solid curves are results in the Born limit, while the dashed and dotted curves denote results with the K* exchange included with different phases: (g@NX*,K;) = (-0.61, -0.371) (dashed curves in (a) and (b)), ($0.61, +0.371) (dotted curves in (a) and (b)), (-0.61, $0,371) (dashed curves in (c) and (d)), and (+0.61, -0.371) (dotted curves in (c) and (d)).
The most important difference between the 1/2- and 1/2+ cases is that the role of C1 may not be as significant as f1 in the production of 1/2+ due t o the absence of the contact term in the production of 112- state. In the Born limit, the main contribution to C1, though dominant, comes from the s- and u-channel, which differs from the Kroll-Ruderman contribution to f1 in 1/2+ production. In Fig. 2, the BT asymmetries are calculated at W = 2.1 and 2.5 GeV in the Born limit and including the K* exchanges. Interestingly, a rough sin ec.m. behavior as the 1/2+ production still appears near threshold, but with different sign. A detailed analysis shows that near threshold, the term
69 of Cl C; is still the dominant one in the BT asymmetry. Here, the dominant contribution to CI is from the s-channel, while the dominant contribution t o C: is from the t-channel kaon exchange via the decomposition q . e7 = a . qa . e7 ia . (ey x k)q . k - iv .kq . (ey x k). Therefore, we have
+
which will be negative since K, = -1.91. In comparison with Eq. ( l l ) , it gives a dynamical reason for the sign difference between these two parities. Meanwhile, the dominance of ClC; only holds near threshold. With the increasing energy, other terms, e.g. C2Cq*,and other mechanisms, such as K' exchange, can easily compete against C1C3f and produce deviations from the sinB,.,. behavior as shown by the asymmetries at W = 2.5 GeV. 4. Discussions and summaries
In summary, we have analyzed the double polarization asymmetry, D,,, in yn + O+K-, and showed it to be a useful filter for determining the parity of O+, provided its spin-parity is either 1/2+ or 1/2-. Due to dynamical reasons, asymmetry D,, near threshold would exhibit a similar behaviour but opposite sign. The advantage of studying polarization observables is that uncertainties arising from the unknown form factors can be partially avoided in a phenomenology. Therefore, although better knowledge of the form factors will improve the quantitative predictions, it should not change the threshold behaviour of D,, dramatically. However, special caution should be given to the roles played by a possible spin-3/2 partner in the u-channel, as well as s-channel nucleon resonances. In particular, as studied by Dudek and Close 25, the spin-3/2 partner may have a mass close to the O+. Thus, a significant contribution from the spin-3/2 pentaquark state may be possible. Its impact on the BT asymmetry needs to be investigated. In brief, due to the lack of knowledge in this area, any results for the BT asymmetry would be extremely important for progress in gaining insights into the nature of pentaquark states and dynamics for their productions 26. Experimental facilities at Spring-8, JLab, ELSA, and ESRF should have access t o the BT asymmetry observable.
Acknowledgments The author thanks Jim Al-Khalili and Frank Close for collaborations on the relevant works. Useful discussions with Volker Burkert and Takashi Nakano
70
on experimental issues, and with Kim Maltman and Bingsong Zou on theoretical points are gratefully acknowledged. Financial supports of the U.K. EPSRC (Grant No. GR/R78633/01 and GR/M82141) are acknowledged. References 1. T. Nakano et al. [LEPS Collaboration], Phys. Rev. Lett. 91, 012002 (2003); V. Barmin et al. [DIANA Collaboration], Phys. Atom. Nucl. 66,1715 (2003); S. Stepanyan et al. [CLAS Collaboration], Phys. Rev. Lett. 91,252001 (2003); J. Barth et al. [SAPHIR Collaboration], Phys. Lett. B572, 127 (2003); V. Kubarovsky et al. [CLAS Collaboration], Phys. Rev. Lett. 92,032001 (2004)
[Erratum-ibid. 92,049902 (2004)l. 2. C. Alt et al., “A49 Collaboration], hep-ex/0310014. 3. D. Diakonov, V. Petrov, and M. Polyakov, 2. Phys. A359, 309 (1997). 4. See e.g. R. Jaffe and F. Wilczek, Phys. Rev. Lett. 91, 232003 (2003); M. Karliner and H. J. Lipkin, hep-ph/0307343, hep-ph/0307243. 5. F.E. Close, Conference summary talk at Hadron2003, hep-ph/0311087. 6. T. Nakano, Proceeding of this conference. 7. V. Burkert, Proceeding of this conference. 8. M.V. Polyakov and A. Rathke, hep-ph/0303138; T. Hyodo et al. nuclth/0307105; W. Liu and C.M. KO, Phys. Rev. C68, 045203 (2003); nuclph/0309023; Y . Oh et al., hep-ph/0310019; B.-G. Yu et al., nucl-th/0312075. 9. S.I. Nam et al., Phys. Lett. B579, 43 (2004). 10. R.L. Workman et al., nucl-th/0404061; R.A. Arndt et al., Phys. Rev. C68, 042201 (2003); nucl-th/0311030; Ya. I. Azimov et al., nucl-th/0307088. 11. S. Nussinov, hep-ph/0307357; R.W. Gothe and S. Nussinov, hep-ph/0308230; J. Haidenbauer and G. Krein, Phys. Rev. C68, 052201 (2003); M. Praszalowicz, Phys. Lett. B583, 96 (2004). 12. C.E. Carlson, C.D. Carone, H.J. Kwee, and V. Nazaryan, hep-ph/0312325. 13. Q. Zhao, Phys. Rev. D69, 053009(2004). 14. Q.Zhao and J.S. Al-Khalili, Phys. Lett. B585, 91 (2004). 15. K. Nakayama and K. Tsushima, hep-ph/0311112. 16. Y. Oh, H. Kim, and S.H. Lee, hep-ph/0312229. 17. M.P. Rekalo and E. Tomasi-Gustafsson, hep-ph/0401050. 18. F.E. Close and Q. Zhao, Phys. Lett. B590, 176 (2004). 19. Y.-R. Liu et al., hep-ph/0312074; P.-Z. Huang et al., hep-ph/0311108; R. Bijker et al., hep-ph/0312380, hep-ph/0403029; H. C. Kim and M. Praszalowicz, Phys. Lett. B585, 99 (2004). 20. B.K. Jennings and K. Maltman, hep-ph/0308286. 21. F. Buccella and P. Sorba, hep-ph/0401083. 22. F.E. Close and J.J. Dudek, Phys. Lett. B586, 75 (2004). 23. D. E. Groom et al. (Particle Data Group), E w . Phys. J . C15, 1 (2000). 24. G.F. Chew, M.L. Goldberger, F.E. Low, and Y. Nambu, Phys. Rev. 106, 1345 (1957). 25. J.J. Dudek and F.E. Close, Phys. Lett. B583, 278 (2004). 26. Q. Zhao and F.E. Close, hep-ph/0404075.
On the Determination of O+ Quantum Numbers and Other Topics of Exotic Baryons E. OSET", T . HYODOb, A. HOSAKAb, F.J. LLANES-ESTRADA", V. MATEU", S. SARKAR" AND M.J. VICENTE VACAS"
"Departamento de Fisica Tedrica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Institutos de Investigacidn de Paterna, Aptd. 22085, 46071 Valencia, Spain bResearch Center for Nuclear Physics (RCNP), Ibaraki, Osaka 567-0047, Japan "Deapartamento de Fisica Teorica I, Universidad Complutense, Madrid, Spain 1. Introduction
In this talk I look into three different topics, addressing first a method t o determine the quantum numbers of the O+, then exploiting the possibility that the O+ is a bound state of K T N and in the third place I present results on a new resonant exotic baryonic state which appears as dynamically generated by the Weinberg Tomozawa AK interaction. 2. Determining the O+ quantum numbers through the K + p -+ r + K + n
A recent experiment by LEPS collaboration at SPring-8/0saka has found a clear signal for an S = +1 positive charge resonance around 1540 MeV. The finding, also confirmed by DIANA at ITEP , CLAS at Jefferson Lab. and SAPHIR at ELSA and other more recent experiments, might correspond to the exotic state predicted by Diakonov et al. in Ref. 5 , but since then much theoretical work has been done to understand the nature of this resonance, see for a recent review of theoretical and experimental work done. Yet, the spin, parity and isospin are not determined experimentally. We present here one particularly suited reaction t o determine the quantum numbers with the process K + p + T+K+n .
71
(1)
72
Figure 1. Feynman diagrams of the reaction K + p
K+
K+
K+
7r+
K+
Kt
Kt
“\,#s.\ =-__ n
r+ Figure 2.
P
r + K + n in the model of Ref. 7.
r+
\
@+
P-
-+
\
K+
KQ , - r x \
@+
n
=--7r+
Feynman diagrams of the reaction K f p t 7r+K+n with the O+ resonance.
A successful model for the reaction (1) was considered in Ref.
consisting of the mechanisms depicted in terms of Feynman diagrams in Fig. 1. The term (a) (pion pole) and (b) (contact term), which are easily obtained from the chiral Lagrangians involving meson-meson and meson-baryon interaction are spin flip terms (proportional to a),while the p exchange term (diagram (c)) contains both a spin flip and a non spin flip part. Having an amplitude proportional to a is important in the present context in order to have a test of the parity of the resonance. Hence we choose a situation, with the final pion momentum p,+ small compared to the momentum of the initial kaon, such that the diagram (c), which contains the S . p,+ operator can be safely neglected. The terms of Fig. 1 (a) and (b) will provide the bulk for this reaction. If there is a resonant state for K+n then this will be seen in the final state interaction of this system. This means that in addition to the diagrams (a) and (b) of Fig. 1, we shall have those in Fig. 2. If the resonance is an s-wave K+n resonance then J p = 1/2-. If it is a pwave resonance, we can have J p = 1/2+, 312’. A straightforward 7,
73 evaluation of the meson pole and contact terms (see also Ref. the K+n -+ &KN amplitudes
-itz = (ai
+ b&zn
. q1+ Ci).
. kin
+ (-a2 - b&in
. q)
lo) leads
+ di)u .q/ ,
to
(2)
where i = 1 , 2 stands for the final state K+n, Kop respectively and kin and q' are the initial and final K+ momenta. The coefficients ai and bi are from meson exchange terms, and ci and di from contact terms. They are given in Ref. l l . When taking into account K N scattering through the O+ resonance, as depicted in Fig. 2, the K+p -+ n+K+n amplitude is given by
-
-
-
-it = -it1 - it1 - it2
(3)
where il and i& account for the scattering terms with intermediate K+n and K'p, respectively. They are given by
(4) for s- and pwave, and i = 1 , 2 for K+n and Kop respectively. The different magnitudes of Eqs. (4) are defined in 1 1 , but the only thing to recall here is the dependence on the momenta of the u . p terms. Invariant mass distributions and angular distributions are given in l l . Here we only want t o discuss the polarization obervables. Let us now see what can one learn with resorting to polarization measurements. Eqs. (4)account for the resonance contribution to the process. The interesting finding there is that if the O+ couples to K+n in s-wave (hence negative parity) the amplitude goes as u . kin, while if it couples in pwave it has a term u .q'. Hence, a possible polarization test to determine which one of the couplings the resonances chooses is to measure the cross section for initial proton polarization 112 in the direction z ( k i n ) and final neutron polarization -112 (the experiment can be equally done with Kop in the final state, which makes the nucleon detection easier). In this spin flip amplitude (-1/2Itl 1/2), the u . kin term vanishes. With this test the resonance signal disappears for the s-wave case, while the u . q/ operator of the pwave case would have a finite matrix element proportional t o q' sin 8. This means, away from the forward direction of the final kaon, the
+
74 I
on ) = 850 MeVlc
den
- I,J =1,1/2+ - - I,Jp=1,3/2'
01
1500
I
I
I
1520
1540
1560
1 30
MI Figure 3. The double differential cross sections of polarized amplitude with 8 = 90 for I = 0 , l and J p = 1/2-, 1/2+, 3/2+.
appearance of a resonant peak in the cross section would indicate a pwave coupling and hence a positive parity resonance. In Fig. 3 we show the results for the polarized cross section measured at 90 degrees as a function of the invariant mass. The two cases with s-wave do not show any resonant shape since only the background contributes. All the other cross sections are quite reduced to the point that the only sizeable resonant peak comes from the I , J p = 0,1/2+ case. A clear experimental signal of the resonance in this observable would unequivocally indicate the quantum numbers as I , J p = 0,1/2+. 3. Is the Of a K T N bound state?
At a time when many low energy baryonic resonances are being dynamically generated as meson baryon quasibound states within chiral unitary approaches it looks tempting t o investigate the possibility of this state being a quasibound state of a meson and a baryon or two mesons and a baryon. Its nature as a K N s-wave state is easily ruled out since the interaction is repulsive. K N in a p-wave, which is attractive, is too weak t o bind. The next logical possibility is t o consider a quasibound state of K T N , which in s-wave would naturally correspond t o spin-parity 1/2+, the quantum numbers suggested in 5 . Such an idea has already been put forward in l 8 where a study of the interaction of the three body system is 1211393,777,15
75
Figure 4. Diagrams considered in the K N interaction.
conducted in the context of chiral quark models, which suggests that it is not easy to bind the system although one cannot rule it out completely. A more detailed work is done in 1 9 , which we summarize here. Upon considering the possible structure of O+ we are guided by the experimental observation that the state is not produced in the K+p final state. This would rule out the possibility of the 0 state having isospin I=l. Then we accept the Of to be an 1=0 state. As we couple a pion and a kaon to the nucleon t o form such state, a consequence is that the K-ir substate must combine to I=1/2 and not I=3/2. This is also welcome dynamically since the s-wave KITinteraction in I=1/2 is attractive (in I=3/2 repulsive) 20. The attractive interaction in I=1/2 is very strong and gives rise to the dynamical generation of the scalar K resonance around 850 MeV and with a large width 20. One might next question that, with such a large width of the K , the O+ could not be so narrow as experimentally reported. However, this large K width is no problem since in our scenario it would arise from KIT decay, but now the KITN decay of the O+ is forbidden as the O+ mass is below the KITNthreshold. One might hesitate to call the possible theoretical O+ state a K N quasibound state because of the large gap of about 200 MeV to the nominal K N mass. The name though is not relevant here and we can opt by calling it simply a K I T N state, but the fact is that the KITsystem is strongly correlated even at these lower energies, and since this favours the binding of the K I T Nstate we take it into account. In order to determine the possible O+ state we search for poles of the KITN -+ K I T N scattering matrix. To such point we construct the series of diagrams of fig. 4. where we account explicitly for the KIT interactian by constructing correlated KITpairs and letting the intermediate KITand nucleon propagate. This requires a kernel for the two meson-nucleon interaction which we now address. We formulate the meson-baryon lagrangian in terms of the SU(3) matrices, B , F p , up and the implicit meson matrix
76
standard in ChPT L = a (Biy’”V,B)-Ml?Tr (BB)+@Tr
(Byl”y5{“,,B})+5FTr 1 ( B y y 5 [up,B ] )
(5) with the definitions in First t,here is a contact three body force simultaneously involving the pion, kaon and nucleon, which can be derived from the meson- baryon Lagrangian term containing the covariant derivative V,. Next we show that a nucleon, kaon and pion see an attractive interaction in an isospin zero state through this contact potential. By taking the isospin I=1/2 n states and combining them with the nucleon, also isospin l/2 , we generate I=O,1 states which diagonalize the scat,tering matrix associated t o tmB
The usual non-relativistic approximation fiypk,u = ko is applied. Since the K n N system is bound by about 30 MeV one can take for a first test k o , po as the masses of the K and n respectively and one sees that the interaction in the 1=0 channel is attractive, while in the 1=1 channel is repulsive. This would give chances to the nN t-matrix t o develop a pole in the bound region, but rules out the 1=1 state. The series of terms of Fig. 4 might lead to a bound state of nN which would not decay since the only intermediate channel is made out of K n N with mass above the available energy. The decay into K N observed experimentally can be taken into account by explicitly allowing for an intermediate state provided by diagrams including K n -+ K n with the n being absorbed by the nucleon in p-wave, which leads to K n N K N . This and other diagrams accounting for the interaction of the mesons with the other meson or the nucleon are taken into account in the calculations l’. What we find at the end is that, in spite of the attraction found, this interaction is not enough to bind the system, since we do not find a pole below the K n N t,hreshold. In order to quantify this second statement we increase artificially the potential tmB by adding to it a quantity which leads t o a pole around & = 1540 M e V with a width of around r = 40 M e V . This is accomplished by adding an attractive potential around five or six tirnes bigger than the existing one. This exercise gives a quantitative idea of how far one is from having a pole. We should however note that we have
77 not exhausted all possible sources of three body interaction since only those tied t o the Weinberg Tomozawa term have been considered. We think that some more work in this direction should be still encouraged and there are already some steps given in ” .
4. A resonant AK state as a dynamically generated exotic baryon Given the success of the chiral unitary approach in generating dynamically low energy resonances, one might wander if other resonances could not be produced with different building blocks than those used normally, the octets of stable baryons and the pseudoscalar mesons. In this sense, in 22 the interaction of the decuplet of 3/2+ with the octet of pseudoscalar mesons is shown t o lead t o many states that have been associated to experimentally well established resonances. The purpose of the present work is to show that this interaction leads also to a new state of positive strangeness, with I = 1 and J p = 3/2-, hence, an exotic baryon which qualifies as a pentaquark in the quark language, but which is more naturally described in terms of a resonant state of a A and a K. The lowest order chiral Lagrangian for the interaction of the baryon decuplet with the octet of pseudoscalar mesons is given by 23
L = iTp@Tp- mTTpTp
(7)
where T:bbcis the spin decuplet field and D v the covariant derivative given by in 2 3 . Let us recall the identification of the S U ( 3 ) component of T to the physical states : T1ll = A++, T 1 1 2 = L A + TlZ2= L A O TZ22= AA ’ f i l ~ 1 1 3= Lc*+ ~ 1 2 3= Lc*O ~ 2 2 3= 2 ~ ’~ -1 3 3- _1__.=*0 ~ 2 3 3= f i l a ] - fi1 E*- 77333 = (1aFor strangeness S = 1 and charge Q = 3 there is only one channel A++K+ which has I = 2. For S = 1 and Q = 2 there are two channels At+Ko and A+K+. From these one can extract the transition amplitudes for the I = 2 and I = 1 combinations and we find 24 3 1 V ( S = 1,I = 2) = -(kO+k’O); V ( S = 1 , I = 1) --(kOfk’O), (8) 4f 4f where k jk’) indicate the incoming (outgoing) meson momenta. These results indicate that the interaction in the I = 2 channel is repulsive while it is attractive in I = 1. This attractive potential and the physical situation
78 is very similar t o the, one of the K N system in I = 0, where the interaction is also attractive and leads to the generation of the A( 1405) resonance 12,13,3,7. The use of V as the kernel of the Bethe Salpeter equation 1 3 , or the N/D unitary approach of both lead to the scattering amplitude
t = (1 - VG)-lV
(9)
In eq. (9), V factorizes on shell 13,3 and G stands for the loop function of the meson and baryon propagators, the expressions for which are given in l 3 for a cut off regularization and in for dimensional regularization. Next we fix the scale of regularization by determining the cut off, qmax, in the loop function of the meson and baryon propagators in order to reproduce the resonances for other strangeness and isospin channels. They are one resonance in ( I ,S ) = (0,-3), another one in ( I ,S ) = (1/2, -2) and another one in ( I ,S ) = (1, -1). The last two appear in 22 around 1800 MeV and 1600 MeV and they are identified with the Z(1820) and C(1670). We obtain the same results as in 22 using a cut off qmax = 700 MeV. With this cut off we explore the analytical properties of the amplitude for S = 1, I = 1 in the first and second Riemann sheets. First we see that there is no pole in the first Riemann sheet. However, if we increase the cut off to 1.5 GeV we find a pole below threshold corresponding t o a AK bound state. But this cut off does not reproduce the position of the resonances discussed above. Next we explore the second Riemann sheet for which we take
where G is the meson baryon propagator and the variables on the right hand side of the equation are evaluated in the first (physical) Riemann sheet. In the above equation ~ C M M, and fi denote the CM momentum, the A mass and the CM energy respectively. We find a pole at fi = 1635 MeV in the second Riemann sheet. This should have some repercussion on the physical amplitude and indeed this is the case as we show below. The situation in the scattering matrix is revealed in figs. 5 and 6 which show the real and imaginary part of the K A amplitudes for the case of I = 1 and I = 2 respectively. Using the cut off discussed above we can observe the differences between I = 1 and I = 2. For the case of I = 2 the imaginary part follows the ordinary behaviour of the opening of a threshold, growing smoothly from threshold. The real part is also smooth, showing nevertheless the cusp at threshold. For the case of I = 1, instead, the strength of the imaginary part is stuck to threshold as a reminder of the
79
Figure 5.
Amplitudes for A K
, , , ,
-0.07
1400
1500
,
, , ,
-+ A K
,
,
for I = I
, , ,
:;,
,
,
1600
1700 1800 1900 C. M. Energy (MeV)
Figure 6. Amplitudes for A K
+AK
for I = 2
,
,
, ,
2000
, ,
j
2100
80
existing pole in the complex plane, growing very fast with energy close to threshold: The real part has also a pronounced cusp at threshold, which is also tied to the same singularity. We have also done a more realistic calculation taking into account the width of the A in the intermediate states. The results are also shown in figures 5 and 6 and we see that the peaks around threshold become smoother and some strength is moved to higher energies. Even then, the strength of the real and imaginary parts in the I = 1 are much larger than for I = 2. The modulus squared of the amplitudes shows some peak behavior around 1800 MeV in the case of I = 1, while it is small and has no structure in the case of I = 2. We propose the study of the following reactions: 1) p p + AA+K+, 2) p p + C-A ++K +, 3) p p + CoA++Ko. In the first case the A+Kf state produced has necessarily I = 1. In the second case the A++K+ state has I = 2. In the third case the A++Kostate has mostly an I = 1 component. The study of these reactions, particularly the invariant mass distribution of A K , and the comparison of the I = 1 and I = 2 cases would provide the information we are searching for. Indeed, the mass distribution is given by
where PCM is the K momentum in the A K rest frame. The mass distribution removing the ~ C M factor in eq. (11) should show the broad peak of I ~ A K + A K ~ ~ seen in fig. 5. Similarly, the ratio of mass distributions in the cases 3) to 2) or 1) to 2), discussed before, should show this behaviour. Given the success of the chiral unitary approach providing dynamically generated resonances in the interaction of the octet of 1/2+ baryons with the octet of pseudoscalar mesons, as well as in the scalar sector of the meson meson interaction 2 5 , the predictions made here stand on firm ground. The experimental confirmation of the results found here would give evidence for another pentaquark state which, however, stands for a simple description as a resonant A K state.
5. Acknowledgments This work is partly supported by DGICYT contract number BFM200300856, the E.U. EURIDICE network contract no. HPRN-CT-2002-00311 and the Research Cooperation program of the japanese JSPS and the spanish CSIC.
81
References 1. T. Nakano et al. [LEPS Collaboration], Phys. Rev. Lett. 9 1 (2003) 012002. 2. V. V. Barmin et al. [DIANA Collaboration], Phys. Atom. Nucl. 66 (2003) 1715. 3. S. Stepanyan et al. [CLAS Collaboration], Phys. Rev. Lett. 9 1 (2003) 252001. 4. J. Barth et al. [SAPHIR Collaboration], arXiv:hep-ex/0307083. 5. D. Diakonov, V. Petrov and M.V. Polyakov, Z. Phys. A359 (1997) 305. 6. R. Bijker, M. M. Giannini and E. Santopinto, arXiv:hep-ph/0403029. 7. E. Oset and M.J. Vicente Vacas, Phys. Lett. B386 (1996) 39. 8. J. Gasser and H. Leutwyler, Nucl. Phys. B250 (1985) 465. 9. V. Bernard, N. Kaiser and U.G. Meissner, Int. J. Mod. Phys. E4 (1995) 193. 10. U.G. Meissner, E. Oset and A. Pich, Phys. Lett. B353 (1995) 161. 11. T. Hyodo, A. Hosaka and E. Oset, Phys. Lett. B 579 (2004) 290 [arXiv:nuclth/0307105]. 12. N. Kaiser, P. B. Siege1 and W. Weise, Nucl. Phys. A 594 (1995) 325 [nuclth/9505043]. 13. E. Oset and A. Ramos, Nucl. Phys. A 635 (1998) 99 [nucl-th/9711022]. 14. J. A. Oller and U. G. Meissner, Phys. Lett. B 500 (2001) 263 [hepph/0011146]. 15. C. Garcia-Recio, J. Nieves, E. Ruiz Arriola and M. J. Vicente Vacas, Phys. Rev. D 67 (2003) 076009 [hep-ph/0210311]. 16. D. Jido, J. A. Oller, E. Oset, A. Ramos and U. G. Meissner, Nucl. Phys. A 725 (2003) 181. 17. J. Nieves and E. Ruiz Arriola, Phys. Rev. D 64 (2001) 116008 [arXiv:hepph/0104307]. 18. P. Bicudo and G. M. Marques, Phys. Rev. D 69 (2004) 011503 [arXiv:hepph/0308073]. 19. F. J. Llanes-Estrada, E. Oset and V. Mateu, Phys. Rev. C in print. arXiv:nucl-th/0311020. 20. J. A. Oller, E. Oset and J. R. Pelaez, Phys. Rev. D 59 (1999) 074001 [Erratum-ibid. D 60 (1999) 0999061. 21. T. Kishimoto and T. Sato, arXiv:hep-ex/0312003. 22. E. E. Kolomeitsev and M. F. M. Lutz, Phys. Lett. B 585, 243 (2004). 23. E. Jenkins and A. V. Manohar, Phys. Lett. B 259 (1991) 353. 24. S. Sarkar, E. Oset and M. J. Vicente Vacas, arXiv:nucl-th/0404023. 25. J. A. Oller, E. Oset and A. Ramos, Prog. Part. Nucl. Phys. 45 (2000) 157.
Mass Spectrum and Magnetic Moments of Pentaquark States” R. BIJKER Universidad Nacional Autdnoma de Mixico, A.P. ro-543, 04510 ivixic0, D.F., ~ i x i c o . E-mail:
[email protected]
M.M. GIANNINI and ESANTOPINTO Dipartamento d i Fisica dell’Universitci di Genova, I.N.F.N., Sezione di Genova, via Dodecaneso 33, 16164 Genova, Italy. E-mail:
[email protected] We discuss the spectroscopy of pentaquarks using a Giirsey-Radicati type mass formula, whose coefficients have been determined previously in a study of qqq baryons. The ground state pentaquark, which is identified with the recently observed 0+(1540) state, is predicted to be an isosinglet anti-decuplet state. Its angular momentum and parity depend on the interplay between the spin-flavour and orbital contributions to the mass operator. We present a general classification scheme for qqqqQ pentaquark states in terms of spin-flavour S U ( 6 ) representations and their decomposition in terms of S U f ( 3 ) @ SU,(2) . Particular attenction is payed to the S4 permutational symmetry of the spin-flavour part of the four-quark wave functions. This classification is general and useful both for experimentalists and model builders. Finally we discuss the magnetic moment of the 0+(1540) in constituent quark model for different values of angular momentum and parity.
1. Introduction
The discovery of the 0+(1540) resonance with positive strangeness S = +1 by the LEPS Collaboration and the subsequent confirmation by various other experimental collaborations has motivated an enormous amount of experimental and theoretical studies of exotic baryons 3 . Since there are no three-quark configurations with these quantum numbers, it is an exotic baryon resonance, whose simplest configuration is that of a uuddg. Its quantum numbers are still mostly unknown, although the absence of a signal for a O++ pentaquark state in the p K + invariant mass spectrum is an aThis work is supported by a grant from Conacyt,Mbxico and I.N.F.N., Italy.
82
83 indication that the observed O+ is most likely t o be an isosinglet I = 0. The width of the O+ is so small that only an upper limit could be established (< 20 MeV or perhaps as small as a few MeV’s 4 ) . More recently, evidence has been found for the existence of another exotic baryon ETb(1862) with strangeness S = -2 by the NA49 Collaboration a t CERN 5 . The O+ and E ; , ; are usually interpreted as members of a flavor antidecuplet with isospin I = 0 and I = 312, respectively and with quark structure uuddS and ddssii. In addition, there is now the first evidence for a heavy pentaquark Oz(3099) in which the antistrange quark in the O+ is replaced by the anticharm quark. The spin and parity of these states have not yet been determined experimentally. For a review of the experimental status we refer to Theoretical interpretations range from chiral soliton models which provided the motivation for the experimental searches, cluster models and various constituent quark models 1 2 . A review of pentaquark models can be found in 1 4 . 9~10911
2. Classification of pentaquark states We consider pentaquark states to be built of the five light ( u,d,s) contituent quarks: the pentaquark wave functions contain contributions connected to the spatial degrees of freedom and the internal degrees of freedom (colour, flavour and spin). In the construction of the classification scheme one is guided by two conditions: the pentaquark wave function should be a colour singlet and it should be antisymmetric under any permutation of the four quarks l 3 The permutation symmetry of the four quark system is given by S, which is isomorphic to the tetrahedral group T d . The labels of the latter group are used t o classify the four quark states by their permutation symmetry character: symmetric A l , antisymmetric A2 or mixed symmetric E , F2 or F1. The corresponding algebraic structure for the internal degrees of freedom is SUsf(6) @ SUc(3). The complete spin-flavour SU(6) classification of q4q states and their full decomposition into spin and flavour states
can be found in Ref. 1 3 . In particular we use the permutational symmetry of the four quark part of the spin-flavour states to classify the pentaquark states 1 3 . The spin-flavour part has to be combined with the colour part and the orbital (or radial) part in such a way that the total pentaquark wave
a4
function is a colour-singlet state, and that the four quarks obey the Pauli principle, i.e. are antisymmetric under any permutation of the four quarks. Since the colour part of the pentaquark wave function is a [222]1 singlet and that of the antiquark a [11]3 anti-triplet, the colour wave function of the four-quark configuration is a [211]3 triplet with F1 symmetry under Td. The total q4 wave function is antisymmetric (A2), hence the orbital-spinflavour part is a [31] state with F 2 symmetry which is obtained from the colour part by interchanging rows and columns
The symmetry properties of the orbital part of the pentaquark wave function should also be discussed. If the four quarks are in a spatially symmetric S-wave ground state with A1 symmetry, the only allowed SUsf(6) representation is [31] with F 2 symmetry. According to Table 6 of Ref. 1 3 , the only pentaquark configuration with F2 symmetry that contains exotic states is [4211111134. On the other hand, if the four quarks are in a P-wave state with F 2 symmetry, there are several allowed SUsf(6)representations: [4], [31], [22] and [211] with Al, F2, E and Fl symmetry, respectively. The corresponding pentaquark configurations that contain exotic states are [51111]~00,[42111]1134,1331111560 and [32211]540, respectively. For each symmetry type of the orbital wave function, the corresponding symmetry of the spin-flavour wave function, as well as the associated pentaquark configurations that contain exotic states, are presented in Table 8 of Ref. 1 3 . The explicit construction of the S4 invariant orbital-spin-flavour pentaquark wave functions will be given in a separate publication 1 5 . In Table 7 of Ref. l 3 a complete list of exotic pentaquark states is given: for each isospin multiplet the states whose combination of hypercharge Y and charge Q cannot be obtained with three-quark configurations are identified. The const,ructed basis for pentaquark states makes it possible to solve the eigenvalue problem for a definite dynamical model and this is valid not only for Constituent Quark Models, but also for diquark-diquark-antiquark approaches, for which the basis is a subset of the one we have constructed. This classification scheme is complete and general, the precise ordering of the pentaquark states in the mass spectrum depends on the choice of a specific dynamical model.
85 3. A Gursey-Radicati mass formula
In order t o study, in a simple way the general structure of the spectrum of exotic pentaquarks, one can consider
M = Mo +Morb + & f .
(2)
MOis a constant. Mort,describes the contribution to the pentaquark mass due t o the space degrees of freedom of the constituent quarks. The last term Msf contains the spin-flavour dependence and it is assummed to have a generalized Giirsey-Radicati form
The first two terms represent the quadratic Casimir operators of the SUsf(6) and the SUf(3) groups, and s, Y and I denote the spin, hypercharge and isospin, respectively. The last two terms in Eq. (3) correspond to the GellMann-Okubo mass formula that describes the splitting within a flavour multiplet 16. It was extended by Giirsey and Radicati l7 to include the terms proportional to B and C that depend on the flavour and the spin representations, which in turn was generalized further to include the spinflavour term proportional to A 1 8 . Effective spin-flavour interactions have been used which schematically represents the Goldstone Boson Exchange (GBE) interaction between constituent quarks In addition, an analysis of the strange and non-strange qqq baryon resonances in the collective stringlike model l8 and the hypercentral CQM " has showed the need of flavour dependent interaction terms. Neglecting their radial dependence, the matrix elements of these interactions depend on the Casimirs of the SUsf(6),the SUf(3) and the SUs(2) groups ' O '9720.
where n is the number of quarks. The contribution of Eq. (4) to the splittings within a given multiplet has the same structure than the Giirsey-Radicati formula of Eq. (3), apart from the Gell-Mann-Okubo term, since the constant with the number of quarks cancels out when evaluating energy differences: the dependence on the different quark numbers is taken into account automatically by the fact that the eigenvalues of the Casimirs for the qqq or qqqqq states can be very different.
86
The coefficients of the GR applied to the qqqqij system should be obtained from a fit of the pentaquark spectrum, but since at the moment we know at most two pentaquark states and assuming that the coefficients do not depend strongly on the structure of the quark system, we give an evaluation of the pentaquark spectrum using the coefficients taken from a prior study of qqq baryons 22. The average energy of any SUsf(6)multiplet depends on the orbital part Morb and on the term linear in the SUsf(6) Casimir, while the terms proportional to B , C , D and E give the splittings inside the SUsf(6)multiplet. We use the Giirsey-Radicati formula of Eq. 3 ( that is without the A CzSu(6)term nor the Morb ) for the calculation of the energy splittings inside SUsf(6)multiplets of the exotic pentaquark states, using the constant Mo in order to normalize the energy scale t o the observed mass of the O+ and the results are given in Table 10 of Ref. 1 3 . The lowest pentaquark is always an '10 anti-decuplet state with isospin I = 0, in agreement with experimental evidence that the 0+(1540) is an isosinglet. For all spin-flavour configurations, there are other lowlying excited pentaquark states belonging to the 27-plet at 1660 MeV and 1775 MeV. The anti-decuplet state with strangeness S = -2 (Y = -1) and isospin I = 3/2 is at 2305 MeV, t o be compared with the recently observed resonance at 1862 MeV 5 , possible candidate for the Z3/2 exotic with charge Q = -2. The degeneracy of the multiplets in Table 10 of Ref. l 3 can be eliminated if one considers the contributions coming from the term A C2su(6) and from the space term Morb but for a consistent treatment of the latter, one needs a specific model, so we have concentrated our attention only on the effects of the term linear in A in Eq. (3). In Table 11 of Ref. l 3 there are the results coming from the generalized GR, Eq. 3, for the energies of all exotic pentaquark states for the four allowed SUsf(6) spin-flavour multiplets. The effect of the spin-flavour A c Z S u ( 6 ) term shifts the different SUsf(6)multiplets with respect to one another, without changing their internal structure. Irrespective of the orbital contribution to the mass that then can be added, the ground state pentaquark is an anti-decuplet flavour state with spin s = 1/2 and isospin I = 0. The treatment of the orbital part is very much dependent on the choice of a specific dynamical model. We have considered only a simple model in which the orbital motion of the pentaquark is limited to excitations up to N = 1 quantum, so that the model space consists of five states: an S-wave state with LP = O+ and A1 symmetry for the four quarks and four excited P-wave states with LP = 1-, three of which correspond to
87 excitations in the relative coordinates of the four-quark subsystem and the fourth to an excitation in the relative coordinate between the four-quark subsystem and the antiquark. The states in this simple model for the orbital motion are characterized by angular momentum L , parity p and Td symmetry t ( Lr = O i l , 1F, and lAl) and the total angular momentum of the pentaquark state is given by J'= L' 2,whereas the parity is opposite to that of the orbital excitation due t o the negative intrinsic parity of the q4q configuration. The angular momentum and parity of the ground state exotic pentaquark depends on the relative contribution of the orbital and spin-flavour parts of the mass operator: if the splitting due to the SUsf(6) spin-flavour term is large compared to that between the orbital states, the ground state pentaquark has positive parity, whereas for a relatively small spin-flavour splitting the parity of the lowest pentaquark state becomes negative. In case of a positive parity ground state, there is a doublet with JP = 1/2+, 3/2+ which, in the presence of a spin-orbit coupling term 13,23, would give rise t o a pair of peaks. The effect of specific dynamical models on the pentaquark spectrum in general, and on the properties of its ground state in particular, using a space dependent S U ( 6 ) breaking interaction, will be presented in more detail in a separate publication 24.
+
4. Magnetic moments Another unknown quantity is the magnetic moment. Although it may be difficult to determine its value experimentally, it is an essential ingredient in calculations of the photoproduction cross sections 2 5 , 2 6 , 2 7 . In the absence of experimental information, one has t o rely on model calculations. In Ref. 28 have analyzed the pentaquark magnetic moments of the lowest flavor antidecuplet for both positive and negative parity in the constituent quark model. The magnetic moments were obtained in closed analytic form, hence it was possible to derive generalized Coleman-Glashow sum rules for the antidecuplet magnetic moments and sum rules connecting the magnetic moments of antidecuplet pentaquarks t o those of decuplet and octet baryons. The magnetic moments for negative parity J P = 1/2pentaquarks are an order of magnitude smaller than the proton magnetic moment, whereas for positive parity JP = 1/2+ they are even smaller for a cancellation between orbital and spin contributions and in partucular the magnetic moment of the O(1540) is found t o be 0.38, 0.09 and 1.05 p~ for J P = 1/2-, 1/2+ and 3/2+, respectively. The numerical values are
88 in qualitative agreement with those obtained in other approaches, such as correlated quark models, QCD s u m rules, MIT bag model and t h e chiral soliton model 29. In conclusion, t h e spectroscopy of exotic baryons will be a key testing ground for models of baryons a n d their structure a n d in particular the measurement of the angular momentum a n d parity of the 0+(1540) may help to distinguish between different models.
References 1. LEPS Collaboration, T. Nakano et al., Phys. Rev. Lett. 91 (2003) 012002. 2. DIANA Collaboration, V.V. Barmin et al., Phys. Atom. Nucl. 66 (2003) 1715; SAPHIR Collaboration, J. Barth et al., Phys. Lett. B 572 (2003) 127; CLAS Collaboration,S. Stepanyan et al., Phys. Rev. Lett. 91 (2003) 252001; V. Kubarovsky et al., Phys. Rev. Lett. 92 (2004) 032001; A.E. Asratyan, A.G. Dolgolenko and M.A. Kubantsev, Phys. At. Nuc1.67 (2004) 682; HERMES Collaboration, A. Airapetian et al., Phys.Lett. B 585 (2004) 213; SVD Collaboration, A. Aleev et al., hep-ex/0401024; ZEUS Collaboration, S. Chekanov at al., Phys. Lett. B 591 (2004) 7; COSY-TOF Collaboration, M. Abdel-Bary et al., hep-ex/0403011. 3. http://www.jlab.org/intralab/calendar/archive03/pentaquark/program.html 4. R.A. Arndt, 1.1. Strakovsky and R.L. Workman, Phys. Rev. C 68, 042201 (2003); Phys. Rev. C 6 8 , 042201 (2003); S. Nussinov, hep-ph/0307357; J. Haidenbauer and G. Krein, hep-ph/0309243; R.N. Cahn and G.H. Trilling, Phys. Rev. D 69 (2004) 011501. 5. NA49 Collaboration, C. Alt et al., Phys. Rev. Lett. 92 (2004) 042003. 6. H1 Collaboration, A. Aktas et al., Phys. Lett. B588 (2004) 17. 7. Q. Zhao and F.E. Close, hep-ph/0404075; M.Karliner and H.J. Lipkin, hepph/0405002. 8. D. Diakonov, V. Petrov and M. Polyakov, Z. Phys. A 359 (1997) 305; H. Weigel, Eur. Phys. J. A 2 (1998) 391; M. Praszalowicz, in Skyrmions and Anomalies, Eds. M. Jezabek and M. Praszalowicz, (World Scientific; Singapore, 1987); M. Praszalowicz, Phys. Lett. B 575 (2003) 234. 9. R. JafTe and F. Wilczek, Phys. Rev. Lett. 91 (2203) 232003. 10. E. Shuryak and I. Zahed, Phys. Lett. B 589 (2004) 21. 11. M. Karliner and H.J. Lipkin, Phys. Lett. B 575 (2003) 249. 12. F1. Stancu, Phys. Rev. D 58 (1998) 111501; C. Helminen and D.O. Riska, Nucl. Phys. A 699 (2002) 624; A. Hosaka, Phys. Lett. B 571 (2003) 55; L.Ya. Glozman, Phys. Lett. B 575 (20003) 18; F1. Stancu and D.O. Riska, Phys. Lett. B 575 (2003) 242; C.E. Carlson, Ch.D. Carone, H.J. Kwee and V. Nazaryan, Phys. Lett. B 579 (2004) 52. 13. R. Bijker, M.M. Giannini and E. Santopinto, preprint hep-ph/0310281, EPJA, in press. 14. B. Jennings and K. Maltman, Phys. Rev. D 69 (2004) 094020. 15. R. Bijker, M.M. Giannini and E. Santopinto, to be published.
89 16. See e.g. M. Gell-Mann and Y. Ne’eman, The eightfold way (W.A. Benjamin, Inc., New York, 1964). 17. F. Giirsey and L.A. Radicati , Phys. Rev. Lett. 13 (1964) 173. 18. R. Bijker, F. Iachello and A. Leviatan, Ann. Phys. (N.Y.) 236 (1994) 69; R. Bijker, F. Iachello and A. Leviatan, Ann. Phys. (N.Y.) 284 (2000) 89. 19. L.Ya. Glozman and D.O. Riska, Phys. Rep. 268 (1996) 263; F1. Stancu, Phys. Rev. D 58 (1998) 111501; L.Ya. Glozman, Phys. Lett. B 575 (2003) 18. 20. C. Helminen and D.O. Riska, Nucl. Phys. A 699,624 (2002). 21. M. M. Giannini, E. Santopinto and A. Vassallo, Eur. Phys. J. A 12 (2001) 447; E. Santopinto, F. Iachello and M.M. Giannini, Eur. Phys. J. A 1 (1998) 307. 22. M. M. Giannini, E. Santopinto and A. Vassallo, to be published. 23. J.J. Dudek and F.E. Close, Phys. Lett. B 583 (2004) 278. 24. R. Bijker, M. M. Giannini, E. Santopinto, to be published. 25. S.I. Nam, A. Hosaka and H.-Ch. Kim, Phys. Lett. B 579 (2004) 43. 26. Q. Zhao, Phys. Rev. D 69 (2004) 053009. 27. K. Nakayama and K. Tsushima, Phys. Lett. B 583 (2004) 269. 28. R. Bijker, M.M. Giannini and E. Santopinto, hep-ph/0403029, Phys. Lett. B, in press; R. Bijker, M.M. Giannini and E. Santopinto, hep-ph/03123807 Revista Mexicana de Fisica, in press. 29. H.-C. Kim and M. Praszalowicz, Phys. Lett. B 585,99 (2004); P.-Z. Huang, W.-Z. Deng, X.-L. Chen and S.-L. Zhu, hep-ph/0311108; Y.-R. Liu, P.-Z. Huang, W.-Z. Deng, X.-L. Chen and S.-L. Zhu, Phys. Rev. C 69, 035205 (2004); W.-W. Li, Y.-R. Liu, P.-Z. Huang, W.-Z. Deng, X.-L. Chen and S.-L. Zhu, hep-ph/0312362.
Pentaquark Spectra in the Diquark Picture CLAUDE SEMAY" Service de Physique Ge'nirale et de Physique des Particules Ele'mentaires, Groupe de Physique Nucle'aire The'orique, Universite' de Mons-Hainaut, Place du Parc 20, B-7000 Mons, Belgium E-mail:
[email protected] BERNARD SILVESTRE-BRAC Laboratoire de Physique Subatomique et de Cosmologie, Avenue des Martyrs 53, F-38026 Grenoble-Cedex, France E-mail:
[email protected] ILYA M. NARODETSKII Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya 25, RUS-117218 Moscow, Russia E-mail: naro @heron.itep.ru The masses of uuddd, uuddS and uussd pentaquarks are calculated in the framework of a semirelativistic effective QCD Hamiltonian, but with all auxiliary fields eliminated. The use of a diquark picture allows a correct treatment of the confinement, supposed here t o be a Y-junction. With diquark masses fitted on the baryon spectra, ground state pentaquarks are found around 2 GeV.
Recent experiments have reported the existence of a very narrow peak in K + n and Kop invariant mass distributions at 1.540 GeVZ3, which is interpreted as a uuddS pentaquark'. Quantum numbers are not known yet but a J p = 1/2+ assignment is preferred. Models using the diquark approximation have been proposed to explain the properties of this state. In the paper by Jaffe3, a good value is obtained for the mass, but the model does not take into account the full confinement dynamics. In the paper by Narodetskii4, the confinement is correctly taken into account, but the formalism used is not free from auxiliary fields (see below) and the diquark aFNRS Research Associate
90
91 [ud] is taken arbitrarily massless. Our purpose here is t o improve this last study. The dominant interaction in a pentaquark is certainly the confinement. As this multiquark is a complicated five-body system, we will assume that it can be reduced to a three-body system, for which a realistic confinement potential can be built. We will assume, as in the work of Jaffe and Wilczek3, that quarks can form diquark clusters inside the pentaquark. All short-range interactions available between quarks (one-gluon exchange5, Goldstone-boson exchange6 and instanton induced7 interactions) predict that the most probable diquark which can be formed is the [ud] pair in colour 3 representation with vanishing spin and isospin. In this case, the pentaquark considered here can be viewed as a antibaryon-like system DDq, where D = [ud], and the confinement can be simulated by a Y-junction 3
where a is the string tension. In this work we will use a very good approximation of this potential, free from three-body complications’
where
in which F‘CM is the centre of mass coordinate. We use an effective QCD Hamiltoniang, but with all its auxiliary fields eliminatedlO
where (YS is the strong coupling constant. The particle self-energy is also taken into account and appears as a contribution depending on the statedependent “constituent” particle mass & )(-
where C(S’i,mi, a, S) is a negative contribution for a fermion and vanishes for a bosong. The inverse gluonic correlation length 6 is around 1 GeV.
92
The mass of the diquark D will be fitted on baryon spectra, considered here as Dq systems. The equivalent two-body energy operator is given by
To consider the nucleon as a pure D n state ( n stands for u or d ) or the A baryon as a pure Ds state is probably not a very good approximation". But our aim is just to obtain a reasonable estimation for the mass of the [ud] diquark. Since the two diquarks are spin singlets, one-gluon exchange and Goldstone boson exchange potentials predict no interaction between the two diquarks, and no interaction between each diquark and the quark. So we can use the Hamiltonians described above without adding any supplementary spin interactions. The possible contributions of instanton induced forces are described elsewhere''. Table 1. Experimental masses for three well-known baryons and two pentaquark candidates.
N = 0.939 GeV
A = 1.116 GeV Z = 1.318 GeV DDS [1/2+] = 1.540 GeV
D,,D,,G
[1/2+] = 1.860 GeV
Some results are presented in Tables 2-6 and compared with experimental data (see Table 1). They are always obtained with a vanishing mass for the n quark and a value of 6 = 1 GeV. We have checked that pentaquark masses are not very sensitive to variations of these parameters. In Table 2, the values chosen for a and as are taken from a previous work about pentaquarks4 and have been used for studies of baryon spectra. The D mass is fitted to the N mass, and the s mass is then fitted to the A mass. This baryon mass is also used to determine the D,, mass. A test of coherence is then performed with the Z mass. Results from Tables 3 and 5 are obtained with a variation of the value of as or a. Results from Table 5 are obtained with the mass of the s quark fixed a t
93 Table 2. Masses of some baryons and pentaquarks in the diquark approximation. The symbol of a particle represents its mass. A quark mass or a diquark mass in a box is fitted from baryon spectra. a = 0.15 GeV2
s = 0.260 GeV
CYS= 0.39
D = 0.350 GeV
n=O
I
D,,
= 0.560 GeV]
N ( D n ) = 0.943 GeV
DDii [1/2+]= 2.242 GeV
A ( D s ) = 1.117 GeV
DDS [1/2+]= 2.368 GeV
A ( D n s n ) = 1.114 GeV
DnsDnsii [1/2+]= 2.525 GeV
Z (Dnss)= 1.277 GeV
Table 3. Same as in Table 2 but for other values of the parameters.
as = 0.50
D = 0.415 GeV
n=O
1 Dns = 0.630 GTV I
N (Dn)= 0.940 GeV
D D A [1/2+]= 2.261 GeV
A (Ds)= 1.117 GeV
DDS [1/2+]= 2.404 GeV
A ( D n s n ) = 1.116 GeV
DnsDnsA [1/2+]= 2.563 GeV
Z (Dnss)= 1.283 GeV
Table 4. Same as in Table 2 but for other values of the parameters.
(YS
= 0.39
n=O
D = 0.285 GeV Dns = 0.515
GeV
the value given by the Particle Data Group1*. Calculations from Table 6 are performed with the D mass arbitrarily fixed at 0, in order to minimize the pentaquark masses. In these cases, the N and E masses are badly reproduced. Whatever the value taken for the diquark masses, the resulting pen-
94 Table 5. Same as in Table 2 but for other values of the parameters.
a = 0.15 GeV2
s
as = 0.39 n=O
= 0.170 GeV
D = 0.455 GeV1 1
D,, = 0.565 GeV
I
I
N ( o n ) =1.026 GeV
DDfi [1/2+]= 2.377 GeV
A ( D s ) = 1.116 GeV
DDS [1/2+]= 2.435 GeV
A ( D n s n ) = 1.118 GeV
Dn,Dnsii [1/2+]= 2.533 GeV
Z (Dnss)= 1.205 GeV Table 6. Same as in Table 2 but for other values of the parameters.
a = 0.15 GeV2 CIS
= 0.39
n=O
N
(on)=0.769 GeV
1 s = 0.415
GeV
I
D=O D,,
= 0.560 GeV
DDfi [1/2+]= 1.934 GeV
A (Ds)= 1.116 GeV
DDS [1/2+]= 2.289 GeV
A (Dnsn)= 1.114 GeV
D,,D,,fi
[1/2+]= 2.526 GeV
Z (Dnss)= 1.418 GeV
taquark masses are found around or above 2 GeV, as far as a realistic confinement is considered. Therefore, we are forced to conclude that the relevance of the diquark picture for pentaquark systems is highly questionable. This work was supported by the agreement CNRS/CGRI-FNRS. References See for instance: T. Nakano et al., Phys. Rev. Lett. 91,012002 (2003). D. Diakonov, V. Petrov, and M.V. Polyakov, Z. Phys. A 359,305 (1997). R.L. JafFe and F. Wilczek, Phys. Rev. Lett. 91,232003 (2003). I.M. Narodetskii et al., Phys. Lett. B 578,318 (2004). S. Fleck, B. Silvestre-Brac, and J.M. Richard, Phys. Rev. D 38,1519 (1988). L.Ya. Glozman et al., Phys. Rev. C 57,3406 (1998). 7. W. Blask et al., Z. Phys. A 337,327 (1990). 8. B. Silvestre-Brac, C. Semay, I.M. Narodetskii, and A.I. Veselov, Eur. Phys. J. C 32,385 (2004). 9. I.M. Narodetskii, Yu.A. Simonov, M.A. Trusov, and A.I. Veselov, Phys. Lett. B 578,318 (2004). 10. C. Semay, B. Silvestre-Brac, and I.M. Narodetskii, Phys. Rev. D 69,014003 1. 2. 3. 4. 5. 6.
95 (2004). 11. D.B. Lichtenberg, W. Namgung, J.G. Wills, and E. Predazzi, Z. Phys. C 19, 19 (1983). 12. C.Semay and B. Silvestre-Brac, 112' uuddB pentaquark and instanton induced forces, submitted to Eur. Phys. J. A. 13. K.Hagiwara et d., Phys. Rev. D 66,010001 (2002).
Pent aquarks and Radially Excited Baryonsa H. WEIGEL Fachbereich Physik, Siegen University Walter-Flex-Stra$e 3, D-57068 Siegen, Germany In this talk I report on a computation of the spectra of exotic pentaquarks and radial excitations of the low-lying' f and $' baryons in a chiral soliton model.
1. Introduction Although chiral soliton model predictions for the mass of the lightest exotic pentaquark, the @+ with zero isospin and unit strangeness, have been around for some time', the study of pentaquarks as baryon resonances became popular only recently when e ~ p e r i m e n t s indicated ~.~ their existence. These experiments were stimulated by a chiral soliton model estimate4 suggesting that such exotic baryons might have a widthb so mall^,^ that it could have escaped earlier detection. Then very quickly the novel observations initiated exhaustive studies on the properties of pentaquarks. Comprehensive lists of such studies are, for example, collected in ref~.~>'O. In chiral soliton models states with baryon quantum numbers are generated from the soliton by canonically quantizing the collective coordinates associated with (would-be) zero modes such as S U ( 3 ) flavor rotations. The lowest states are members of the flavor octet (J" = f ') and decuplet representations (J" = $+). Due to flavor symmetry breaking the physical states acquire admixtures from higher dimensional representations. For the J" = $+ baryons those admixtures originate dominantly from the antidecuplet, 10,and the 27-plet'l. The particle content of these representations is depicted in figure 1. They also contain states with quantum numbers that cannot be built as three-quark composites but contain additional quarkantiquark pairs. Hence the notion of exotic pentaquarks. aThis work is supported in parts by DFG under contract We-1254/8-1. chiral soliton models the direct extraction of the interaction Hamiltonian for hadronic decays of resonances still is an unresolved issue. Estimates are obtained from axial current matrix e l e r n e n t ~ ~ In~view ~ ~ of ~ ~what ~ . is known about the related A -+ .irN transition matrix element8, such estimates may be questioned.
96
97
Figure 1. A sketch of the S u ~ ( 3representations ) m and 27 with their exotic baryon members: O+, 2 3 1 2 , @27,A27, r27, n 2 7 and 027. As usual various isospin projections are plotted horizontally while states of different hypercharge are spread vertically.
So far, the O+ and Z3/2 with masses of 1537 f 10MeV and 1862 f 2MeV have been observed, however, the single observation of 2 3 1 2 is not undisputed12. Soliton models predict the quantum numbers I ( J " ) = O( ) 'f for O+ and for E3/2. Experimentally these quantum numbers are not yet confirmed. It is natural to wonder about the nature of states in higher dimensional representations that do carry quantum numbers of three-quark composites, such as the N' and C' in figure 1. Radial excitations13 of the octet nucleon and C are expected t o have masses similar t o N' and C'. Hence sizable mixing should occur between the antidecuplet and an octet of radial excitations. In a rough approximation this corresponds t o the picture that pentaquarks are members of the direct sum 8 @ 10 which is also obtained in a quarkdiquark approach14. The possible mixing between radially excited octet and antidecuplet baryons was recognized already earlierl5>l6showing that the full picture is more complicated. A dynamical model was d e ~ e l o p e d l to investigate such mixing effects and also to describe static properties of the low-lying J" ='f and J" = baryons. Essentially that model has only a single free parameter, the Skyrme constant e which should be in the range e M 5.0.. .5.5. Later the mass of the recently discovered O+ pentaquark was predicted with reasonable accuracy in the same model6. In this talk I will present predictions for masses of the Z3/2 and additional exotic baryons that originate the 27-plet from exactly that model without any further modifications. The latter may be considered as partners of O+ and Z3/2 in the same way as the A is the partner of the nucleon. In section 2 of this talk I will review the quantization of the rotational and radial degrees of freedom of a chiral soliton. I will present numerical results on the spectrum in section 3 and summarize in section 4. A complete description of the material presented in this talk may be found in ref.17.
g(f')
%'
98
2. Collective Quantization of the Soliton
I consider a chiral Lagrangian in flavor SU(3). The basic variable is the chiral field U = exp(iX,@/2) that represents the pseudoscalar fields ( u = 0 , . . . ,8). Other fields may be included as well. For example, the specific model used later also contains a scalar meson. In general a chiral Lagrangian can be decomposed as a sum, C = Cs CSB, of flavor symmetric and flavor symmetry breaking pieces. Denoting the (classical) soliton solution of this Lagrangian by !Yo(?) states with baryon quantum numbers are constructed by quantizing the flavor rotations
+
U ( F , t )= A(t)Uo(r‘)At(t), A ( t ) E SU(3)
(1)
canonically. According to the above separation the Hamiltonian for the collective coordinates A(t) can be written as H = HS HSB. For unit baryon number the eigenstates of HS are the members of SU(3) representations with the condition that the representation contains a state with identical spin and isospin quantum numbers (such as e.9. the nucleon or the A). In order to include radial excitations that potentially mix with states in higher dimensional SU(3) representations the corresponding collective coordinate [ ( t )is introduced via13,15>16
+
u(+) = ~ ( t ) ~ , ( j ( t ) ? ) ~ t ( t ) .
(2)
Changing to z ( t ) = [ [ ( t ) ] - 3 / 2the flavor symmetric piece of the collective Hamiltonian for a given S U ( 3 ) representation of dimension p reads
1 J(J+l)+-C2(,u)+s, 2P (3) where J and C 2 ( p ) are the spin and (quadratic) Casimir eigenvalues associated with the representation p. Note that m = rn(z),a = a ( z ) ,. . . ,s = s(x) are functions of the scaling variable to be computed in the specified soliton m 0 d e 1 ~ ~ For 9 ~ ~a .prescribed ,u there are discrete eigenvalues (&p,n,,) and eigenstates (Ip,n,)) of Hs. The radial quantum number np counts the number of nodes in the respective wave-functions. I now employ these to compute matrix elements of the full Hamiltonian H p , n p ; p t , n > ,= &p,n,,dp,p/dn,,,n>,
-
(p~~,nplitr (’bAX8At)
. (4)
This “matrix” is diagonlized exactly (rather than in some approximation scheme) yielding the baryonic states IB, rn) = C,,np C$:d,”’lp,n,) . Here B refers to the specific baryon and m labels its excitations. Before presenting numerical results for the spectrum of the Hamiltonian (4) I would like
99 Table 1. Mass differences of the eigenstates of the Hamiltonian (4) with respect to the nucleon in MeV. Experimental data1 refer to four and three star resonances, unless otherwise noted. For the Roper resonance [N(1440)] I list the Breit-Wigner (BW) mass and the pole position (PP) estimate’. The states ”?” are potential isospin $ Z candidates with yet undetermined spin-party.
B
175 284
Input 173 284
177 254
382
380
379
258 445 604 730
276 460 617 745
293 446 591 733
:::
501 BW
i’f loll(?)
640 841 1036 1343
680 878 1068 1386
1
I
m = l
m=O e=5.0 e=5.5 expt.
901 -
m=2
1081
1129
1068
1096
1515
1324
974 1112 1232 1663
1010 1148 1269 1719
:i
(*I
941 (**)
1141 -
to stress that quantizing the radial degree of freedom is also demanded by observing that the proper description of baryon magnetic moments requires a substantial feedback of flavor symmetry breaking on the soliton size1*.
3. Results
I divide the model results into three categories. First there are the lowlying J = f and J = $ baryons together with their monopole excitations. Without flavor symmetry breaking these would be pure octet and decuplet states. Second are the J = $ states that are dominantly members of the antidecuplet. Those that are non-exotic mix with octet baryons and their monopole excitations. Third are the J = $ baryons that would dwell in the 27-plet if flavor symmetry held. The J = $ baryons from the 27-plet are heavier than those with J = $ and will thus not be studied here. 3.1. Ordinary Baryons and their Monopole Excitations
Table 1 shows the predictions for the mass differences with respect to the nucleon of the eigenstates of the full Hamiltonian (4) for two values of the Skyrme parameter e. The agreement with the experimental data is quite astonishing. Only the Roper resonance (IN,l)) is predicted a bit on the low side when compared t o the empirical Breit-Wigner mass but agrees with the estimated pole position‘. This is common for the breathing mode CFor other resonances the discrepancy between the Breit-Wigner mass and the pole position is much smaller and there is no need to distinguish between them.
100
approach in soliton models13. All other first excited states are quite well reproduced. For the $+ baryons the energy eigenvalues for the second excitations overestimate the corresponding empirical data somewhat. In the nucleon channel the model predicts the m = 3 state only about 40MeV higher than the m = 2 state, ie. still within the regime where the model is assumed t o be applicable. This is interesting because empirically it is suggestive that there might exist more than only one resonance in that energy region2’. For the baryons with m = 2 the agreement with data is on the 3% level. The particle data group1 lists two “three star” isospin-f Z resonances at 751 and lOllMeV above the nucleon whose spin-parity is + not yet determined. The present model suggests that the latter is J“ = f , while the former seems to belong to a different channel. The present model gives fair agreement with available data and thus supports the picture of coupled monopole and rotational modes. Most importantly, the inclusion of higher dimensional SUF (3) flavor representations in three flavor chiral models does not lead to the prediction of any novel states in the regime between 1 and 2GeV in the non-exotic channels.
;+
3.2. Exotic Baryons from the Antidecuplet
Table 2 compares the model prediction for the exotics O+ and E3/2 to available data2>3and to a chiral soliton model calculationz1 that does not include a dynamical treatment of the monopole excitation. In that calculation parameters have been tuned to reproduce the mass of the lightest exotic pentaquark, O+. The inclusion of the monopole excitation increases the mass of the 2 3 / 2 slightly and brings it closer to the empirical value. Furthermore, the first prediction4 for the mass of the 2 3 1 2 was based on identifying N(1710) with the nucleon like state in the antidecuplet and thus resulted in a far too large mass of 2070MeV. Other chiral soliton model studies either take ME^,^ as inputz2,adopt the assumptions of ref. or are less predictive because the model parameters vary considerablylO. Without any fine-tuning the model prediction is only about 30-50MeV higher than the data. In view of the approximative nature of the model this should be viewed as good agreement. Especially the mass difference between the two potentially observed exotics is reproduced within lOMeV. 3.3. Baryons from the 27-plet
As seen from figure 1, the 27-plet contains states with the quantum numbers of the baryons that are also contained in the decuplet of the low-lying
101 Table 2. Masses of the eigenstates of the Hamiltonian (4) for the exotic baryons O+ and Z312. The absolute energy scale is set by the nucleon mass. Experimental data are the average of refs2 for O+ and the NA49 result for 23/23.I also compare the predictions for the ground state ( m = 0) to the treatment of ref.21. All energies are in GeV.
B O+ E3/2
e=5.0 1.57 1.89
e=5.5 1.59 1.91
m=O expt . 1.537f0.010 1.862f0.002
WKZ1 1.54 1.78
e=5.0 2.02 2.29
m=l e=5.5 2.07 2.33
expt. -
Table 3. Predicted masses of the eigenstates of the Hamiltonian (4) for the exotic J = baryons with m = 0 and m = 1 that originate from the 27-plet with hypercharge ( Y ) and isospin (I) quantum numbers listed. I also compare the m = 0 case to treatments of refs.21,22,23.All numbers are in GeV. B
m=O
2.06
2.07
m = l e=5.0 e=5.5 2.10 2.14 2.28 2.33 2.50 2.56 2.12 2.17 2.35 2.40 2.54 2.59
g
J = baryons: A , E * and =*. Under flavor symmetry breaking these states mix with the radial excitations of decuplet baryons and are already discussed in table 1. Table 3 shows the model predictions for the J = baryons that emerge from the 27-plet but do not have partners in the decuplet. Again, the experimental nucleon mass is used to set the mass scale. Let me remark that the particle data group' lists two states with the quantum numbers of N27 and A27 at 1.72 and 1.89GeV, respectively, that fit reasonably well into the model calculation. In all channels the m = 1 states turn out to be about 500MeV heavier than the exotic ground states. When combined with the m = 1 states of A, C*, and Z* in table 1 it is observed that the masses of states that are degenerate in hypercharge decrease with isospin, that is Mla,l) < M I N ~ ~M1rz7,o) , ~ ) , < Mic*,1) < MIA^^,^), Mlnz7,0) < M/s*,l)> and Mlnz7,0) < Mln,l).
g
4. Conclusion
In this talk I have discussed the interplay between rotational and monopole excitations for the spectrum of pentaquarks in a chiral soliton model. In this approach the scaling degree of freedom has been elevated to a dynamical quantity which has been quantized canonically at the same footing as the
102
(flavor) rotational modes. Then not only the ground states in individual irreducible SUF(3) representations are eigenstates of the (flavor-symmetric part of the) Hamiltonian but also all their radial excitations. I have treated flavor symmetry breaking exactly rather then only at first order. Thus, even though the chiral soliton approach initiates from a flavor-symmetric formulation, it is capable of accounting for large deviations thereof. The spectrum of the low-lying f' and baryons is reasonably well reproduced. Also, the model results for various static properties are in acceptable agreement with the empirical data15. This makes the model reliable to study the spectrum of the excited states. Indeed the model states can clearly be identified with observed baryon excitations; except maybe an additional P11 nucleon state although there exist analyses with such a resonance. Otherwise, this model calculation did not indicate the existence of yet unobserved baryon states with quantum numbers of three-quark composites. The computed masses for the exotic O+ and E3/2 baryons nicely agree with the recent observation for these pentaquarks. At this stage the model contains no more adjustable parameter. The mass difference between mainly octet and mainly antidecuplet baryons thus is a prediction while it is an input quantity in most other appro ache^^^^^,^^^^^^'^. Thus the present predictions for the masses of the spin-; pentaquarks should be sensible as well and are roughly expect between 1.6 and 2.1GeV.
:+
Acknowledgments
I am grateful t o the organizers for providing this pleasant and worthwhile workshop. Furthermore I acknowledge interesting discussions with G. Holzwarth, R. L. Jaffe, J. Schechter, and H. Walliser. References 1. A. V. Manohar, Nucl. Phys. B 248 (1984) 19; L. C. Biedenharn, Y. Dothan,
in From SU(3) To Gravity, E. Gotsman, G. Tauber, eds., p 15; M. Chemtob, Nucl. Phys. B 256 (1985) 600; M. Prasalowicz, in Skyrmions and Anomalies, M. Jezabek, M. Prasalowicz, eds., World Scientific (1987), p. 112; H. Walliser, Nucl. Phys. A 548 (1992) 649; H.Walliser, in Baryons as Skyrme Solitons, G. Holzwarth, ed., World Scientific (1994), p. 247 2. T. Nakano et al. [LEPS Coll.], Phys. Rev. Lett. 91 (2003) 012002; V.Barmin et al. [DIANA Coll.], Phys. Atom. Nucl. 66 (2003) 1715 [Yad. Fiz. 66 (2003) 17631; S. Stepanyan et al. [CLAS Coll.], Phys. Rev. Lett. 91 (2003) 252001; J. Barth et al. [SAPHIR Coll.], hep-ex/0307083; V. Kubarovsky, S. Stepanyan [CLAS Coll.], AIP Conf. Proc. 698 (2004) 543; A. Asratyan et al.,
103
3. 4. 5. 6. 7. 8.
9. 10. 11.
12.
13.
14. 15. 16. 17. 18. 19. 20. 21. 22. 23.
arXiv:hep-ex/0309042; V. Kubarovsky et al., [CLAS Coil.], Phys. Rev. Lett. 92 (2004) 032001 [Erratum-ibid. 92 (2004) 0499021; A. Airapetian et al., [HERMES Coll.], Phys. Lett. B 585 (2004) 213; S. Chekanov et al., [ZEUS Coll.], arXiv:hep-ex/0405013. R. Togoo et al., Proc. Mongolian Acad. Sci., 4 (2003) 2; A. Aleev et al., [SVD Coll.], arXiv:hep-ex/0401024; M. Abdel-Bary et al. [COSY-TOF Coll.], arXiv:hep-ex/0403011 C. Alt et al. "A49 Coll.], Phys. Rev. Lett. 92 (2004) 042003 D. Diakonov, V. Petrov, M. Polyakov, Z. Phys. A359 (1997) 305 R. L. Jaffe, arXiv:hep-ph/0401187 H. Weigel, Eur. Phys. J. A 2 (1998) 391; AIP Conf. Proc. 549 (2002) 271 M. Praszalowicz, Phys. Lett. B 583 (2004) 96 H. Verschelde, Phys. Lett. B 209 (1988) 34; S. Saito, Prog. Theor. Phys. 78 (1987) 746; G. Holzwarth, A. Hayashi, B. Schwesinger, Phys. Lett. B 191 (1987) 27; G. Holzwarth, Phys. Lett. B 241 (1990) 165; A. Hayashi, S. Saito, M. Uehara, Phys. Lett. B 246 (1990) 15, Phys. Rev. D 46 (1992) 4856; N. Dorey, J. Hughes, M. Mattis, Phys. Rev. D 50 (1994) 5816 B. K. Jennings, K. Maltman, arXiv:hep-ph/0308286 J. R. Ellis, M. Karliner, M. Praszalowicz, arXiv:hep-ph/0401127 N. W. Park, J. Schechter, H. Weigel, Phys. Lett. B 224 (1989) 171; For a review and more references on s U ~ ( 3 soliton ) models see H. Weigel, Int. J. Mod. Phys. A 11 (1996) 2419 H. G. Fischer, S. Wenig, arXiv:hep-ex/0401014; M. I. Adamovich et al., [WA89 Coll.], arXiv:hep-ex/0405042. C. Hajduk, B. Schwesinger, Phys. Lett. B 140 (1984) 172; A. Hayashi, G. Holzwarth, Phys. Lett. B 140 (1984) 175; I. Zahed, Ulf-G. Meifher, U. Kaulfuss, Nucl. Phys. A 426 (1984) 525; J. Breit, C. R. Nappi, Phys. Rev. Lett. 53 (1984) 889; J. Zhang, G. Black, Phys. Rev. D 30 (1984) 2015 R. L. JaRe, F. Wilczek, Phys. Rev. Lett. 91 (2003) 232003 J. Schechter, H. Weigel, Phys. Rev. D 44 (1991) 2916 J . Schechter, H. Weigel, Phys. Lett. B 261 (1991) 235 H. Weigel, arXiv:hep-ph/0404173, Eur. Phys. J. A,in print. B. Schwesinger, H. Weigel, Phys. Lett. B 267 (1991) 438, Nucl. Phys. A 540 (1992) 461 K. Hagiwara et al. [PDG], Phys. Rev. D 66 (2002) 010001 M. BatiniC, et al., Phys. Rev. C 51 (1995) 2310 [Erratum-ibid. C 57 (1998) 10041; D. G. Ireland, S. Janssen, J . Ryckebusch, arXiv:nucl-th/0312103 H. Walker, V. B. Kopeliovich, J . Exp. Theor. Phys. 97 (2003) 433 [Zh. Eksp. Teor. Fiz. 124 (2003) 4831. D. Borisyuk, M. Faber, A. Kobushkin, arXiv:hep-ph/0312213 B. Wu, B. Q. Ma, Phys. Lett. B 586 (2004) 62
Models of Meson-Baryon Reactions in the Nucleon Resonance Region T.-S. H. LEE', A. MATSUYAMA', T. SAT03 1 Physics Division, Argonne National Laboratory Argonne, IL 60439, U S A 2 Department of Physics, Schizuoka University, Schizuoka, Japan 3 Department of Physics, Osaka University, Osaka, Japan It is shown that most of the models for analyzing meson-baryon reactions in the nucleon resonance region can be derived from a Hamiltonian formulation of the problem. An extension of the coupled-channel approach to include mrN channel is briefly described and some preliminary results for the "(1535) excitation are presented.
1. Introduction With very successful experimental efforts in the past few years, we are now facing a challenge to interpret very extensive data of electromagnetic meson production reactions in terms of the structure of nucleon resonances (N*). To achieve this goal, we need to perform amplitude analyses of the data in order to extract N * parameters. We also need to develop reaction models to analyze the dynamical content of the extracted N* parameters. At the present time, we can use the N* data to test the predictions from various QCD-based hadron models. In the near future, we hope to understand N* parameters from Lattice QCD. In the A region, both the amplitude analyses and dynamical reaction models have been well developed. We find that these two efforts are complementary. For example, the y N -+ A M1 transition strength extracted from all amplitude analyses is GM(O)= 3.18 & 0.04 which is about 40 % larger than the constituent quark model prediction. This difference is understood1I6 by developing dynamical reaction models within which one can show that the discrepancy is due to the pion cloud which is not included in the commonly considered constituent quark model prediction. In the second and third resonance regions, the situation is much more complicated because of many open channels. It is necessary to develop coupled-channel approaches for learning about the N* properties. The main objective of this contribution is to review the development in this direction. We will also describe a newly developed coupled-channel model which is aimed at accounting for rigorously the mrN unitarity condition. In section 2, we will introduce a Hamiltonian formulation within which most of the current models of electromagnetic meson production reactions can be derived and compared. The extension of the coupled-channel approach to account for explicitly the mrN channel is then described in section 3. A summary is given in
104
105
Baryons
---
Mesons
Figure 1. Tree diagrams for meson-baryon reactions. N' is a nucleon resonance state. section 4. 2 . Derivation of Models
The starting point of our derivation is to assume that the meson-baryon ( M B ) reactions can be described by a Hamiltonian of the following form (1)
H=Ho+V, where HO is the free Hamiltonian and
V= +2. (2) Here ubg is the non-resonant(background) term due to the mechanisms such as the tree-diagram mechanisms illustrated in Fig. l(a)-(d), and u R describes the N* excitation Fig. l(e). Schematically, the resonant term can be written as
where ri defines the decay of the i-th N* state into meson-baryon states, and Mi" is a mass parameter related t o the resonance position. The next step is to define a channel space spanned by the considered mesonbaryon ( M B ) channels: yN, T N , $V, T A , p N O N , ... The S-matrix of the meson-baryon reaction is defined by
S ( E ) a , b = da,b - 2Tid(E - H O ) T a , b ( E )
1
(4)
where ( a ,b) denote M B channels, and the scattering T-matrix is defined by the following coupled-channel equation
106
Here the meson-baryon propagator of channel c is
where
P
g P ( E )=
(7)
Here P denotes taking the principal-value part of any integration over the propagator. If g ( E ) in Eq.(5) is replaced by g P ( E ) ,we then define the K-matrix which is related to T-matrix by
Ta,b(E)= Ka,b(E)- E T O , C ( E ) [ ~ T - ~HO)]cKc,b(E). (E
(8)
C
By using the two potential formulation, one can cast Eq.(5) into
The first term of Eq.(9) is determined only by the non-resonant interaction tzb(E) =' 2 b
+
v ~ ~ C g C ( E ) t ~ b ( E ')
(11)
C
The resonant amplitude Eq.(lO) is determined by the dressed vertex r N * , a ( E )= r N * , a +
rN*,bgb(E)t:a(E),
(12)
b
and the dressed propagator
[G(E)-']i,j(E) = ( E - M&Pi,j
- C i , j ( E ).
(13)
Here A4&*is the bare mass of the resonance state N * , and the self-energy is
Note that the meson-baryon propagator g a ( E )for channels including an unstable particle, such as TA, pN and oh', must be modified to include a width. In the Hamiltonian formulation, this amounts to the following replacement
107 where the energy shift is
Here I?" describes the decay of p, (T or A in the quasi-particle channels. Eq.(5), Eqs.(9)-(16), and Eq.(8) are the starting points of our derivations. From now on, we consider the formulation in the partial-wave representation. The channel labels, ( a , b , c ) , will also include the usual angular momentum and isospin quantum numbers. 2.1. Unitary Isobar Model ( U I M ) 2.1.1. M A I D
The Unitary Isobar Model developed3 by the Mainz group is based on the on-shell relation Eq.(8). By including only one hadron channel, n N (or ON ), Eq.(8) leads to
T T ~ ,=7eidrN ~ COS&N K T ~ , .- , ~
(17)
where b n is~ the pion-nucleon scattering phase shift. By further assuming that K = V = vbg v R , one can cast the above equation into the following form
+
TTN,7N(
V I M ) = esnNcosbThi[v~gN,yN]+
TT%,yN(E)
.
(18)
N:
The non-resonant term vbg in Eq.(18) is calculated from the standard Born terms but with an energy-dependent mixture of pseudo-vector (PV) and pseudoscalar (PS) n N N coupling and the p and w exchanges. For resonant terms in Eq.( 18), MAID uses the following Walker's parameterization5
where f : N ( E ) and f { N ( E )are the form factors describing the decays of N*, r t o t is the total decay width, Ai is the y N -+ N* excitation strength. The phase is required by the unitary condition and is determined by an assumption relating the phase of the total production amplitude to the n N phase shift and inelasticity. 2.1.2. JLab/Yeveran U I M
The Jlab/Yerevan UIM4 is similar to MAID. But it implements the Regge parameterization in calculating the amplitudes at high energies. It also uses a different procedure to unitarize the amplitudes.
Both MAID and JLab/Yeveran UIM have been applied extensively to analyze the data of n and 7 production reactions. Very useful new information on N* have been extracted.
108 2.2. Multi-channel K-matrix models 2.2.1. SAID
The model employed in SAID3 is based on the on-shell relation Eq.(8) with three channels: yN, r N , and r h which represents all other open channels. The solution of the resulting 3 x 3 matrix equation can be written as
T-,N,,N(SAID)= A d 1 + ~ T = N , , N+)ART,N,,N,
(20)
where
In actual analysis, they simply parameterize A1 and A R as M
A1 = [ v y ~ , , ~+]
F n z Q l m + n ( z )I
(23)
n=O
where ko and qo are the on-shell momenta for pion and photon respectively, z = d-/ko, Q L ( ~is) the legendre polynomial of second kind, E, = Ey - m,(1 m , / ( 2 m ~ ) )and , p n and Pn are free parameters. SAID calculates vyN,N,,N of Eq.(23) from the standard PS Born term and p and w exchanges. The empirical r N amplitude T,N,,N needed to evaluate Eq.(20) is also available in SAID. Once the parameters Is, and p , in Eqs.(23)-(24) are determined, the N* parameters are then extracted by fitting the resulting amplitude T y ~ ,at, en~ ergies near the resonance position to a Breit-Wigner parameterization(simi1ar to Eq.(19)). Very extensive data of pion photoproduction have been analyzed by SAID. The extension of SAID to also analyze pion electroproduction data is being pursued.
+
2.2.2. Giessen Model
The coupled-channel model developed by the Giessen group can be obtained from Eq.(8) by taking the approximation K = V . This leads to a matrix equation involving only the on-shell matrix elements of V
Ta,b(Giessen) = c [ ( 1
+ i v ( E ) ) - ' ] ~ , ~ v ~ ,.b ( E )
(25)
C
The interaction V = vbg f v R is evaluated from tree-diagrams of various effective lagrangians. The form factors, coupling constants, and resonance parameters are
109 adjusted to fit both the .rrN and 7 N reaction data. They include up to 5 channels in some fits, and have identified several new N* states. But further confirmations are needed to establish their findings conclusively. 2.2.3. KSU Model
The Kent State University (KSU) model’ can be derived by noting that the nonresonant amplitude tbg, defined by a hermitian vbg in Eq.(ll), define a S-matrix with the following properties S 2 b ( E )= ba,b - 27ri6(E - Ho)t2b(E)
=C W $ ) ~ ( E ) ~ $ ) ( E ) ,
(26) (27)
C
where the non-resonant scattering operator is
= ba,c f ga(E)t:$(E).
wL,)(E)
(28)
With some derivations, the S-matrix Eq. (4) and the scattering T-matrix defined by Eqs.(9)-(14) can then be cast into following form
sa,b(E)=
w ~ ~ ’ T ( E ) R c , d ( E ) w >~ ~ ) ( E )
(29)
c,d
with Rc,d(E)= bc,d 4- 2iT:d(E) .
(30) (31)
Here we have defined T:d(E)
=
r ~ ~ , c ( E ) [ G ( E ) ~ , ~ r ~ ~ , d ( E ) . (32) i,j
The above set of equations is identical to that used in the KSU model of Ref.8. In practice, the KSU model fits the data by parameterizing T R as a Breit-Wigner resonant form T R x r / 2 / ( E- M - i r / 2 ) and setting w(+) = B = BlBz . * .Bn, where Bi = e o p ( i X A i ) is a unitary matrix. The KSU model has been applied to .rrN reactions, including pion photoproduction. It is now being extended to investigate K N reactions.
-
2.3. The CMB Model
A unitary multi-channel isobar model with analyticity was developedg in 1970’s by the Carnegie-Mellon Berkeley(CMB) collaboration for analyzing the xiV data. The CMB model can be derived by assuming that the non-resonant potential vbg is also of the separable form of v R of Eq.(3)
110 The resulting coupled-channel equations are identical to Eqs.(9)-(16), except that t 2 b = 0 and the sum over NT is now extended to include these two distance poles L and H . By changing the integration variables and adding a substraction term, Eq.(14) can lead to CMB's dispersion relations
Thus CMB model is analytic in structure which marks its difference with all K-matrix models described above. The CMB model has been revived in recent years by the Zagreb group'' and a Pittsburgh-ANL collaboration" to extract the N * parameters from fitting the recent empirical n N and y N reaction amplitudes. The resulting N* parameters have very significant differences with what are listed by PDG in some partial waves. In particular, several important issues concerning the extraction of the N* parameters in S11 channel have been analyzed in detail. 2.4. Dynamical Models
A. In the A region Keeping only one resonance N * = A and two channels a , b = nN,y N , Eqs.(9)(14) are reduced to what were developed in the Sato-Lee (SL) model'. In solving exactly Eqs.(9)-(14), the non-resonant interactions v2N,aN and vFN,,, are derived from the standard PV Born terms and p and w exchanges by using an unitary transformation method. In the Dubna-Mainz-Taiwan (DMT) model6, they depart from the formulation Eqs.(9)-(14) by using the Walker's parameterization defined by Eq.(19) to describe the resonant term t R of Eq.(9). Accordingly, their definition of the non-resonant amplitude also differs from Eq.(ll): t 5 in the right-hand side of Eq.(ll) is replaced by the full amplitude T c , b . Furthermore, they follow MAID to calculate the non-resonant interaction from an energy-dependent mixture of PS and PV Born terms. Extensive data of pion photoproduction and electroproduction in the A region can be described by both the SL and DMT models. However, the extracted y N 4 A form factors, in particular their bare form factors, are significantly different.
B. In the second and third resonance regions Eqs.(9)-(16) are used in a 2-N* and 3-channel ( n N , q N , and 7rA) study12 of nN scattering in S11 partial wave, aiming at investigating how the quark-quark interaction in the constituent quark model can be determined directly by using the reaction data. Eqs.(9)-(16) are also the basis of examining the N* effects13 and
111
one-loop coupled-channel effects14 on w meson photoproduction and the coupledchannel effects on K photoprod~ction'~. The coupled-channel study of both 7rN scattering and y N -+ 7rN in 4 1 channel by Chen et a133 includes 7rN, q N , and yN channels. Their 7rN scattering calculation is performed by using Eq.(5), which is of course equivalent to Eqs.(9)-(14). In their yN + 7rN calculation, they neglect the y N -+ qN -+ 7rN coupled-channel effect, and follow the procedure of the DMT model to evaluate the resonant term in terms of the Walker's parameterization (Eq.(19)). They find that four N* are needed to fit the empirical amplitudes in S11 channel up to W = 2 GeV. A coupled-channel calculation based on Eq.(5) has been carried out by Jiilich group17 for 7rN scattering. They are able to describe the 7rN phase shifts up to W = 1.9 GeV by including 7rN, Q N , 7rA, p N and u N channels and 5 N* resonances : &(1232), &1(1535), &1(1530), Sll(1650) and 013(1520). They find that the Roper resonance Pll(l440) is completely due to the meson-exchange coupled-channel effects. A coupled channel calculation based on Eq.(5) for both 7rN scattering and y N + 7rN up to W = 1.5 GeV has been reported by f i d a and Alarbi". They include 7rN, yN, q N , and 7rA channels and 4 N* resonances : p33(1232), F'11(1440), S11(1535), and 013(1520). The parameters are adjusted to fit the empirical multipole amplitudes in a few low partial waves. Much simpler coupled-channel calculations have been performed by using separable interactions. In the model of Gross and Suryalg, such separable interactions are from simplifying the meson-exchange mechanisms in Figs l.(a)-c) as a contact term like Fig. l(d). They include only 7rN and yN channels and 3 resonances: P33(1232), P11(1440) and 013(1520), and restrict their investigation up to W < 1.5 GeV. To account for the inelasticities in P11 and 0 1 3 , the N * -+ 7rA coupling is introduced in these two partial waves. The inelasticities in other partial waves are neglected. A similar separable simplification is also used in the chiral coupled-channel models20>21for strange particle production. There the separable interactions are directly determined from the leading contact terms of SU(3) effective chiral lagrangian and hence only act on s-wave partial waves. They are able to fit the total cross section data for various strange particle production reaction channels without introducing resonance states. It remains to be seen whether these models can be further improved to account for higher partial waves which are definitely needed to give an accurate description of the data even at energies near production thresholds.
3. Unitary mrN Model All of the models described in section 2 rely on the assumption that the ~ 7 r N continuum can be expanded in terms of quasi-two-particle channels such as nA, u N , and p N . These models are of course not satisfactory since they do not account for all of the effects due to the coupling with the n n N channel. It is necessary to develop a reaction model which also satisfies the 7rrN unitarity
112
Data lrom SAID
.
15
I 1
-5
I
.
1200
1400
1600
1800
1
2 W [MeV]
W [MeV]
Figure 2.
condition exactly, This can be done by extending the Hamiltonian Eqs.(l)-(3) to include a vertex interaction r v to account for the p -+ m r and u -+ m r decays and to include possible non-resonant 7 - r ~interaction v X X . Such a formulation and numerical methods for performing unitary calculations of two-pion production cross sections are being pursued by Lee, Matsuyama, and Sat0 (LMS)22. Here we only briefly describe this unitary mrN model. The coupled-channel equations from LMS can also be cast into the form of Eqs.(9)-(16) except that the driving term of Eq.(ll) is replaced by
with
The driving term of the above integral equation is
Note that i # j specifing the sum over N* states in the above equation is to avoid the double counting of mrN effect which is already included in the dressed propagator defined by Eq.(15). We have applied this unitary mrN formulation to investigate T N stattering and y N -+ .rrN in S11 channel up to W = 2 GeV. The channels included are n N , q N , .rrA and y N . The needed non-resonant interactions are generated from tree-diagrams Figs.l(a)-(d) using the unitary transformation method. Two N* states are included in the fits to the T N scattering amplitude and the Eo+
113 amplitude of y N -+ TN. Our results for Eo+ amplitudes are shown in Fig.2. We see that we are not able t o fit the data at W > 1.63 GeV and hence only the extracted N*(1535) parameters are reliable. Our results are shown in the Table below and compared with the values from Chen et a133 (DMT) and the quark model prediction of C a p ~ t i c k ~ It ~is. interesting t o note that LMS’s bare value of the N*(1535) -+ yN helicity amplitude Allz is close to the quark model prediction. Both the DMT and LMS predict that the meson cloud effect, the differences between the dressed values and bare values, is to reduce the bare values t o the dressed values. This is rather different from the situation in the A region where the meson cloud is to enhance the transition strength. The differences between DMT and LMS values reflect their significant differences in calculating the coupled-channel effects.
MR
r R
%(%)
DMT16
1528 f 1 95 f 5
40 f 1
LMSZ2
1538
36
Quark
122
Alp 81 3 (dressed) 108 f4 (bare) 61.24 (dressed) 77.64 (bare) 76
+
To obtain reliable information for the second S11 resonance at about 1.6 GeV, we are in the process of including pN and oN channels. The importance of these two channels can be examined in a unitary calculation of 7rN -+ mrN cross sections. This is achieved by using the Spline-function expansion method which was developed in our previous investigations of 7rNN problem. Our results of the partial cross sections of TN -+ T T N in S11 channel are shown in Fig.3. Clearly, p N channel must be included for a dynamical interpretation of the second N* and to establish whether there exists third or even fourth N* in this channel. Our approach is clearly different from the investigation of Chen et al.33 who include only T N and qN channels and the fits t o the data are achieved by including up to four N * .
4. Summary
We have given a unified derivation of most of the models for electromagnetic meson production reactions in the nucleon resonance region. An extension of the coupled-channel approach t o include mrN channel is briefly described and some preliminary results for the N*(1535) excitation have been presented. Our complete calculations will be published elsewhere22.
114 I
I
I
0.6 -
0.5
-
.g 0.4 w
5
.
0.3
-
0.2
-
0.1
-
3.2
1.4
1.6
18
2
Figure 3. Calculated n N -+ n n N cross sections in ,911 channel. The partial cross sections through intermediate 7rA (pi-D), p N (rho-N) and o N (Sigma-N) are also shown to compare with the coherent sum of these channels (Total), Acknowledgments This work is support in part by U.S. Department of Energy, Office of Nuclear Physics, under Contract No. W-31-109-ENG-38, and in part by Japan Soceity for Promotion of Science, Grand-in-Aid for Scientific Research (C) 15540275. References 1. T. Sat0 and T.-S. H. Lee, Phys. Rev. C 54, 2660 (1996); Phys. Rev. C63, 055201 (2001). 2. Kamalov and S.N. Yang, Phys. Rev. Lett. 83, 4494 (1999); S.S. Kamalov, S. N. Yang, D. Drechsel, 0. Hanstein, and L. Tiator, Phys, Rev, C64, 032201(R) (2001), 3. D. Drechsel, 0. Hanstein, S.S. Kamalov, and L. Tiator, Nucl. Phys. A645, 145 (1999) 4. I. G. Aznauryan, Phys. Rev. C68, 065204 (2003) 5. R.L. Walker, Phys. Rev. 182, 1729 (1969) 6 . R.A. Amdt, 1.1. Strakovsky, R.L. Workman, Int. J. Mod. Phys. A18, 449 (2003) 7. G. Penner and U. Mosel, Phys. Rev. C66, 055211 (2002); C66, 055212 (2002). 8. D. M. Manley, Int. J. of Mod. Phys., A18, 441 (2003); 9. R.E. Cutkosky, C.P. Forsyth, R.E. Hendrick, and R.L. Kelly, Phys. Rev. D20, 2839 (1979).
115 10. M. Batinic, I. Slaus, and A. Svarc, Phys. Rev. C51, 2310 (1995) 11. T.P. Vrana, S.A. Dytman, and T.4. H. Lee, Phys. Rept. 328, 181 (2000). 12. Yoshimoto, T. Sato, M. Arima, and T.-S. H. Lee, Phys. Rev. C61 065203 (2000). 13. Y. Oh, A. Titov, and T.-S. H. Lee, Phys. Rev. C63, 025201 (2001). 14. Y. Oh and T.-S. H. Lee, Phys. Rev. C66, 045201 (2002). 15. W.-T. Chiang, F. Tabakin, T.-S. H. Lee and B. Saghai, Phys. Lett. B517, 101 (2001). 16. G.-Y. Chen, S.S. Kamalov, S. N. Yang, D. Drechsel, and L. Tiator, Nucl. Phys. A723, 447 (2003). 17. 0. Krehl, C. Hanhart, S. Krewald, and J. Speth, Phys. Rev. C62, 025270 (2000) 18. M. G. Ehda and H. Alharbi, Phys. Rev. C68, 064002 (2003). 19. F. Gross and Y.Surya, Phys. Rev. C47, 703 (1993); Y.Surya and F. Gross, Phys. Rev. C 53, 2422 (1996). 20. N. Kaiser, T. Waas, and W. Weise, Nucl. Phys. A612, 297 (1997). 21. E. Oset and A. Ramos, Nucl. Phys. A635, 99 (1998). 22. T.-S. H. Lee, A. Matsuyama, and T. Sato, in preparation 23. S. Capstick, Phys. Rev.D46, 2864 (1992).
Review on Kaon-Hyperon Electromagnetic Production on the Nucleon in the Resonance Region K.-H. GLANDER
Physikalisches Institut, B o n n University, Nussallee 12, 53115 Bonn, Germany E-mail:
[email protected] The measurement of photon and electron induced reactions with open strangeness is one of the central issues in modern hadron physics. A huge amount of data on nearly all isospin channels on the production of ground state hyperons are coming out from all over the world. In addition to total and differential cross sections and recoil polarization measurements now other polarization observables become available from experiments using polarized beams and targets. The so far measured data suggest contributions from resonance production. Coupled channel analysis of new data should help to develop models with more predictive power on unmeasured observables and to extract resonance informations in these reactions. One might expect to establish new resonances decaying into kaon hyperon final states.
1. Introduction The d a t a situation on kaon-hyperon photoproduction befor 1990 (see e.g. HEPDATA, T h e Durham H E P Databases) was scanty. Nearly no data exist for instance for t h e reaction yp + K+Co from that time. For yp + K + A there are only few data points measured by 12 groups between 1958 and 1973, which do not cover the full kinematics (especially t h e d a t a for backward produced kaons are rare). As was shown by Adelseck et al.' these different d a t a sets are quite inconsistent. T h e SAPHIR detector2 at t h e electron stretcher facility ELSA measured for t h e first time differential cross sections and recoil polarizations for t h e reactions y p + K + A , y p + K+Co and y p + K°C+ covering t h e full range for t h e kaon production angle. From the first d a t a taking period from 1992 t o 1994 t h e reactions y p -+ K + A and y p + K+Co were analyzed u p t o a photon energy of 2.0 GeV3 and the reaction yp + K°C+ u p t o a photon energy of 1.55 GeV4. As result of single as well as in coupled channel calculations on these channels Bennhold et al. suggested a n evidence for a so called missing resonance 0 1 3 (1895)59617'8 t o explain the resonance-like structure in t h e cross section for p(y, K + ) A observed by SAPHIR at W 1900 MeV (Fig. 1). Such a 0 1 3 resonance has been predicted within quark model calculations1891' in this mass range.
-
116
117
3.5 3.0 2.5
,-.2.0 2.v
1.5
I .o 0.5 0.0 1.6
I .7
1.8
1.9
2.0
2.1
2.2
W (GeV)
Figure 1. Total cross section for K+A photoproduction on the proton. The dashed line shows the calculations by Bennhold et al. without the 013(1895) resonance, while the solid line is obtained by including the 013(1895). The solid circles are SAPHIR data from the 1992-1994 data taking period 3 . The open circles show old ABBHHM data 2 5 . 576,7,8
Because the importance of finding the missing resonances experimentally in order to give a complete picture in quark model framework, a controverse discussion about the need of the Dl3 in explaining kaon photoproduction data started after the claim for the evidence of this resonance, e.g.12>13314715, and the discussion is still going on. To take the systematic studies of Janssen et al. just as an example, this group found that the data description is improved by including the 0 1 3 (1895) resonance in their effective Lagrangian approach, although they point out that also a P13, P11 and S11 in the same mass region were able to describe the SAPHIR data from the 1992-1994 data taking Most models on kaon photoproduction, either single channel or coupled channels descriptions, are using a tree-level effective Lagrangian approach. A serious problem of these model descriptions are the ambiguities they have so far. One has to choose the resonances to be included. The coupling constants have to be fixed, addressing moreover the question of compatibility with SU(3) predictions. The choice of hadronic form factor is not totally free because of gauge invariance but there are still ambiguities left. The same holds for the treatment of background terms. So more data on cross sections with better resolution and errors and especially data on polarization observables are certainly needed to fix the model parameters to minimize the ambiguities and gain more predictive power on unmeasured observables. The older SAPHIR data on cross sections and recoil polarizations on the reactions yp -+ K'h and y p + K f C o were remeasured by SAPHIR/ELSA1' and CLAS/JLAB17. These data now cover the full kaon production angular range with a twice better resolution with also raised energy resolution at the same time, extending the photon energy range up to the continuum region. First measurements on photon beam asymmetries" for the same reactions were done
118
by LEPS/SPring8 for forward produced kaons with 0.6
3.0
.
W (GeV)
W (GeV)
Figure 2. Total cross sections for the six isospin channels of kaon photoproduction on the nucleon. The solid data points for K+ production are SAPHIR measurements from the 1992-1994 data taking period 3, the open data points are older data from ABBHHM 2 5 . The data for KO production are from Ref.lg. The solid curve shows model calculations of Bennhold et al. from 1999 and the dashed line shows an older calculation of Bennhold et al. from 1996 '.
Data on total and differential cross sections and the recoil polarization will come out soon for the reaction y p + K°C+ by the SAPHIR and the CLAS collaboration with substantially improved precision and resolution. From CLAS one can expect in future data on the beam asymmetry C and the beam-recoil observables Ck and Ci and kaon photoproduction data on the neutron. Spring8 will measure beam asymmetry data on the reaction y p -+ K°C+ and yn -+ K'C- and differential cross sections for all mentioned channels. Data can be expected to be published also from GRAAL/ESRF, CB/ELSA, NKS/LNS and other experiments to come. To pick out NKS/LNS as an example this experiment will measure data on y n -+ K o A close to threshold and add so another interesting but never measured isospin channel to world data. As fig. 2 illustrates measurement of all six isospin channels are able to give strong constraints on model calculations. Data on different polarization observables like Oa, Ob, T , G, E , . . . can be expected to be measured by different experiments in near future.
119 Especially the experiments at JLAB provided us through the last years with amazing data on electroproduction. The huge amount of already measured data on cross sections and polarization observables for kaon-hyperon photo- and electroproduction and the still growing data base will lead to a better understanding of the reaction mechanisms. To give an impression some selected topics will be presented in the next sections. 2. Differential cross sections for 7 p + K + A
Fig. 3 shows the differential cross section for yp + K'A for selected kaon production angles measured by CLAS17 together with older SAPHIR data3. The data in Fig. 4 are new SAPHIR data16. The good energy and angle resolution of the new CLAS and SAPHIR data allows to resolve a structure which can be seen around a mass of W M 1900 MeV for backward produced kaons. For very forward produced kaons (cos(Ohys)= 0.85) CLAS observed another structure, which is slightly different in shape and shifted to a mass around W z 1950 MeV. This structure has been interpreted as an evidence for a second resonance or an interference phenomenal7. However, this structure in forward direction is not confirmed by SAPHIR. Anyway, the new data show up new structures which have to be explained by models. As already mentioned, Bennhold et aZ. in their fits to the older SAPHIR data predicted a structure in the differential cross section of yp + K + A in backward and (less pronounced) in forward direction at W M 1900 MeV caused by the suggested O l ~ ( 1 8 9 5 ) ~The . structures in the differential cross sections are also well described by Janssen et al.12,13, while the calculations of Penner and Mosel et aZ.15 do not hit the data in the backward direction21. Recalculations of all models using the new data sets are still going on. 3. Hyperon polarization for 7 p + K + A and 7 p + K + X o The hyperon polarization of A and Co in the reactions yp + K + A and yp + K+Co were measured by SAPHIR3>16and CLAS17 covering the full kaon production angular range and the photon energy range from threshold up to the continuum region. The polarization measurements are added by some SAPHIR data on the C+ polarization4722in the reaction -yp + K°C+. Because the latter have still less accurancy and resolution in kaon production angle and photon energy only the A and Co polarizations are discussed here. The following observations are made (see e.g. new SAPHIR data in fig. 5, for CLAS data see17127): The polarization parameters vary strongly with the production angle of the kaon. They are in general opposite in sign for A and Co. The shapes of the angular dependence indicate the same signature throughout the whole energy range: it tends to be positive for A (negative for Co) at backward angles, passes zero in the central region of
120
y + p 31
+ K'+A 1
n
-Q
I
I
I
n -
1.6
1.7
1.8 1.9
2
2.1
2.2 2.3
W (GeV) Figure 3. Differential cross section for K + A photoproduction on the proton for selected kaon production angles measured by CLAS l7 together with older data from SAPHIR 3
cos(O&ys)% sphere.
0 and shows negative (positive) values in the forward hemi-
The magnitude of the polarizations parameters varies with energy, for yp -+ K + A less than for yp -+ KtCo. The Co is maximally polarized (Pco = f1) at forward and backward kaon production angles for photon energies above 1.45 GeV. The opposite signs of the angular dependence of the polarization parameters for A and Co are predicted from SU(6)23 if the same production mechanism for the s-quark is assumed in both reactions. The persistence of the shape is surprising, especially for the A and Co production below a photon energy of 1.3 GeV, where resonance contributions of S11(1650), P11(1710) and P13(1720) are found to contribute strongly. Note that the energy bin width for the polarization measurement was chosen to be comparable to the width of the resonances. Current model calculations, which are successful to describe the cross sections in the ranges of energy and production angle for both reactions of previous data, do not describe the polarizations of A and Co simultaneously. The polarizations measured for A and Co are similar in shape and magnitude to many other results obtained with other beams and up to highest e n e r g i e ~ ~ ~ , ' ~ ,
121 w
-n
2
1 . 6 1.7 1 8 1.9
1 0 8
2 1 2.2 - 0 9 < cos
or<
-0.L
I
O
K
'
1.5 '
'
2
w
ICdJ
1.6 1.7 1.8 1.9
2.3.-3: 0.8
.
2
2.1 -0.8
2.2
< co5 < :o
2.3
Ice\ ...
2 -0.
2.5
E, LGeVl Figure 4. Differential cross section for K + A photoproduction on the proton for selected kaon production angles measured by SAPHIR 1 6 . The curves are from KAON-MAID 20
thus suggesting a general s-quark production scheme26. A presentation of polarization measurements by CLAS and interpretions in a simple quark picture can be found also in2?. 4. Beam asymmetry for yp
+K+A
and -yp
+K + X o
The beam asymmetry C is the asymmetry of cross sections with photons polarized perpendicular or parallel to the production plane. The measurement of this asymmetry is helpful for the understanding of kaon photoproduction, because this observable is sensitive to the background contributions of meson exchanges in the t-channel. For the natural parity exchange of K* a beam asymmetry C = 1 is expected. The unnatural parity exchange of K or K1 mesons leads to C = -1. So even the sign of C is a helpful information. Furthermore, model calculations by Bennhold et aL6 and Janssen et al.13 showed the huge sensitivity of the beam asymmetry to the model ingredients like the inclusion of certain resonances or the treatment of background. So the measurement of C can help to fix the model parameters. The LEPS collaboration at Spring8 has measured the beam asymmetry C for the reactions "yp+ K + A and "yp+ K+Co for the first time for E, = 1.5 - 2.4 GeV and 0.6
122 1 l O G e V 1.1 0 GcV < E,
OSOCeV<+<
-1
1.05 GeV 1
Pp
1
0
-1
< E. < 1.25 GeV
< 1.30 GeV
0
1
1MGeV
< E, < 1.60 GeV
-1
1.25 GeV < E. < 1.45 GeV
0.3 0.6
04 03
04
-1
1.45 GeV < E,
1
0.3
1
0
1 60GeV
< E, C 2 . W G e V
0
< 2.00 GeV
2.00 GeV < 5 < 2.60 GeV
1
-1
0
1
cos(0~) 2.00 GeV < E. < 2.60 GeV
1-1
._.
0.8
0.6
03
0
0
43 4d -0.6
.03 &Id 4.6
-0.3
-0.3
1
\ \
4.6
.
1
1
0
1
0
1
.I
0
1
1
0
cos(02) Figure 5. New SAPHIR data l6 on polarizations PA and P E o for the reactions y p K + A and y p -+ K + C o . Two different methods were used in the analysis 16.
-+
for understanding the reaction mechanism and t o test the presence of baryon resonances. There is special interest in such resonances, which are predicted in quark models but are undiscovered so far.
5. X p h o t o p r o d u c t i o n on the proton
Because of the suggestion of the missing resonance Ols(1895) t o be contributing to the reaction yp t K + A the main interest in kaon photoproduction was concentrated on this channel. But the huge amount of data on C photoproduction in the channels yp + K+Co and yp t K°C+ is striking as well. The latter are useful for coupled channels analyses since isospin symmetry can help to fix model parameters (compare Fig. 2) instead of doing single channel analysis only. Moreover, the data on yp t K+Co and yp t K°C+ seem to provide interesting information about contributing A resonances. Isobar model calculations for yp + K+Co based on previous SAPHIR data512' state that the bump in the total cross section of yp t K+Co at E-, = 1.45 GeV could stem from the A resonances S31(1900) and P31(1910). The existence of a A-resonance S31(1900) are not able to predict should be of great interest, since quark models LIKE A-resonances with negative parity around a mass of 1900 MeV. So the question arises, if one is able to extract clearly such a state out of the C photoproduction data. A combined analysis of Co and C+ production data should be helpful to this as is discussed in3'.
123
cOMPARISON WITH MODELS 0.8 0.0 02 0.4
by Mart. & Bennhold 1%C 6 1 0 1221)1
02 4.4 4 -0.0 .8
.e
0.8
i
0.8
................
0.0
1
-
without D,,(1960)
with ~ ~ ~ ( 1 9 6 0 )
hy Jansuei~ct ni' I'KC 63 01320'1
A) Small cut-off mass B) A* in u-channel C)No restriction on gKYp
COSO,
Currently, no models reproduce our data, perfcctly.
The figure is taken from ". Beam polarization asymmetries for the reactions and yp + K+Co as a function of c o s ( 0 S T ) for different photon energy and by Janssen et al. bins. Theoretical predictions using the KAON-MAID program are compared with the experimental data. Figure 6.
yp
+ K+A
6. Elect roproduct ion
A huge data base on kaon electroproduction is provided by JLAB. Data on structure functions are given for UT E L U L , E U T T and ~ ~ O L Induced T . and transferred hyperon polarizations and beam asymmetries were already measured. Additional data takings especially with polarized beam and target are still going on. For details see the JLAB homepage (http://www.jlab.org).
+
7. Summary The past years brought us a huge amount of data on cross sections and polarization observables for photon- and electron-induced production of kaon-hyperon pairs. Together with new data still t o come this will lead towards a better understanding of electromagnetic kaon production. The combination of soon available photoproduction data on the proton and the neutron in coupled channels approach will be very helpful to extract resonance parameters and other model ingredients. Electroproduction data will help t o disentangle the different background contributions from each other and from resonance contributions because they provide in addition the different Q2 dependence of these contributions and the additional longitudinal degree of freedom for the photon polarization. After fixing the mod-
124
els it might be possible to extract the kaon form factor as well. Acknowledgments
It is a pleasure for me to thank the organizers for their kind invitation to this very nice and fruitful conference. I enjoyed the discussions with many of the participants. References
1. R. A. Adelseck, B. Saghai, Phys. Rev. C42, (1990). 2. W. J. Schwille et al. (The SAPHIR Collaboration): Nuclear Instruments and Methods in Physics Research 1994, A344, 470-486 (1994). 3. M. Q. Tran et al. (The SAPHIR Collaboration): Phys. Lett. B445, 20-26 (1998). 4. S. Goers et al. (The SAPHIR Collaboration): Phys. Lett. B464, 331-338 (1999). 5. C. Bennhold, T. Mart, A. Waluyo, H. Haberzettl, G. Penner, T. Feuster, U. Mosel: Preprint nucl-th/9901066. 6. T. Mart and C. Bennhold: Phys. Rev. C 61, (R)012201 (2000). 7. C. Bennhold, H. Haberzettl, T. Mart: Proceedings of the Second International Conference on Perspectives in Hadronic Physics, edited by Sigfrido Boffi, Claudio Ciofi degli Atti & Mauro Giannini (World Scientific, 1999); Preprint nucl-th/9909022 8. C. Bennhold, A. Waluyo, H. Haberzettl, T. Mart, G. Penner, U. Mosel: Preprint nucl-th/0008024 9. Aachen-Berlin-Bonn-Hamburg-Heidelberg-Munchen Collaboration, Phys. Rev. 188, 2060 (1969). 10. S. Capstick, W. Roberts: Phys. Rev. D58,074011 (1998). 11. U. Loring, B. Ch. Metsch, H. R. Petry: Eur. Phys. J. A10, 395 (2001). 12. S. Janssen, J . Ryckebusch, W. Van Nespen, D. Debruyne, T. Van Cauteren: Eur. Phys. J . A l l , 105 (2001). 13. S. Janssen, J. Ryckebusch, D. Debruyne, and T. Van Cauteren: Phys. Rev. C65, 015201 (2001). 14. B. Saghai: Preprint nucl-th/0105001. 15. G . Penner and U. Mosel: Phys. Rev. C66, 055212 (2002). 16. K.-H. Glander et al. (The SAPHIR Collaboration): Eur. Phys. J . A19, 251 (2004). 17. J. W.C. McNabb, R. A. Schumacher, L . Todor, et al. (CLAS Collaboration), Phys. Rev. C69 042201(R) (2004) J. W.C. McNabb, Ph.D. Thesis, Carnegie Mellon University (2002) (unpublished). Data are available at www.jlab.org/Hall-B/general/clas-theskhtml. 18. R. G. T. Zegers, M. Sumihama et al. (The LEPS Collaboration): Phys. Rev. Lett. 91, 092001 (2003). 19. C. Bennhold et al.: Nucl. Phys. A639, 209c (1998). 20. see MAID-2000 on http://www.kph.uni-mainz.de; KAON-MAID is based on: Kaon photoproduction: F.X. Lee, T. Mart, C. Bennhold, H. Haberzettl, L.E.
125 Wright , nucLth/9907119 Kaon electroproduction: C. Bennhold et al., nucl-th/9909022 21. K.-H. Glander (SAPHIR Collaboration): Proceedings of the International Symposium SENDAIO3 on the Electrophoto-production of Strangeness on Nucleons and Nuclei, edited by K. Maeda, H. Tamura, s.-N. Nakamura & 0. Hashimoto (World Scientific, 2004) 22. R. Lawall et al. (The SAPHIR Collaboration): publication on y p + K°C+ in preparation. 23. See e.g. W. Thirring: Acta Physica Austriaca Sup. I1 (1966). 24. E. Paul: Italian Phys. Society 1992, Vol. 44, Proc. of the Conference on THE ELFE PROJECT, Mainz 1992, p. 379. 25. K. Heller: Proc. of the 9th International Symposion on High Energy Spin Physics, Bonn 1990, Springer ISBN 3-540-54127-6. 26. Th. A. DeGrand and H. Miettinen: Phys. Rev. D24, 2419 (1981). 27. M. D. Mestayer (CLAS Collaboration): Proceedings of the International Symposium SENDAI03 on the Electrophoto-production of Strangeness on Nucleons and Nuclei, edited by K. Maeda, H. Tamura, S.-N. Nakamura & 0. Hashimoto (World Scientific, 2004). 28. M. Sumihama (LEPS collaboration): Talk given at the International Symposium SENDAI03 on the Electrophoto-production of Strangeness on Nucleons and Nuclei 29. S. Janssen, J. Ryckebusch, D. Debruyne, T. Van Cauteren: Phys. Rev. C 66, 035202 (2002) 30. K.-H. Glander (SAPHIR Collaboration): Proceeding of the VIII International Conference on Hypernuclear 0 Strange Particle Physics HYP2003, to be published in Nuclear Physics A.
Role of the Baryon Resonances in the and K + Photoproduction Processes on the Proton B. SAGHAI DAPNIA, DSM, CEA/Saclay, 91 191 Gif-sur- Yvette, France E-mail:
[email protected] r Very recent q and K+ photoproduction data on the proton from threshold up t o EPb % 2.6 GeV are interpreted within a chiral constituent quark formalism, which embodies all known nucleon and hyperon resonances. Possible contributions from an additional Sil resonance are presented.
1. Introduction Recent experimental and theoretical investigations on the photoproduction of mesons' are providing us with new insights into the baryon spectroscopy. The present manuscript is devoted to the interpretation of the processes
Y P -+ 17 P K + A .
(1)
7
Those reactions have been widely studied via Effective Lagrangian Approaches (ELA) for both ~ p m e s o n ~and ' ~ ~kaon6>7)8y9710 ~>~ channels. Such studies, often based on the Feynman diagrammatic technique and embodying s-,u-, and t-channel exchanges, have produced various models differing mainly in their content of baryon resonances. The number of exchanged particles dealt with in those isobaric models is limited" by the number of related free parameters, which increases rapidly from 1 to 5 per resonance", in including resonances with spin >3/2. Given the large number of known resonances (see Table l),such a shortcoming renders those phenomenological approches i n a p p r ~ p r a i t e 'in ~ the search for new baryon resonances predicted by various QCD-inspired formalism^'^. The latter topic is of special interest in the present work. The content of our chiral constituent quark approach, based on the broken SU(6) 8 O ( 3 ) symmetry, is outlined in the next Section. Comparisons between our models and data are reported in Section 3 and concluding remarks are given in Section 4. 2. Theoretical Frame
The starting point of the meson photoproduction in the chiral quark model is the low energy QCD Lagrangian''
L: = T,J [~'(ia'
+ V' + Y~A') - m] + . . . $J
126
(2)
127
Table 1. Daryon resonances from rDG [13], with mass tations are
respectively.
+
where )t is the quark field in the S U ( 3 ) symmetry, V P = (Eta,< [aP
in which the pseudoscalar mesons, 7r, K , and q, are treated as Goldstone bosons so that the Lagrangian in Eq. (2) is invariant under the chiral transformation. Therefore, there are four components for the photoproduction of pseudoscalar mesons based on the QCD Lagrangian,
where N i ( N f )is the initial (final) state of the nucleon, and w(wm) represents the energy of incoming (outgoing) photons (mesons). The pseudovector and electromagnetic couplings at the tree level are given
128 respectively by the following standard expressions:
The first term in Eq. (4) is a seagull term. The second and third terms correspond to the s- and u-channels, respectively. The last term is the t-channel contribution and is excluded here due to the duality hypothesis17. The contributions from the s-channel resonances to the transition matrix elements can be written as
with k = llcl and q = IqI the momenta of the incoming photon and the outgoing meson respectively, f i W the total energy of the system, e - ( k 2 + q 2 ) / 6 a E o a form factor in the harmonic oscillator basis with the parameter a:, related to the harmonic oscillator strength in the wave-function, and MN* and r(q) the mass and the total width of the resonance, respectively. The amplitudes AN*are divided into two parts'': the contribution from each resonance below 2 GeV, the transition amplitudes of which have been translated into the standard CGLN amplitudes in the harmonic oscillator basis, and the contributions from the resonances above 2 GeV treated as degenerate. The contributions from each resonance is determined by introducinglg a new set of parameters C N ' , and the substitution rule d" + CN. AN', so that MZf = C&.M&T;with M F f the experimental value of the observable, and M&T calculated in the quark model18. The SU(6) 8 O(3) symmetry predicts CN. = 0.0 for S11(1650), D13(1700), and Dls(1675) resonances, and CN* = 1.0 for other resonances in Table 2. Thus, the coefficients CN* measure the discrepancies between the theoretical results and the experimental data and show the extent t o which the S U ( 6 )8 O(3) symmetry is broken in the process investigated here. One of the main reasons that the SU ( 6) 8 O ( 3 ) symmetry is broken is due to the configuration mixings caused by the one-gluon exchange2'. Here, the most relevant configuration mixings are those of the two S11 and the two Dl3 states around 1.5 to 1.7 GeV. The configuration mixings can be expressed in terms of the mixing angle between the two SU(6) 8 O(3) states I N ( 2 P ~>) and p y 4 P ~>,) with the total quark spin 1 / 2 and 312. To show how the coefficients CN. are related to the mixing angles, we express the amplitudes d N * in terms of the product of the photo and meson transition amplitudes d N * CX< NIHmJN*>< N*IHelN
>,
(8)
where H m and He are the meson and photon transition operators, respectively. For example, for the resonance S11(1535) Eq. (8) leads t o
129 Table 2. Nucleon resonances with A4 5 2 GeV and their assignments in SU(6) @ O(3) configurations, masses, and widths. States Mass Width
1.650
0.150
1.520
0.130
1.700
0.150
1.675
0.150
1.720
0.150
1.680
0.130
1.440
0.150
1.710
0.100
1.900
0.500
2.000
0.490
Then, the configuration mixing coefficients can be related to the configuration mixing angles
3. Results and Discussion 3.1. 17-photoproduction channel
we have fitted all z 650 data points from recent measurements for both differential cross-sections21720310 and single polarization a s y m m e t r i e ~ ~The ~ . adjustable parameters of our models are the q N N coupling constants and one SU(6) 8 O(3) symmetry breaking strength coefficient ( C p) per resonance, except for the resonances s11(1535) and s11(1650) on the one hand, and 013(1520) &3(1700) on the other hand, for which we introduce the configuration mixing angles 0 s and 6 0 . The first model includes explicitly all eleven known relevant resonances, mentioned above, with mass below 2 GeV, and the contributions from the known excited resonances above 2 GeV for a given parity. assumed to be degenerate and hence written in a compact form1*. In Fig. 1, we compare this model (dashed curves) to the data at nine incident photon energies. As shown in our earlier w ~ r k s ~such ~ , a~model ~ , reproduces correctly the data at low energies ( E p b 5 1 GeV). Above, the model misses the data. A possible reason for these theory/data discrepancies could be that some yet unknown resonances contribute to the reaction mechanism. We have investigated possible r81e played by extra 4 1 , P11, and
130
0.0 ' ~ ~ ~ ~ " ~ ~ ' " ' " ' " -1.0 -0.5 0.0 0.5 -1.0
"
'
~
-0.5
~
~
~
0.0
'
"
'
'
0.5
"
"
"
-1.0
'
~
~
-0.5
~
UJ
--
~
'
0.0
'
'
"
'
0.5
'
'
"
'
1.0
cos(0,) Figure 1. Differential cross section for the process y p + q p : angular distribution at nine incident photon energies ( E Y b ) ,with the corresponding total center-of-mass energy (W) also given; units are in GeV. The dashed curves are from the model embodying all known three and four star resonances. The full curves show the model including, in addition, a new S11 resonance, with M=1.780 GeV and r=280 MeV. CLAS (circles) and GRAAL (stars) data are from Refs. [23] and [22], respectively. Pi3 resonances, with three free parameters (namely the resonance mass, width, and strength) in each case. By far, the most significant improvement was obtained by a third ,911 resonance, with the extracted values M=1.780 GeV and r=280 MeV. The configuration mixing angles came out to be 8S=1Zo and 8 ~ = - 3 5 " ,in agreement with the Isgur-Karl model2' and more recent prediction^^^. The outcome of this latter model is depicted in Fig. 1 (full curve) and shows very reasonable agreement with the data, improving the reduced x2, on the complete data-base] by more than a factor of 2.
3.2. Associated strangeness photoproduction channel
The above formalism has also been used to investigate all 1640 recent data points on the differential cross sections26y27 for the y p -+ K+R reaction. The adjustable parameters here are the K Y N coupling constant and one SU(6)@0(3)symmetry
'
"
"
~
131 Table 3. Summary of models (a) to (e). Model
Data
# of data points
a b
JLab & SAPHIR JLab JLab SAPHIR SAPHIR
1640 920 920 720 720
C
d e
Reduced x2 3.7 3.0 1.6
3Td s 1 1
M=1.852 GeV ; r=187 MeV
2.1
1.4
M=1.835 GeV ; r=246 MeV
breaking strength coefficient (CjvB) per nucleon resonance, as in the case of the rpchannel (Table 2). Other nucleon resonances and all hyperon resonances in Table 1 are included in a compact forrnl8 and bear no free parameters. Figures 2 and 3 show our preliminary results for three excitation functions at 0 g M = 31.79', 56.63", and 123.37' as a function of total center-of-mass energy ( W ) . The choice of the angles is due to the published data by the JLab groupz6. Given the significant discrepencies between the two data sets, the minimization procedure was performed as follows:
(4
Both data sets were fitted simultaneously, leading to curve (a) in figures 2 and 3.
(ii) Data sets from JLabZ6 and SAPHIR27 were fitted separately. The curve (b) in Fig. 2 is obtained by fitting only the JLab data, while the curve (d), Fig. 3, comes out from a fit only on the SAPHIR data. (iii) The curves (a), (b), and (d) correspond to models embodying all known resonances. At this stage, a third S11 resonance was introduced, in line with the 7 case. With this additional resonance, the data from JLab and SAPHIR were fitted seperately and the outcomes are the curves (c) and (e) in Figs. 2 and 3, respectively. The model (a) gives a reduced x2 of 3.7 (Table 3). Adding a third 5'11 resonance, improves it slightly (x2=3.5). However, fitting separately each set of data, shows a significant sensitivity to the introduction of a third S11 resonance. Due to this latter new resonance, for the JLab data the x2 goes from 3.0 to 1.6, and for the SAPHIR data it gets reduced from 2.1 to 1.4. We notice that in both cases, the SAPHIR data are better reproduced within our approach. 3.3.
New
S11 resonance
Several authors17~28i29~30~31,32,33~34 have reported on a third S11 resonance with a mass around 1.8 GeV (see Table 4). Our chiral constituent quark approach applied to the y p -+ qp,K+R reactions puts the mass in the range of 1.780 to 1.852 GeV and the width between 187 and 280 MeV. This dispersion is, at least partly, due to the discrepancies among data reported by different collaborations. The extracted values for the mass and width from the yp + q p process are consistent with those predicted by the authors of Ref.zg (M=1.712 GeV and r=184 MeV), and our previous findings17. Moreover, for the one star &1(2090) resonance" the Zagreb group T N and q N coupled channel analysis3' produces
132 I
'
I
'
I
0
SAPHIR
'
I
'
I
T
I - '
0.4 0.2 0.0 n
a3.$ 00.2.3 W
G
5
On1
'EI 0.0
I
I
I
I
I
I
I
I
0.2 0
I
JLab Q 123.4 deg. SAPHIR
0.1
0.0 1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
W (GeV) Figure 2. Differential cross section for the process y p + K + A as a function of total center-of-mass energy (W) in GeV. All the curves embody all known resonances. The dashed curve (a) is from a fit to data from both JLab [25] and SAPHIR [26]. The dotted curve (b) is obtained by fitting only JLab data. The full curve (c) corresponds to this latter data set with an additional Sll resonance.
the following values M = 1.792 f 0.023 GeV and I? = 360 f 49 MeV. The BES Collaboration reported31 on the measurements of the J / $ -+ ppq decay channel. In the latter work, a partial wave analysis leads to the extraction of the mass and width of the Sll(l535) and Sll(l650) resonances, and the authors find indications for an extra resonance with M = 1.800 f 0.040 GeV, and r
133
0.4 0.2 0.0 n
2
0.3
W =f.
0.2
ca
0.1
3 \
0
t3
'CJ 0.0
I
0.2
I,
T -
SAPHIR
I
I
I
I
I
JLab Q 123.4 deg. Q
SAPHIR
0.1 0.0 1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
W (GeV) Figure 3. Same as Fig. 2, except for curves (d) and (e). The dotted curve (d) is obtained by fitting only SAPHIR data. The full curve (e) corresponds to this latter data set with an additional Sll resonance.
= 1 6 5 ~ MeV. ~ ~ 5 A more recent work32 based on t h e hypercentral constituent quark model, predicts a missing 5'11 resonance with M=1.861 GeV. Finally, a self-consistent analysis of pion scattering and photoproduction within a coupled channel formalism, i c o n c l ~ d e son ~ ~t h e existence of a third S11 resonance with M =1.803 f 0.007 GeV.
134
Table 4. Summary of studies on a 3Td S11 resonance. Mass
(GeV) 1.780 1.835 1.852 1.730 1.792 1.800 1.861 1.846
Width (MeV) 280 246 187 180 360 165
Comment CQM applied t o y p + q p CQM, applied to y p + K + A data from SAPHIR CQM, applied to y p + K + A data from JLab K Y molecule TN and qN coupled-channel analysis J / q decay Hypercentral CQM Pion photoproduction coupled-channel analysis
Ref. Sec. 3.1 Sec. 3.2 Sec. 3.2
28;
29 30 31 32 33
4. Summary and Concluding remarks
In this contribution, the results of a chiral constituent quark model have been compared with the most recent published data on the yp -+ qp, KfA processes, with emphasize on a third S11 resonance. Our results are consistent with findings by other authors29130,31,32~33, showing evidence for such a new resonance, with M ~ 1 . GeV 8 and l? ~ 2 5 MeV. 0 In the case of the q photoproduction channel, we need to extend our analysis to the very recent data from ELSA13. The associated strangeness production channel suffers at the present time from discrepancies between the two copious data set from JLab and SAPHIR. New data from GRAAL will hopefully provide us with a better vision of the experimental situation. Within our approach, a more comprehensive interpretation of the K'A channel is underway with respect to the polarization o b ~ e r v a b l e s as well as to the o b ~ e r v a b l e s of ~ ~the ' ~ y~p -+ K+Co. To go further, the coupled channel effects37338339j40,41,42 have to be considered. The effect of the multi-step process y p + .rrN + K + A has been reported4' to be significant at the level of inducing 20% changes on the total cross section of the direct channel (yp + K'A). The dynamics of the intermediate states 7rN -+ K Y , as well as final states interactions K Y -+ K Y , with Y A, C have been recently studied41 within a dynamical coupled-channel model of mesonbaryon interactions. Those efforts deserve to be extended to the multi-step processes y p + 7 r ~ + q p , K+A , K + c O , KOC+, and also embody the final state interactions. It is a pleasure for me to thank K.H. Glander and R. Schumacher for having provided me with the complete set of SAPHIR and JLab data, respectively, prior to publication. I am indebted to my collaborators W.T. Chiang, C. Fayard, T.-S. H. Lee, Z. Li, T. Mizutani, and F. Tabakin.
135 References 1. See e.g. W.J. Briscoe, R.A. Arndt, 1.1. Strakovski, R.L. Workman, nucl-
ex/0310003. 2. N.C. Mukhopadhyay, J. F. Zhang, and M. Benmerrouche, Phys. Lett. B3, 1 (1995); M. Benmerrouche, N.C. Mukhopadhyay, J. F. Zhang, Phys. Rev. D51, 3237 (1995); N.C. Mukhopadhyay, N. Mathur, Phys. Lett. B444, 7 (1998); R.M. Davidson, N. Mathur, N.C. Mukhopadhyay, Phys. Rev. C62, 058201 (2000). 3. W.-T. Chiang, S.N. Yang, L. Tiator, D. Drechsel, Nucl. Phys. A700, 429 (2002); W.-T. Chiang et al., Phys. Rev. C68, 045202 (2003). 4. V.A. Tryasuchev, Phys. Atom. Nucl. 65, 1673 (2002). 5. I.G.Aznauryan, Phys. Rev. C68, 065204 (2003). 6. S.S. Hsiao, S.R. Cotanch, Phys. Rev. C28, 1668 (1983); R.A. Williams, C.R. Ji, S.R. Cotanch, Phys. Rev. C46, 1617 (1992). 7. R.A. Adelseck, C. Bennhold, L.E. Wright, Phys. Rev. C32, 1681 (1985); T. Mart, C. Bennhold, Phys. Rev. C61, 012201 (2000). 8. R.A. Adelseck, B. Saghai, Phys. Rev. C42, 108 (1990); J.C. David, C. Fayard, G.H. Lamot, B. Saghai, Phys. Rev. C53, 2613 (1996). 9. B.S. Han, M.K. Cheoun, K.S. Kim, I-T. Cheon, Nucl. Phys. A691, 713 (2001). 10. S. Janssen, D.G. Ireland, J. Ryckebusch, Phys. Lett. B562, 51 (2003); S. Janssen, J. Ryckebusch, T. Van Cauteren, Phys. Rev. C67, 052201 (2003);
D.G. Ireland, S. Janssen, J. Ryckebusch, nucl-th/0312103. 11. B. Saghai, nucl-th/0310025. 12. M. Benmerrouche, R.M. Davidson, N.C. Mukhopadhyay, Phys. Rev. C39, 2339 (1989); T. Mizutani, C. Fayard, G.H. Lamot, B. Saghai, Phys. Rev. C58, 75 (1998). 13. K. Hagiwara et al., Particle Data Group, Phys. Rev. D66, 010001 (2002). 14. B. Saghai, nucZ-th/OlO5001. 15. See e.g. S. Capstick, W. Roberts, Prog. Part. Nucl. Phys. 45, 5241 (2000);
and references therein; S. Capstick, these proceedings. A. Manohar, H. Georgi, Nucl. Phys. B234, 189 (1984). B. Saghai, Z. Li, Eur. Phys. J . A l l , 217 (2001). Z. Li, H. Ye, M. Lu, Phys. Rev. C56, 1099 (1997). Z. Li, B. Saghai, NucZ. Phys. A644, 345 (1998). N. Isgur, G. Karl, Phys. Lett. B72, 109 (1977); N. Isgur, G. Karl, R. Koniuk, Phys. Rev. Lett. 41, 1269 (1978). 21. B. Krusche et al., Phys. Rev. Lett. 74, 3736 (1995). 22. F. Renard et al. (The GRAAL Collaboration), Phys. Lett. B528, 215 (2002). 23. M. Dugger et al. (The CLAS Collaboration), Phys. Rev. Lett. 89, 222002
16. 17. 18. 19. 20.
(2002). 24. A. Bock et al., Phys. Rev. Lett. 81, 534 (1998); J. Ajaka et al., ibid 81,1797 (1998). 25. He Jun, Dong Yu-bing, Phys. Rev. D68 017502 (2003); J . Chizma, G. Karl, ibid D68 054007 (2003). 26. J.W.C. McNabb et al. (The CLAS Collaboration), Phys. Rev. C69, 042201
136
(2004). 27. K.H. Glander et al. (The SAPHIR Collaboration), Eur. Phys. J. A19, 251 (2004); K.H. Glander, these proceedings. 28. B. Saghai, Z. Li, nucl-th/0305004. 29. Z. Li, R. Workman, Phys. Rev. C53, R549 (1996). 30. A. Svarc, S. Ceci, nucl-th/00090.24;A. Svarc, these proceedings. 31. J.-Z. Bai et al., Phys. Lett. B510, 75 (2001). 32. M.M. Giannini, E. Santopinto, A. Vassallo, nucl-th/O30.2019. 33. G.-Y Chen, S. Kamalov, S.N. Yang, D. Drechsel, L. Tiator Nucl. Phys. A723, 447 (2003); S. Kamalov, these proceedings. 34. V.A. Tryasuchev, Phys. Atom. Nucl. 67, 427 (2004). 35. V. Cred6 et al., (CB-ELSA Collaboration), hep-e~/0311045. 36. R.T.G. Zegers et al. (The LEPS Collaboration), Phys. Rev. Lett. 91, 092001 (2003). 37. J. Car0 Ramon, N. Kaiser, S. Wetzel, W. Weise, Nucl. Phys. A672, 249 (2000). 38. J.A. Oller, E. Oset, A. Ramos, PTOg. Part. Nucl. Phys. 45,157 (2000). 39. G. Penner, U. Mosel, Phys. Rev. C66, 055212 (2002). 40. W.-T Chiang, F. Tabakin, T.-S. H. Lee, B. Saghai, Phys. Lett. B517, 101 (2001). 41. W.-T Chiang, B. Saghai, F. Tabakin, T.-S. H. Lee, nucl-th/0404062, to appear in Phys. Rev. C. 42. T.-S. H. Lee, these proceedings.
SI1Resonances in
7r
and q Channels”
, DIETER DRECHSElL AND LOTHAR TIATOR Institut f u r Kernphysik, Universitat Mainz, 55099 Mainz, Germany
SABIT KAMALOVb
GUAN-YEU CHEN AND SHIN NAN YANG Department of Physics, National Taiwan University, Taipei, Taiwan 10764, Republic of China A self-consistent analysis of pion scattering and pion photoproduction within a coupled channels dynamical model is presented. The results indicate the existence of a third and a fourth 5’11 resonance with the masses 1846 f 47 and 2113 & 70 MeV. In the case of pion photoproduction, we obtain background contributions to the imaginary part of the S-wave multipole which differ considerably from the result based on the K-matrix approximation. Within the dynamical model these background contributions become large and negative in the region of the ,911 (1535) resonance. Due to this fact much larger resonance contributions are required in order to explain the results of the recent multipole analysis. For the first ,911 (1535) resonance we obtain as a value of the electromagnetic helicity amplitude: A l l z = 72 f 2 x 10-3GeV-1/2.
1. Introduction
At present t h e resonance properties are extracted mainly from 7rN scattering, 27r a n d 7 production and pion photoproduction using different approaches (for details see Refs. 1 , 2 , 3 , 4 ) . T h e first coupled channel analysis t h a t combines pion a n d e t a d a t a was done in Ref. within t h e isobar model. Later, more sophisticated models were developed which account for background contributions. Most of t h e m are based o n t h e solution of coupled-channels equations by use of t h e K-matrix approximation, i.e., by ignoring off-shell intermediate scattering states. O n t h e other hand, in t h e analysis of pion scattering a n d pion photoproduction within dynamical models 5,6,7,t h e off-shell dynamics (i.e., t h e dynamics at short distance) is taken into account. Within this framework we have recently developed a meson-exchange (MEX) model for pion-nucleon scattering which gives good agreement with t h e data u p t o 400 MeV pion lab energy. In addition, we have also constructed a dynamical model for pion electromagnetic production 9 J 3 which aThis work is supported in part by the National Science Council/ROC under grant NSC 90-2112-M002-032, by the Deutsche Forschungsgemeinschaft (SFB 443), and by a joint project NSC/DFG TAI-113/10/0 bPermanent address: Laboratory of Theoretical Physics, JINR Dubna, 141980 Moscow region, Russia.
137
138 describes well the no photo- and electro-production data near threshold l1 and most of the existing data up to the second resonance region. Recently we extended our meson-exchange .rrN model in the S11 channel up to 2 GeV by explicitly introducing a set of S11 resonances into the model 12. The results are then fed into the pion photoproduction model to analyze the existing multipole. The Sll channel is of interest for several reasons. First of all, the first resonance S11(1535), which lies very close to the qN threshold, has a remarkably large q N branching ratio. This necessitates the inclusion of the QN channel into our MEX .rrN model. Secondly, the analysis based solely on pion photoproduction always underestimate the A l p helicity amplitude of &1(1535) with a value around 60 x 10-3GeV-1/2, while extractions from the ( 7 , ~data ) give a value close t o and above 100 x 10-3GeV-1/2 13. Lastly, there have been suggestions l 4 > l 5that there could exist a third S11 resonance in the neighborhood of 1800 - 1900 MeV, in addition t o the well-known resonances at 1535 and 1650 MeV. A consistent analysis of both T N scattering and pion photoproduction reactions can shed new light on the mentioned issues concerning helicity amplitudes and higher resonances. 2. T N scattering
Our basic equation is
where i and j denote the .rr, or q channel and E = W is the total center mass energy. Eq. (1) is a system of three dimensional coupled integral equations which is derived from the four dimensional Bethe-Salpeter equation using a threedimensional reduction scheme with a corresponding relativistic propagator, g k , for the free IcN system (Ic = .rr, or q). In general, the potential uij is a sum of non-resonant (u;) and bare resonance (v$) terms,
The non-resonant term v,”, for the T N elastic channels contains contributions from the s- and u-channel Born terms and t-channel contributions with p, and u exchange. The parameters in v,”, are fixed from the analysis of the pion scattering phase shifts for the s- andp-waves at low energies (W < 1300 MeV). In channels involving the eta, u g is taken to be zero because of the small qNN coupling 16. In the case with only one resonance contributing in the S11 channel the bare resonance contribution, uG(E), can be symbolically expressed in the form of
139 where 4 and 4’ are the pion (or eta) momenta in the initial and final states, 9 (0) . . 43)
and M(O) are the bare resonance vertex couplings and bare mass, respectively, are form factors which depend on cut-off parameters, hi(j).We refer the readers to Ref. for details. In Eq. (3) we have added a phenomenological term rPa(E)in the resonance propagator in order to take into account the decay of the resonance into the mrN channel. Therefore, our resonance propagator is not purely ”bare” but includes renormalization (or ”dressing”) effects due to the coupling with the ~ T channel. N This term is parameterized in the same way as in Ref. 17. In the channel of interest, 4 1 , there are two well-known four-star resonance states, s11(1535) and S11(1650), and one one-star resonance, &1(2090). In the Hypercentral Constituent Quark Model l4 a third and a fourth S11 resonance with energies 1860 and 2008 MeV were predicted. The generalization of our coupled channels model for multiple resonances with the same quantum numbers is straightforward, namely
ficj)
*
with additional parameters for the bare masses, ~ T decay N widths, coupling constants and cut-off parameters for each resonance. We first start with the analysis of Re t i j and Im t i j for pion scattering and eta production in the energy range 1100 MeV < W < 1750 MeV where the Sll(l535) and S11(1650) resonances are very pronounced. The results of our best fit of txa in this energy range with only these two resonances included are shown in Fig. 1 by the dotted curves. We are not able to improve our results in the region W > 1800 MeV without additional 4 1 resonances. Next we extend the energy range up to W = 2000 MeV and add a third resonance with the parameters for the first resonance fixed as obtained above. Our results for this case are shown by the dash-dotted curves, which correspond to a bare mass of the third S11 resonance M i o ) = 1901 MeV. We find that this value is very stable and changes only within 2% if the energy range is increased up to 2200 MeV. However, this does not remove the remaining discrepancy, in particular for the imaginary part at W > 2000 MeV. We find that the only way to improve the agreement with the data in this energy range is to introduce a fourth resonance. Our final fit results with four 5’11 resonances are shown by the solid lines in Fig. 1. The obtained value for the bare mass of the fourth ,911 resonance is M i o ) = 2160 MeV. Note that in Fig. 1 the background contributions (dashed curves) are defined by the equation
which are hereafter called the ”nonresonant background, i.e., the background with nonresonant rescattering. In the following Fig. 2 we show our results for the t-matrix of the TN -+ T$V reaction in the S11 channel, which clearly indicate the presence of the 77 decay mode in the second and third S11 resonances.
140 0.50
1.0
0.8
0.25
0.6
0.00 0.4
-0.25
-0.50
1000
0.2 1300
1600 W (MeV)
1900
2200
0.0 1000
1300
1600 W(MeV)
1900
2200
Figure 1. Real and imaginary parts of the 5'11 pion scattering amplitude. Dashed curves: nonresonant background contribution ffr. Dotted, dash-dotted, and solid curves: total t,, amplitude obtained after the best fit with two, three, and four S11 resonances, respectively. Data points: results of the single energy analysis from Ref. 1 8 .
0.4 0.3 0.2 0.1 0.0
-0.1 -0.2 -0.3 -0.4 1400
1600
1800 W(MeV)
2000
0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3 -0.4 2200 1400
1600
1800 W (MeV)
2000
2200
Figure 2. Real and imaginary parts of the S11 amplitude for the .rrN --f 7 N reaction. Dashed, dash-dotted, and solid curves are the results obtained with R1, R1 Rz, and Ri R2 R3 contributions, respectively. We did not find evidence for a fourth S11 in this reaction. Data points: results of the partial wave analysis from Ref. 3 .
+ +
+
Our final results for the obtained resonance parameters are summarized in Table 1. Here we also compare with the results of the GW-Giessen collaboration, Pitt-ANL collaboration and Kent State University (KSU) group, taken from Ref. '.
141 Table 1. S11 resonance parameters obtained from nN scattering and n N + q N reaction, and comparison with the results of the Pitt-ANL, KSU and GW-Giessen groups taken from Ref. 4. Recent PDG values from Ref. 13.
I
R2
Ri
1520(6) 1542(3) 1528(1) M R (MeV) 1549(7) 1520-1555 95(10) 112(19) 111(9) r R (MeV) 232(19) 100-200 40(7) 35(5) rTirR(qlo) 41(3) 30(1) 35-55 40(7) 51(5) 50(4) rl)/rR (%) 63(3) 30-55
1677(6) 1689(12) 1649(1) 1690(11) 1640-1680 195(14) 202(40) 108(14) 206(13) 145-190 75(4) 74w 32(5) 60(7) 55-90 W3) 6(1)
5(3) 11(1) 3-10
R3 1893(18) 1822(43) 2000(1) -2090 265(31) 248(185) 132(16) -
R4
2183(21) __ __
427(26) -
__
__ __ __
44(5)
43(2)
17(7)
10(3) __ __
12(7) 41(4) 3(2) __ __
__ __ __ __
3(6)
__ __ __ __
our result Pitt-ANL KSU GW-Giessen PDG2002 our result Pitt-ANL KSU GW-Giessen PDG2002 our result Pitt-ANL KSU GW-Giessen PDG2002 our result Pitt-ANL KSU GW-Giessen PDG2002
3. Pion photoproduction The above analysis of elastic .rrN scattering indicates the existence of four Sll resonances. Let us now check this result by an independent analysis of pion photoproduction using the dynamical model developed in Refs. 6,9923, hereafter called the DMT (Dubna-Mainz-Taipei) model. Concerning the details of the DMT model, we refer the reader t o Ref. The t-matrix for pion photoproduction in the dynamical model is
with %,,k the transition potential for the yN + k N reaction ( k = 7r or q), t k r the full k N scattering t-matrix of Eq. (l), and g k the free k N propagator. If the transition potential wyr consists of two terms,
where v& is the background transition potential and v&(E) the contribution of a bare resonance R, we may decompose the resulting t-matrix into two terms t , x ( E ) = t?tr?T(E)+t7tr?T(E),
(8)
142 where
In our numerical calculations we have neglected the contribution of the 9 channel in the intermediate states in Eq. (9), because this contribution is found to be much smaller than for the 7~ channels. We further note that all the processes which start with the excitation of the resonance by the bare y N R vertex are summed up in tf,. Using the decomposition of Eqs. (8-10) we can now extract the value of the bare y N R vertex. The corresponding background t& is called ”resonant background since it contains the full pion scattering t-matrix. Note that, for example, in Ref. l 9 the background is defined differently,
where i;, is defined by Eq. ( 5 ) . This definition corresponds to the so-called nonresonant (smooth) background, because it contains none of the resonance contributions. The corresponding resonance term,:i = t,, - $ , describes a resonance with a dressed y N R vertex. The standard physical multipoles in a channel Q = { l , j , I } corresponding to Eq. (9) can be expressed as
where FL:) is the pion-scattering amplitude and M ( q ) the relativistic pionnucleon reduced mass. We mention in passing that the so-called ”K-matrix” approximation, as in the case of MAID 17120 and many other models, neglects the principal value integral in Eq. (12), and parametrizes the background in terms of on-shell pion rescattering only. In this case, the off-shell rescattering associated with the principal value integral contribution is phenomenologically absorbed in the resonance parameters, while in the DMT model it is considered as a part of the background. Therefore, the resonance parts in DMT and K-matrix approach are different: in the DMT model the resonance is described by the amplitude t:, with a bare electromagnetic vertex and, as we will see below, in the models based on the K-matrix approximation, the resonance description is essentially given by with a dressed electromagnetic vertex. Following Ref. 17, we assume a Breit-Wigner form for the resonance contribution tq;Q((W),
it,
143
where f T R is the usual Breit-Wigner factor describing the decay of a resonance R with total width FR(W) and physical mass MR. The expressions for frR, f T ~ and I'R we given in Ref. 17. In the DMT model the electromagnetic form factor Ag describes the bare y N R vertex. This is a free parameter to be determined from the experimental data.
Figure 3. Imaginary parts of the multipoles. Dashed and dash-dotted curves in the left panel: background contributions obtained using K-matrix approximation and DMT model, respectively. Solid curve is the result obtained with two ,911 resonances. Solid curves in the right panel: total multipole with four S11 resonances. The individual contributions from each resonance (with bare electromagnetic vertex) are shown by the dotted curves. The corresponding resonance parameters are given in Table 2. Data points: results of the single energy multipole analysis from Ref. 2 1 .
In Fig. 3 (Ieft panel) we see that the resonant background in the DMT model (dash-dotted curve) is very important, in particular for W > 1450 MeV where it becomes large and negative. This is in contrast to the prediction based on the K-matrix approximation (dashed curve). The difference comes mainly from the principal value integral contribution in Eq. (12). Such a background will thus require a much stronger resonance contribution in order to describe the results of the recent partial wave analysis of Ref. 21. Consequently, the dynamical model predicts much larger values for the electromagnetic form factors (or helicity amplitudes A l l 2 ) than those obtained with the K-matrix approximation. In order to estimate the new values for the resonance parameters, we will first fit Im @o+ in the photon energy range 1075 < W < 2300 MeV only, thereby assuming that = C",=, The results of our fit are presented in Fig. 3 and Table 2. We would like to stress that, since the DMT background is large and negative even at W > 1770 MeV, the best fit requires two new S11 resonances with masses 1800 MeV and 2042 MeV, in addition to the well known resonances s11(1535) and &1(1650). In fact the x2 of the fit improves from 64 to 3.5 by introducing these two additional resonances. This result clearly indicates that, in agreement with our previous findings for pion scattering, our pion photoproduction model calls for a low-lying third S11 resonance which may be one of the missing resonances predicted by quark models 1 4 .
144 Table 2. Estimation of the Sll resonance parameters obtained by fitting Im p E ~ +in the energy range 145 MeV < E, < 2000 MeV (1075 MeV < W < 2300 MeV), with four Sll resonances. In brackets: quark model predictions of Ref. l 4 for the masses M R . Helicity amplitudes A1/2 are given in units lop3 GeV-1/2. Ri Rz R3 R4
0.40 0.75 0.44 0.43
[
1 5 2 3 f 3 (1524) 1677 f 3 (1688) 1799 f 9 (1861) 2042 f 16 (2008)
97f7 116 f 8 314 f 11 288 f 29
110f7 83 f 6 129 f 9 61 f 8
Our final value for the bare helicity amplitude of the first &1(1535) resonance is A112(bare) = 116 f 3 x 10-3GeV-1/2. This value was obtained by analyzing the observables (differential cross sections, beam, target and recoil asymmetries). The dressed value for the All2 can be calculated directly from Im pE,$yz)using well known relations 22. Subtracting the contributions from the nonresonant background (11) and other S11 resonances we obtain A1/2(dressed) = (72 f 2) x 10-3GeV-1/2. Another separation of the resonance and background contributions can be obtained by use of the K-matrix approximation for pion rescattering. In this case the corresponding helicity amplitude AIp(K-matrix)= (67 f 2) x 10-3GeV-1/2, which is very close to the dressed value obtained above. 4. Conclusion
We have performed a self-consistent analysis of pion scattering and pion photoproduction within a coupled channels dynamical model. In the case of pion photoproduction, we obtain background contributions to the imaginary part of the Swave multipole which differ considerably from the result based on the K-matrix approximation. Within the dynamical model these background contributions become large and negative in the region of the Sll(l535) resonance. Due to this fact much larger resonance contributions are required in order to explain the results of the recent multipole analyses. For the first S11(1535) resonance we obtain as values of the bare and dressed electromagnetic helicity amplitudes: Al12(bare) = (116 f3) x 10-3GeV-1/2 and A1/2(dressed) = (72 f2) x 10-3GeV-1/2. Similar bare and dressed values can be derived from eta photoproduction if one takes the same total width ( r R = 95 f 5 MeV) as in pion scattering and pion photoproduction. 1750 MeV, our analysis yields considerable At invariant energies W strength, which can be described by a third and a fourth S11 resonance with the masses 1846 f47 and 2113 f 70 MeV. Such resonances are also predicted by quark models 14.
>
References
1. C. Bennhold and H. Tanabe, Nucl. Phys. A350,625 (1991).
145
2. M. Batinic, I. Slaus and A. Svarc, Phys. Rev. C51, 2310 (1995). 3. T. P. Vrana. S. A. Dytman and T.-S. Lee, Phys. Rep., 328, 181 (2000). 4. Bennhold et al. Proc. of NSTAR2001 workshop, M a i m 2001 , eds D. Drechsel and L. Tiator (World Scientific, 2001), p.109. 5. H. Tanabe and K. Ohta, Phys. Rev. C31, 1876 (1985). 6. S. N. Yang, J. Phys. G11,L205 (1985). 7. S. Nozawa, B. Blankleider and T.-S. H. Lee, Nucl. Phys. A513, 459 (1990); S. Nozawa and T.-S. Lee, Nucl. Phys. A513, 511 (1990). 8. C. T. Hung, S. N. Yang, and T.-S.H. Lee, J. Phys. G20, 1531 (1994); Phys. Rev. C64, 034309 (2001). 9. S. S. Kamalov and S. N. Yang, Phys. Rev. Lett. 83,4494 (1999). 10. S. S. Kamalov, S. N. Yang, D. Drechsel, 0. Hanstein, and L. Tiator, Phys. Rev. C64, 032201(R) (2001). 11. S. S. Kamalov, G.-Y. Chen, S. N. Yang, D. Drechsel, and L. Tiator, Phys. Let. B522,27 (2001). 12. G.-Y. Chen, S. S. Kamalov, S. N. Yang, D. Drechsel, and L. Tiator, Nucl. Phys. A721, 401 (2003). 13. Particle Data Group, Phys. Rev. D66, 010001-1 (2002). 14. M. M. Giannini, E. Santopinto, A. Vassallo, Nucl. Phys. A699, 308 (2002). 15. B. Saghai and Zhenping Li, nucl-th/0202007. 16. L. Tiator, C. Bennhold and S. S. Kamalov, Nucl. Phys. A580, 455 (1994). 17. D. Drechsel, 0. Hanstein, S.S. Kamalov, and L. Tiator, Nucl. Phys. A645, 145 (1999). 18. R. A. Arndt, I. I. Strakovsky, R. L. Workman, and M. M. Pavan, Phys. Rev. C52, 2120 (1995). 19. T. Sato and T.-S.H. Lee, Phys. Rev. C54, 2660 (1996). 20. S. S. Kamalov, D. Drechsel, L. l'iator, and S. N. Yang, Proc. of NSTAR2001 workshop, M a i m 2001, eds D. Drechsel and L. Tiator (World Scientific, 2001), p.197, (s.a.) nucl-th/0106045. 21. R. A. Arndt, W. J. Briscoe, I. I. Strakovsky, and R. L. Workman, Phys. Rev. C66, 055213 (2002). 22. R. A. Arndt, R. L. Workman, Zh. Li, and L. D. Roper, Phys. Rev. C42, 1864 (1990).
Experimental Review on
w
Production
F.J. KLEIN The Catholic University of America, Washington, D C 20064 P.L. COLE Jefferson Lab, Newport News, VA 23606 and Idaho State University, Pocatello, ID 83209 Over the past the three decades, the electro- and photoproduction of omega mesons have been studied predominantly with respect t o diffractive and pion-exchange in the t channel. However, quark model calculations predict a significant coupling of the baryon resonances to the w N channel, where many of the so-called missing baryon resonances are expected t o couple strongly t o both y N and w N . But, due to the overall low cross section and the inherent difficulty in distinguishing N' decay from t-channel processes, the w N channel has not been thoroughly explored. With the advent of high-duty-cycle accelerators and large-acceptance detectors in the 199Os, wp production is increasingly being investigated with respect to departures from diffraction-like behavior in the effort t o extract s-channel contributions using electromagnetic probes.
MODEL CALCULATIONS The first model calculations on w production focused on t-channel exchange processes to describe the dominant features of the w data available in the 1960s and 1970s. In the forward region, the Vector Meson Dominance (VDM) model provides an excellent description of the interaction of high-energetic (transverse) photons with matter. The incident photon dissociates into a virtual qij pair with J x = l - , which then scatters off the target nucleon. The photoproduction of u s comes about through the isoscalar component in diffractive scattering, whereby the quantum numbers of the vacuum (Pomeron) are e ~ c h a n g e d . ' ~However, ~~~>~ when the virtual qij pair is an isovector state, a no must be exchanged to allow for an w meson to appear in the final state.5 The peripheral behavior of w N production at low energies is well described by 7r0-exchangewith a dressed g x w y coupling for the dominant parity odd component (unnatural parity) and u- or f2-exchange for the positive-parity (natural-parity) exchange.6i11>8We note that all models agree that pion-exchange dominates by far the w N channel at low energies. A comparatively good description of vector meson electro- and photoproduction has been obtained by Y. Oh et aL8 This collaboration employs a Regge parameterization for Pomeron exchangeg as well as scalar (a),pseudoscalar ( T ,7) and tensor (fz)-exchange in the t channel and N-exchange in the u channel. Above the resonance region, the model of J.-M. Laget1l1lo affords even a
146
147 better description of the photo- and electroproduction of ws. He makes use of a two-gluon parameterization in Pomeron exchange with Reggeized pseudoscalarand tensor-exchanges and N-exchange in the u channel. SU(6) 8 O(3) symmetric quark models predict a large variety of excited baryon states,l1>l2of which most have not yet been experimentally confirmed or are still poorly established. These models predict comparatively large COUplings of these resonances not only to the y N channel, but also to the q N , AT, p N , and w N channels as well. These latter channels are experimentally mostly terra incognita. Of particular interest are those channels which provide isospin selectivity, such as the qN and the w N reactions, since then only N*s (and not the A*s) may contribute in s-channel processes. Such selectivity greatly simplifies extracting the underlying resonant states. In the relativized quark model of F. Close and Z.P. Li,13 the meson couples as point-like particle to the quark configuration in the baryon. Calculations based on this model by Z.P. Li and Q. Zhao1471511G predict considerable contributions to w N from the subthreshold states s11(1535) and &3(1520). Near threshold, the dominant contributions arise from the F15(1680) and the &(1720). At slightly higher energies, the F15(ZOOO) plays an increasing role and - slightly suppressed - from p13(1900). The model incorporates T exchange - built-in in a consistent way and Pomeron exchange based on Regge phenomenology. The model also includes the nucleon pole, the Roper, as well as seven other resonances in the SU(6) 8 O(3) symmetry limit in s- and wchannel transitions through effective Lagragians for the quark-photon and quark-vector-meson interactions. The model of Y . Oh, A.I. Titov, and T-S.H. Lee' employs N* -+ y N and N* + w N amplitudes, where these amplitudes include configuration mixing effects due to quark-quark interactions. They explicitly include baryon resonances by incorporating Breit-Wigner descriptions and vertex functions provided by the relativized quark model of Capstick and Roberts.12 Whereas for higher E-, Pomeron exchange governs the total and differential cross sections at low Itl, at lower energies pion exchange completely dominates the cross sections for the forward angles. This collaboration predicts that in the resonance region, the dominant contributions arise from the missing P13(1910) as well as the 013(1960) - which is identified with the PDG 013(2080) - and the G17(2190), with lesser contributions from the Fl5(200O). The inclusion of rescattering effects near threshold l7 allows for describing the experimental data at threshold (E-, < 1.25 GeV). Here, the domininant contributions are from the subthreshold resonance 0 1 3 (1520) and the near-threshold resonance Fls(1680). ~
EXPERIMENTAL RESULTS Although the lightest two vector mesons, p and w, have roughly the same mass of 770 MeV and 782 MeV, respectively, they possess very different decay widths," 150 MeV and rW= 8.4 MeV. Without directly detecting the decay prodi.e. I?, ucts, we cannot effectively distinguish these two vector mesons kinematically. At best one will only see a small w peak situated on top of the broad po spectrum obtained from the corresponding invariant or missing mass distributions. For a
-
148 complete understanding of the dynamics, we require models that fit the distributions arising from these two vector mesons, which necessarily must include effects from p-w mixing and the interference of p decay with the s-wave m-background. With high-resolution and large-acceptance detectors, we may experimentally disentangle the w from the p. By directly measuring the decay products in either the w + r + K r o(88.8%)and thew + r o y (8.5%) channels allows one t o unambiguously distinguish the omega vector meson. But there remains the issue of the three-pion or the combinatoric three-y background for statistically extracting the omega signal. Hence experiments with electromagnetic probes for w production must rely on the detector's capability t o resolve multiprong events.
-
1
3 ::; L
Figure 1. ep + e'pw data at Q2=0.5 GeV2 from Hall C (JLab): Angular distributions for different averaged W and for lc$*I < 30° in comparison to DESY data at Q2=0.77 GeV2, W=1.82 GeV. The curves are from model calculation^.^^'^ This figure is from Ref.20
3
*c 0.7
2
0.6 0.5 0.4
0.3 0.2 0.I
0'
20
40
60
80
IW
I20
I40
164
I80
Electroproduction experiments performed with two-arm spectrometers therefore face the difficulty of disentangling p and w mesons." The recent electroproduction data near threshold at Q2=0.5 GeV2 were obtained using the high resolution spectrometers in Jefferson Lab's Hall C.20 The w yield was extracted by means of a maximum likelihood fit, which serves to account for the phase-space background in po and w production. In Fig.1 one sees a significant enhancement of backward production in the data. This behavior indicates large contributions from baryon exchange and is fully consistent with the Li-Zhao model (solid curve). Electroproduction data from CLAS, the Iarge acceptance spectrometer in Hall B of Jefferson Lab, at Q2 > 0.5 GeV2, covering the hadronic mass range from W=1.75 GeV t o W=2.20 GeV are being analyzed, especially with regard t o extraction of resonant contributions.21 The analysis of CLAS data at Q2 > 2.0 GeV2, W > 2.0 GeV has recently been completed and will be ready for publication later this year.22 The preliminary data are presented in the lower two panels of Fig. 2. One sees that the Regge-based model of Laget" reproduces the photoproduction data quite well. However, the electroproduction data show a considerable enhancement at large values of It!, which can be accounted for by introducing a t dependence in the r w y form factor, thus suggesting a more point-like coupling at higher t.
149
Figure 2. Differential cross section for w photoproduction (left panels) and w electroproduction (right panels) above the resonance regions (W M 2.5 GeV). Data points are from left), (upper right), 2 3 ( i ~ ~ left), er 22(Iower right).
32( upper
The curves are from the Laget model:" for the dotted curves the 7rw7 form factor has only a Q2 dependence, for the solid curves it has an additional t dependence.1° This figure is taken from Ref.22
Early experiments on photoproduction of w used bubble-chamber detectors, and hence suffered from low s t a t i s t i ~ s They . ~ ~ observed ~ ~ ~ ~ the ~ ~ dominant features of w production: 7ro-exchange and at central production angles some departure from a characteristic exponential falloff in the differential cross section. A dip structure in the differential cross section around u = -0.14 GeV2 was observed27 in the backward angles for w production for photon energies between 2.8 and 4.5 GeV. This structure can be described within the framework of Regge theory as NQ exchange." The backward angle 1977 Daresbury data taken at 3.5 and 4.7 GeV are well reproduced via exchange in the u channel of the nucleon Regge trajectory.'' Using a beam of linearly-polarized photons afforded by the Compton backscattering facility of Spring-8, the LEPS experiment has initiated new studies on the photoproduction of w s at backward angles. However, since only the forward-going proton can be measured in the LEP detector, the w extraction suffers from disentangling ws from pos within the multi-pion ba~kground.~' Very few experiments up to now have made use of polarized photon beams. Linearly-polarized photon beams, for example, allow for separating the contributions from natural-parity (i.e. diffractive scattering) and unnatural-parity exchange (i.e. one-pion exchange) in the t-channel by analyzing the decay angu~ first experiment to exploit lar distribution arising from w + ~ ' 7 r - 7 r O . ~The ; ~ ~ made use of backward this parity filter feature was a SLAC e ~ p e r i r n e n tthey Compton scattering to produce linearly polarized photons at 2.8, 4.7, and 9.3
150
GeV. The analysis of the w decay distributions showed that the contribution of unnatural-parity exchange diminishes with increasing energy. This result was further confirmed by CERN experiments in the early 1980s which collected data on w photoproduction at much higher photon energies.33 At these higher energies - far above the resonance regime - these experiments show that the cross section and decay distributions can be explained purely in terms of VMD. The reaction proceeds almost entirely through natural-parity exchange in the t channel and is therefore s-channel helicity conserving, as is to expected from diffractive photoproduction. Other high energy w production data taken at C0rne11~~ and FNAL35 confirm these results. The GRAAL collaboration is studying w photoproduction from threshold to E,=1.5 GeV. They employ a beam of linearly-polarized photons produced via Compton backscattering. By requiring a three-prong trigger and a reconstructed T O , the three-pion channel is well identified and the w-peak is extracted via sideband subtraction. The resulting differential cross section shows large uchannel contributions and the extracted beam asymmetry C is strongly negative for B*(w)FZ 90°. C, however, approaches zero in the very forward and backward d i r e ~ t i o n The . ~ ~ authors of this paper are presently analyzing the photoproduction of The linearly-polarized photon beam was produced with the coherent bremsstrahlung facility in Hall B of Jefferson Lab and the data were collected in the energy range of 1.8 < E, < 2.2 GeV. Results are expected within a year.
1.75
1.80
1.85
1.90
4s [GeV]
1.95
2.00
Figure 3. Total cross section for y p -+ u p : data from 3 9 ( * ) , 3 r ( 0 ) , 2 5 ( x ) , pared to coupled-channel fit results.3s Figure taken from Ref.
24(0)com-
New unpolarized photoproduction data have been taken at SAPHIR and CLAS. The final analysis of SAPHIR data at Bonn3' comprises considerably larger statistics than previous data from SAPHIR.40 The differential cross section (cf. Fig. 4) confirms the previously observed deviations from t-channel exchanges, especially near threshold where the angular distribution is almost flat. The new
151
data resolve variations in the total cross section that have not been observed in earlier (low-statistics) results, particularly an excess at W FZ 1.78-1.81 GeV (cf. Fig. 3). The large set of data points allowed for integration of the wN channel into a coupled-channel analysi~.~' The partial-wave decomposition of the w p cross section in Fig. 3 shows P11(1710) dominance near threshold (dotted line) and further non-negligible resonant contributions only in JT = ;+, i.e. q3(1720) and q3(1900) (dashed-dotted line). r0 exchange (dashed line) dominates the cross section behavior above W FZ 1.82 GeV.
Figure 4. Differential cross section for y p t u p : d a t a points and curves as in Fig. 3. The figure is taken from Ref.39
The three-pion decay of w allows for accessing the tensor polarization of this vector meson The decay angular distributions of the SAPHIR data have been analyzed with regard to the spin density matrix elements (cf. Fig. 5 ) . The extracted matrix elements confirm the earlier behavior observed in the differential cross section that the forward production is strongly dominated by TO-exchange, except at the near-threshold regime. In the intermediate and backward directions, there is a significant departure from what one would expect from t-channel exchange processes. Since these matrix elements are related to the off-diagonal polarization components, we are observing behavior not consistent with VDM or one-pion-exchange mechanisms. This analysis of the extraction of the density matrix elements, moreover, is in the resonance region and is unique. Earlier experiments on w production were performed at higher energies, namely, at SLAC32 and CERN.33 It is therefore imperative that this analysis be extended to energies in the resonance region with experiments employing polarized beam and/or po-
152 larized targets to provide the information necessary for delineating the individual processes which govern w N production.
Figure 5 . Spin density matrix elements in the Helicity frame. The matrix elements were extracted from the w decay distributions from the SAPHIR data.39
The preliminary w photoproduction data from CLAS 42 show a very similar behavior. The decay distributions confirm the different behavior of w production in forward and non-forward directions. The differential cross section has been extracted in photon energy bins of 50 MeV between E7=1.15 GeV to E7=2.3 GeV. Part of the data is presented in Fig. 6. The data has been compared to the Y.Oh model’ with Pomeron- and pion-exchange parameters adjusted to fit the published CLAS data at E7=3.1-3.9 GeV.23 The dotted curve represents the contributions due to t-channel exchange processes, the dashed curve the resonant contribution - with couplings according to the relativized quark model,” and the solid curve the incoherent sum.
SUMMARY There has been considerable theoretical and experimental progress in w production with electromagnetic probes over the past several years. High statistics data have been or are being - published, which offer the opportunity to investigate non-dominant contributions to the w N channel. Experiments analyzing the decay angular distribution of w + 7r+7r-7ro as functions of the photon energy and the production angle (or four-momentum transfer squared) and experiments using polarized beams are poised to provide crucial information necessary for disentangling the various contributions in w photo- and electroproduction. Several models have been developed that describe not only the main features of w production at low energies (TO-exchange) but also other t-channel exchange processes as well as resonant contributions in the s-channel. Theoretical predictions from all these models show that precise data on polarization observables are urgently needed to disentangle the various contributions. We wish to thank the organizers of this conference for giving us this opportunity to present the experimental and theoretical progress in this interesting field of physics. ~
153 I
L
8 n 1 2.
I
0.5
G O % U
l
w-1.8
Ge'l
0.5
0 1
0.5
0
-1
-0.5
o
0.5
-n
-0.5
o
0.5
1
cose
Figure 6. Preliminary CLAS data on w photoproduction compared to the model of Y.0h:8 Here, the dotted curve represents t-channel contributions, the dashed curve the resonant contributions, and the solid curve the incoherent sum.
References 1. M. Ross and L. Stodolsky, Phys. Rev. 149 (1966) 1172. 2. N.M. Kroll, T.D. Lee, and B. Zumino, Phys. Rev. 157 (1967) 1376. 3. K. Schilling, in: Springer Tracks in Modern Physics 63 (1972) 31; D. Schildknecht, ibid. 57. 4. A. Donnachie and G. Shaw, in: Photomagnetic Interactions of Hadrons, Vo1.11, Plenum Press (1978) 169. 5. H. Fraas, Nucl. Phys. B36 (1972) 191. 6. B.Fkiman and M.Soyeur, Nucl. Phys. A600 (1996) 477. 7. J.-M. Laget, Phys. Lett. B489 (2000) 313; F. Can0 and J.-M. Laget, Phys. Lett. B551 (2003) 317. 8. Y.Oh, A. Titov, T.-S.H. Lee, Phys. Rev C63 (2001) 025201; Y. Oh and T.-S.H. Lee, Phys. Rev. C66 (2002) 045201. 9. A. Donnachie and P.V. Landshoff, Nucl. Phys. B244 (1984) 322. 10. J.-M. Laget, work in progress. 11. N. Isgur and G. Karl, Phys. Lett. B72 (1977) 109;
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-
The GDH-Experiment at MAMI Recent Results and Future Plans” HANS- JURGEN ARENDS (for the GDH- and A2-Collaborations) Institut fur Kernphysik, Johannes Gutenberg-Uniuersitat Mainz 0-55099 Mainz E-mail:
[email protected] In the framework of the GDH experiment at MAMI, the helicity dependence of all partial photoreaction channels in the energy range from 200 to 800 MeV have been investigated. Helicity experiments are a sensitive tool to study resonance properties. This is shown in several examples on single and double pion production, yielding valuable information on the A(1232), 013(1520), si1(1535), and Pii(1440) resonances.
1. The GDH-experiment
T h e GDH-Collaboration has taken data on proton and deuterium targets at MAMI and ELSA between 1998 and 2003 using circularly polarized photons and longitudinally polarized nucleons provided by t h e Bonn frozen-spin target. A summary of t h e present status is shown in Fig.1, where t h e helicity difference Au = ~ 3 / 2 ~ 1 1 for 2 the total cross section on t h e proton is compared t o t h e unpolarized cross section. As the large ” helicity-blind” background of non-resonant photoproduction has almost disappeared in Au, one can expect the helicity difference to b e a valuable observable t o study t h e properties of nucleon resonances. Therefore, a detailed investigation of all partial reaction channels in the photon energy range of 200 MeV < E-, < 800 MeV was carried out, which could b e separated in t h e MAMI experiment due t o the properties of t h e DAPHNE detector3. 2. Helicity Structure of Partial Reaction Channels on the Proton
2.1. Single Pion Production in the A-Region
In t h e low-energy region around t h e A(1232)-resonance7 t h e two single pion production channels give t h e dominant part of t h e G D H integral. Since t h e A has been studied extensively over many decades and a huge number of high quality aThis work is supported by Deutsche Forschungsgemeinschaft (SFB443)
155
156 3
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GDH-ELSA: 1.9 GeV
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200 100
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Photonenergie [Mev]
Figure 1 . Helicity difference Au = u3I2- u1l2and unpolarized total photoproduction cross section on the proton. The data are from MAMI and ELSA z.
data is available, one cannot expect to find any surprises here when looking at the double helicity observables. However, it can be taken as a confirmation, that the E2/M1 ratio of the N + A transition obtained from the helicity observables (see Fig. 2) is fully consistent with the results from other methods. The full data
150
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350
400
450
500
Er (MeV) - u l / 2for the reaction ?@ + pao (Ref.4) in Figure 2. The helicity difference Au = comparison with results from MAID. Solid curve: E2/M1=-2.5%, dashed curve: E2/M1 = 0, dotted curve: E2/M1=-5.0%.
set from the GDH experiment in the A-region is contained in Ref.4.
157 2.2. Single Pion Production i n the 013(1520)-Region
At higher energies around the region of the second resonances where the resonance properties are known much less, we can hope to gain new information. The helicity difference reveals a high sensitivity t o the 0 1 3 (1520)-resonance. The multipoles E2- and M2- ( E l and M2 transitions, respectively) are related to the helicity amplitudes in the following way: (013)
N
E2- - 3M2-
,
As/:!( 0 1 3 )
-
d(E2-
+Mz-) .
Our new results5 on no production are AllS = -38 f 3 (PDG4: -24 f 9) and A3/2 = 147 f 10 (PDG4: 166 f 5), all in units of GeV-l/’. Expressed in terms of the CGLN multipoles, the ratio A4,- /E2- increases from 0.45 (PDG values) to 0.56. alW
3 0
50
0
=I--, uo
---
SAID 5w
,
,
rm
,
,
,
, no
,
,
,
,I
b(
I*o
El(MeV)
Figure 3. The preliminary total cross section (left) and helicity difference Au = u 3 / 2 u1/2 (right) for the reaction ?@+ n ~ in + comparison with results from MAID and SAID.
In a similar way the single-n+ production was investigated in the second resonance region. Preliminary data on the total unpolarized and polarized cross section are shown in Fig. 3 in comparison with the results of MAID and SAID. The differences of the two analyses are much more pronounced in the polarized case. This originates from significant differences in the balance of the Eo+ and E2- multipoles, which enter with opposite signs in Au. From these examples it becomes obvious that double-polarization experiments serve many more purposes than just measuring the GDH integral, in particular that they provide a very sensitive tool to study resonance properties. For completeness we list the CGLN multipoles (in bracket: the electromagnetic transitions) of some other resonances. The Roper resonance N* (1440) with multi-
158 pole M l - ( M l ) contributes with the same sign as s-wave pion production, the N* (1535) appears as a resonance in the multipole Eo+( E l ) just above 17 threshold and dominates the 77 photoproduction process, as was also confirmed by the GDH-e~perirnent~. 2.3. Double P i o n Production
The double pion production channels n7r+xo, p7r+7r-, and p7r07ro were separately analyzed in the MAMI experiment'. As an example we show the helicitydependent cross section for ;Jp+ n7rfiro in Fig. 4. 60
-3
50 40
n
b*
30 20 10
0 400
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600 700 u (MeV)
800
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w (MeV)
Figure 4. The total cross section u~ and the helicity difference Au = u 3 / 2- ul/2for the reaction ?$ -+ n&nO. The theoretical predictions are given by the solid lines l 2 , dashed lines l o , and dotted lines 1 3 . The data are from MAMI '.
The interesting and previously unexpected feature is the peaking of the respective cross section at E, % 700 MeV or W % 1480 MeV, definitely below the positions of the 013(1520) and Sll(1535) resonances. This is an experimental proof that two-pion production can not be simply explained by a resonance driven mechanism (s-channel contribution), but that it takes large non-resonant effects such as Born terms and vector meson exchange in the t-channel. It is also evident from Fig. 4 that the present models can only describe the data in a semi-quantitative way. The same holds true in the case of the px+x- reaction. The corresponding datag are shown in Fig. 5 for the separated helicity parts uIl2 and u3I2. The helicity 312 part shows a resonant behaviour, whereas al/2is a smoothly rising function of the photon energy. Obviously, this reaction peaks at about 650 MeV, even lower than the previous one, corroborating the statement made above on the complicated nature of the reaction mechanisms. Preliminary data are also available for the pr07ro final state which is of particular interest because of its high sensitivity to the resonance contributions. In this case, the intermediate AT excitation term is in fact strongly suppressed with
159
E Q
50 L " ' " " " " "
=L
40
" ' " " " " " " " " " " " " ' ~
r, \
s: b
.
30 20
10 0
Figure 5.
Preliminary helicity-dependent cross sections u 3 / 2 and u1/2 for the reaction
T J ~ + p . r r f ~ - . The theoretical predictions are given by the solid and long-dashed lines l o , dashed and dot-dashed lines 13. The data are from MAMI '. respect to the nr-ro and p r + r - reactions and, due to isospin, no intermediate pcontribution is possible. There are two models that reproduce equally well the total p r o r o cross section up to about 800 MeV although with completely different interpretations. The Valencia model" predicts the dominance of the intermediate &3(1520) excitation with subsequent 013(1520) + A f r o and A+ + p r o decays. In contrast the Murphy-Laget model'' predicts a dominant excitation of the P11(1440) resonance followed by P11(1440) -+ p a and u -+ r0rodecays, where u represents a correlated pair of pions in a relative s-wave. Our preliminary data are shown in Fig. 6. According to both models, the 0 1 3 (1520) resonance is largely responsible for the observed u 3 p cross section, via the process yN -+ &(1520) + r A + r r N . However, there is also a non-negligible u!/2 cross section, which points to significant non-resonant effects and to mechanisms involving the intermediate excitation of additional spin-1/2 resonances, such as 9 1 (1440) or Sll(l535). In a recent paper, Hirata et a1.I2(HKT) investigate effects of non-resonant photoproduction. From comparing their results to the total unpolarized cross section they conclude that the pseudoscalar r N N coupling (PS) is preferable over the pseudovector coupling. However, the helicity-dependent data are described better assuming pseudovector coupling (PV). More detailed information on double pion production is contained in M. Ripani's15 presentation at this conference.
3. Deuteron experiment
A pilot experiment on a polarized deuterated butanol target has been carried out at MAMI in 1998. First preliminary results of the total cross section on the deuteron (see Fig. 7) and the partial channel -$+ pplr- 19, based on a small
160
;
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o3n
Figure 6 . Preliminary helicity dependent cross sections u3/2 and ul/2 for the reaction -Jp' --t p?ro7ro from MAMI 14. The theoretical predictions are from the ValencialO and
HKT12 models.
subset of the data, are available.
Figure 7. Preliminary helicity-dependent total cross section for the deuteron compared to theoretical predictions from Ref. 16,17918.
161
J
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Figure 8. Progression of the target polarization during the experiment with the standard and the new target material (labelled Fin 11).
The full data taking was carried out in the first half of 2003 using again the Bonn frozen-spin target2'. In the course of the experiment the degree of polarization could be increased from 35% to more than 70% due to a new target material based on trityl-doped D-butanol'l. This development is a major step forward in the polarized target technology. The progression of the target polarization measured during the experiment with the two target materials is shown in Fig. 8. The data analysis is in p r ~ g r e s s ~ ~ ~ ~ ~ ~ ~ ~ . 4. Future Plans
In order to extend the experimental possibilities of MAMI, a fourth stage is presently under construction, which will increase the beam energy to 1.5 GeV. This Harmonic Double Sided Microtron (HDSM), see Fig. 9, mainly consists of two pairs of of 90' bending magnets with a field gradient for compensation of vertical edge focussing and two linear accelerators operated at different frequencies, 2.45 GHz and 4.90 GHz, resulting in a high longitudinal phase stability. The HDSM is expected to come into operation end of 2005. As a standard detector to be used with the tagged photon beam a combination of the Crystal Ball (CB) detector and TAPS as a forward wall is currently being commissioned. The CB consists of 672 optically isolated NaI(T1) crystals, 15.7 radiation lengths thick. The counters are arranged in a spherical shell with an inner radius of 25.3 cm and an outer radius of 66.0 cm. Charged particles can be measured by the central tracker consisting of a scintillator barrel and the DAPHNE cylindrical multi-wire proportional chambers. The TAPS wall is composed of 522 BaF2 detectorsz5 arranged in a hexagon. The apparatus is schematically shown in Fig. 10. The high granularity, large acceptance and good energy resolution make
162
Figure 9.
General layout of the Harmonic Double Sided Microtron (HDSM).
this setup a unique instrument for the detection of multi-photon final states.
Figure 10. Crystal Ball detector with inner tracker and TAPS forward wall.
The tagger will be upgraded t o cope with the increased beam energy. Linearly and circularly polarized photons will be available. A polarized frozen-spin target is presently under development to allow for double polarization experiments with the new facilities. The physics program includes a measurement of the magnetic moment of the
163 A(1232) via radiative production, single and double pion production on nucleons and nuclei, 7 and K production with the emphasis on polarization observables. The study of the helicity dependence of partial reactions will be continued and extended to higher energies. References 1. J. Ahrens et al., Phys. Rev. Lett. 87,022003 (2001). 2. H. Dutz et al., Phys. Rev. Lett. 91,192001 (2003); H. Dutz et al., submitted to Phys. Rev. Lett. (2004). 3. G. Audit et al., Nucl. Instr. Methods A 301,473 (1991). 4. J. Ahrens et al.,Eur. Phys. J A, (2004) in print. 5. J. Ahrens et al., Phys. Rev. Lett. 88, 232002 (2002). 6. K. Hagiwara et al.,(Particle Data Group Collaboration), Phys. Rev. D 66 010001 (2002). 7. J. Ahrens et al.,Eur. Phys. J A 17,241 (2003). 8. Ahrens J, et al. (GDH and A2 Collaborations). Phys. Lett. 551 49 (2003). 9. Lang M. PhD thesis, University of Mainz (2004), to be published. 10. J . Nacher et al., Nucl. Phys. A 695 295 (2001); J. Nacher et al., Nucl. Phys. A 697 372 (2002). 11. L. Murphy and J.-M. Laget, report (DAPNIA-SPHN-95-42), (1995). 12. M. Hirata, N. Katagiri, T. Takaki, Phys. Rev. C 67 034601 (2003). 13. H. Holvoet, PhD thesis, University of Gent (2001). 14. F. Zapadtka, PhD thesis, J. Ahrens et al., Phys. Rev. Lett. (2004), to be published. 15. M. Ripani, invited talk at this conference. 16. H. Arenhovel, The GDH for the deuteron, Proc. GDH2000, Mainz (World Scientific, Singapore, 2001), eds. D. Drechsel and L. Tiator, p. 67. 17. A. Fix, private communication. 18. M. Schwamb, private communication. 19. C. Rovelli, Diploma thesis, University of Pavia (2002). 20. C. Bradtke et al., Nucl.Instr.Meth. A 301 473 (1999). 21. St. Goertz et al., Highest polarizations in deuterated compounds, to be published in Nucl.Instr.Methods, Section A, and Proceedings of the 9th International Workshop on Polarized Targets and Techniques, Bad Honnef, 2003. 22. 0. Jahn, Ph.D. thesis, University of Mainz (in preparation). 23. T. Rostomyan, Ph.D. thesis, University of Gent (in preparation). 24. S. McGee, Ph.D. thesis, Duke University (in preparation). 25. R. Novotny, IEEE Trans. Nucl. Sci. 38 (1991) 379.
Double-Polarization Experiments using Polarized HD at LEGS A. M. Sandorfila, K. Ardashev2, C. Bade3, 0. Bartalini4, M. Blecher5, A. Caracappa', C. Commeaux7, A. D'Angelo4, A. d'Angelo4, R. Di Salvo4, J. P. Didelez7, A. Fantini4, K. Hicks3, S. Hoblit', A. Honig', C. Gibson2 T . Kageya5, M. Khandakerg, F. Lincoln', A. Lehmann2, M. Lowry', M. Lucas3, J. Mahon3, L. Miceli', D. Moricciani4, B. M. Preedom2, B. Norum", C . Schaerf', H. Stroher", C. Thorn', K. Wang", C. S. Whisnant' and X. Wei'. (The LEGS Spin Collaboration) Brookhaven National Lab., Upton, N Y U. of South Carolina, Columbia, S C Ohio Univ., Athens, OH Univ. d i Roma-II/Tor- Vergata and INFI-sezione diRoma, Rome, Italy Virginia Tech. d State Univ., Blacksburg, V A James Madison Univ., Harrisonburg, V A IP2N3 Orsay, France *Syracuse Univ., Syracuse, N Y Norfolk State Univ., Norfolk, V A lo Univ. of Virginia, Charlottesville, V A Forschungszentrum, Jiilich, Germany
'
''
A solid, polarized HD target has been developed for the measurement of doublepolarization observables in the A resonance region. The focus of the experimental program is a comparison of pion photo-production amplitudes for the neutron and proton and the associated spin-dependent sum rules.
While three constituent quarks provide a simple picture of the nucleon core, in recent years the pion cloud has come to be viewed as a critical part of the physical nucleon. Lee and Sat0 have shown that the pion cloud surrounding the constitutent quarks provides a dressing that markedly alters the nucleon's apparent deformation. Similarly, Wiese has shown that the pion cloud accounts for about half the nucleon's polarizability. The cloud i s associated with pion loops and, for excitations less than 0.5 GeV, photo-pion production diagrams containing pion loops are mostly non-resonant and so mainly isospin-1/2. These will be very different for the neutron and proton. As such, the best window into this cloud is a comparison between the neutron and the proton. Multipole predictions for the integrands of both the Gerasimov-Drell-Hearn (GDH) and the forward spin-polarizability sum rules flip sign below about 220
164
165 MeV, resulting in a large cancellation to the sum rule values from the low energy region. The sign change in the ~ 3 / 2- al/2helicity difference cross section is entirely due to the charged-T production channels and comes about from an interference between the A photo-production amplitude and non-resonant multipoles. The isospin-3/2 amplitudes for the proton and the neutron are the same. The predicted convergence of GDH(n) and GDH(p) to different values is due to their very different isospin-1/2 components. For the proton, these are reasonably well understood. For the neutron, they are poorly known. The integral of the ~ 3 / 2- ul/,spin difference, weighted by l/E;, gives the forward spin-polarizability. Chiral calculations of this quantity have large p5 terms, which come from interferences between the isospin-3/2 A and other multipoles, and so converge slowly. However, convergence is expected to be much more rapid for the [neutron - proton] difference. As yet there are no direct measurements of this quantity in the low energy region that dominates this sum rule. The recent Mainz GDH(p) data''2 were restricted to photon energies above 200 MeV and their evaluations of the spin sum rules have used MAID multipoles to extrapolate to pion threshold, a 15% correction. (It has been assumed that this correction is exact and any remaining discrepancies with the GDH sum rule must be due to somewhat ill-defined high energy components.) Measurements at Mainz on deuterium can cover a similar range for inclusive cross sections, but the exclusive channels needed to isolate reactions on the neutron are limited to energies above -300 MeV by the necessity to detect recoiling protons in order to identify the P-T- channel. The goal of experiments at LEGS is to measure exclusive (y, T ) cross sections and three different polarization asymmetries (El G and C) on polarized proton and deuteron targets over a range of energies from near r-threshold to 420 MeV. This combination of four independent observables, measured over a large angular range will form the basis of an analysis to extract the free neutron multipoles from a new joint theoretical effort with T.-S. H. Lee, T. Sat0 and A. Matsuyama. Measurements on the proton will check the Maim results and extend them to lower energies. The proton and neutron data will be collected simultaneously, thus providing a key comparison with minimal systematic uncertainties. The LEGS-Spin-Collaboration (LSC) has been developing a new type of polarized hydrogen target. The new target consists of molecular HD in the solid phase. In SPHICE, Strongly Polarized Hydrogen-deuteride ICE, both the H and the D nuclei can be highly polarized and oriented at will. Over 80% of the target consists of the polarizable molecular species of interest, and contributions from the remaining 20% can be subtracted from measurements in which the HD is pumped away. SPHICE is a frozen-spin target, manufactured at very high fields and low temperatures in a dilution refrigerator. Small amounts of ortho-H2 and para-D2 impurity are used to induce p ~ l a r i z a t i o n ~Since > ~ . these impurities decay to the magnetically inert para-H2 and ortho-D2, the target spins are frozen by waiting at low temperature for many time constants. Heat generated by these decays are conducted away by approximately two thousand 50 micron diameter aluminum
166 wires which comprise about 20% of the target by weight. After transferring to an in-beam dewar with a modest holding field, the polarization decays with a time constant that depends on the holding temperature and this ranges from many days to months. The factor ultimately determining the time required to hold the target in the polarization conditions is the concentration of para-D2. This spin 1, J = 1 molecule also couples to the H and D spins and has a decay time (to the inert ortho-D2 state) approximately 3 times longer than that of ortho-H2. This places stringent requirements on the purity of the HD. Targets are produced in a top-loading dilution refrigerator containing a 15T/17T superconducting solenoid long enough to produce up to three 5 cm x 2.5 cm 0 targets simultaneously. The base temperature of this system at high field is about 8 mK, although Kapitza resistence between the HD and the aluminum cooling wires is expected to limit the HD temperature to about 12 mK. Once the spins are frozen in, the field is reduced, the system is warmed to 2 K, and a Transfer Cryostat (TC) is inserted. This device, containing both LN2 and LHe jackets, has a central portion that can translate and rotate making it possible to screw the TC cold finger into the target mount and withdraw the target from the refrigerator. While in the TC, polarization is maintained with a small magnet. The target may then be either inserted into the In-Beam-Cryostat (IBC) or into a storage dewar for later use. Many of the double-polarization experiments that will utilize SPHICE targets require measuring absolute polarized cross sections over large solid angles. For this we have constructed a large acceptance calorimeter, the Spin-Asymmetry (SASY) array. This detector is rather well matched to the detection of neutrals in our kinematic regime while leaving open a large central core that can accommodate other detectors. In a first round of measurements this space is used to house plastic scintillators that complete the coverage for recoil neutron detection and provide full angular acceptance for the D(y,7ron) reaction. In a second round of measurements a large-bore solenoid and chambers for magnetic analysis of charged particles will be installed. The latter is essential for isolating charged pion decays from polarized neutrons at LEGS energies. Completely exclusive experiments can tag the target nucleon in polarized deuterium by detecting the corresponding recoil nucleon. However, for charged 7r-production, absorption of protons in the target cryostat severely limits this ability to differentiate between the y p -+ 7r+n and y n -+ 7r-p reactions and for beam energies less than about 280 MeV, less than half of the angular distribution can be probed in this way. The only way to circumvent this limitation and avoid large extrapolations in angle and energy is to measure the charge of the photo-produced pion. For this, a Time-Projection-Chamber (TPC) surrounded by a 1.8 Tesla super-conducting solenoid is being constructed. In November of 2001, a polarized HD target was successfully transferred to an In-Beam Cryostat (IBC) and the first double-polarization data were collected in a short demonstration experiment. This target underwent extensive testing before being exposed to beam. When finally put in the beam, its polarizations were PH = 30% and PD = 5%. During the 111 days that the target was held at low temperatures the para-Da concentration decreased by a factor of 477. The
167
relaxation times measured in-beam were TF = 13 days and TF = 36 days. Some of the high quality data obtained in only 3 days of running with this target have been presented e1sewhe1-e~'~. Since then we have been preparing the new equipment needed for a full program of experiments. In Spring, 2004, an aged target with polarizations of PH = 52% and PD = 20% was produced and initial studies suggested very long relaxation times at in-beam conditions. Extensive new measurements are beginning. Here we present some new results from the initial 3-day experiment run in 2001.
-100 -2ou
Figure 1. The difference of helicity dependent cross sections for D(r,mon) compared to a recent three-body impulse calculation for deuterium and multipole predictions for the free neutron from SAID and MAID.
The D(7,r"n) reaction has been studied over its full angular range, with yrays from r"-decay detected in the NaI/Pb-glass/scintillating-plastic calorimeter
168
of SASY and recoil neutrons detected in plastic scintillators. Absolute neutron detection efficiencies were determined from separate H(y,Tfn) measurements. The difference of angle-integrated helicity-dependent cross sections for D(y,Ton) are shown in Figure 1 for the short November/Ol experiment. (Here we used the conventional definition of helicity, h = & . ?j , so that u l p represents the cross section for the case in which photon and target spins are parallel.) Three calculations are shown in the figure. The dotted and dashed curves are predictions for “free” neutron reactions from the SAID and MAID multipoles, respectively. The dotted curve is taken from an old SAID solution that predates the Mainz GDH proton data of Refs. 1, 2, while the MAID03 solution includes those new data. The Mainz proton data potentially affect the isospin 3/2 amplitude, which is the same for neutron and proton targets. Nonetheless, differences between the dotted and dashed curves are minimal. The solid curve is an “impulse”-level prediction from T.-S. H. Lee7 for the reaction on deuterium. Work is ongoing to include the contributions from finalstate interactions, pion-rescattering and intermediate-TNN interactions. The freeneutron amplitude is the crucial input to these three-body calculations and the goal is to constrain the free n(y, T ) process by fitting D(y, TN) calculations to such data, minimizing x 2 by adjusting coupling constants and off-shell parameters that determine the free-neutron multipoles. This will require minimal uncertainties in polarization data. However, the data of Figure 1 were collected in only three days of running with a 5% polarized deuterium target. Significant reductions in these uncertainties are expected in the near future. This work is supported by the U.S. Department of Energy under Contract No. DE-AC02-98CH10886, by the US.National Science Foundation and by the Istituto Nazionale de Fisica Nucleare, Italy. References
1. J. Ahrens et al., Phys. Rev. Lett. 84, 5950 (2000). 2. J. Ahrens et al., Phys. Rev. Lett. 87, 22003 (2001). 3. A. Honig, Q. Fan, X. Wei, A. M. Sandorfi and C. S. Whisnant, Nucl. Inst. Meth. A356,39 (1995). 4. N. Alexander, J . Barden, Q. Fan, and A. Honig, Rev. Sci. Instrum. 62,2729 (1991). 5. A. M. Sandorfi, for the LEGS-Spin Collaboration, GDH 2002: Proceedings of the Znd International Symposium on the Gerasimov-Drell-Hearn S u m Rule and the Spin Structure of the Nucleon, Genova, Italy, July 2002, p. 147, World Scientific, Ed. M. Anghinolfi, M. Battaglieri, and R. De Vita. 6. C. S. Whisnant, for the LEGS-Spin Collaboration, LOWq-03: Znd Workshop on Electromanetic Reactions at Low Momentum Transfer, Saint hlary’s University, Halifax, NS, Canada, July 16-18, 2003. 7. T.-S. H. Lee, private communication.
CLAS Results from the First and Second Resonance Regions L.C. SMITH@,I.G. AZNAURYAN~,v . BURKERT~,H. EGIYAN~,K. J O O ~ FOR THE CLAS COLLABORATION a University of Virginia, Charlottesville, VA 22901, USA Yerevan Physics Institute, 375036 Yerevan, Armenia Thomas Jefferson National Laboratory, Newport News, VA 23506, USA University of Connecticut, Storrs, C T 06269, USA
A unitary isobar model (UIM) and dispersion relations (DR) were used to analyze precision CLAS meson electroproduction measurements which include longitudinally polarized electron beam asymmetry and cross section data for the p ( Z , e’p)7r0 and p ( Z , e‘.rr+)n reactions, and unpolarized cross sections for p ( e , e’p)q. Photocoupling amplitudes extracted for the resonances &(1232), P11(1440), D l ~ ( 1 5 2 0 ) and s11(1535) show good agreement between the UIM and DR approaches. For the first time accurate results are obtained for longitudinal photocouplings in the second resonance region.
1. Introduction
The first and second resonance regions are dominated by four states with large .rrN couplings: &(1232), 9 1 (1440), 013(1520) and Sll(1535). Their identification from -yp + .rrN data is straightforward, using a partial wave and isospin analysis of the .rrN decay angular distributions. A current challenge in hadronic physics is to understand the properties of these states within a framework consistent with QCD. Pion electroproduction provides new information not available using real photons. First, measuring the Q2 dependence of the photocoupling amplitudes probes a range of distance scales within the nucleon, revealing spatial information about the constituents. Second, polarization of the virtual photon allows study of both longitudinal and transverse modes of resonance excitation. This information can provide strong constraints for the increasingly sophisticated phenomenological, quark model and lattice QCD calculations now becoming available. In this paper we summarize results obtained for each of the above resonances using a unitary isobar model/dispersion relation analysis of CLAS high precision .rr+, .rro electroproduction data at Q2 = 0.4 and 0.65 GeV2.
169
170 2. Analysis
2.1. Unitary Isobar Model The unitary isobar model (UIM) used in this analysis follows the approaches developed by Drechsel 1 7 2 . Resonant contributions to multipoles are described using s-channel Breit-Wigner forms with energy dependent width r, where the masses and widths are found by fitting the experimental data. The background includes nucleon pole terms in the s- and u-channels as well as the t-channel T , p and w exchanges. These Born terms incorporate nucleon and pion form factors, which are parameterized taking into account recent measurements. To improve the description of the background contributions above the first resonance region, a gradual transition to Regge-pole amplitudes is introduced For each multipole the background is unitarized according to the K-matrix approximation:
where h;:
is the T N scattering amplitude.
2 . 2 . Fixed-t Dispersion Relations
The dispersion relations (DR) analysis used in this work is based on the approach previously used to analyze pion photoproduction data Using princples of causality and analyticity, the real and imaginary parts of the invariant amplitudes are related as follows: 314.
where Ri are the residues in the nucleon pole terms. The imaginary parts of the amplitudes are saturated with contributions from A(1232) and higher mass resonances. The resonant amplitudes for A(1232) are found by solving integral equations for multipoles analogous to Eq.2. The amplitudes for other resonances are parameterized in Breit-Wigner form and fitted similarly as in the UIM. In addition, the non-resonant contributions to imaginary parts of Eo+ and SO+ were found using dispersion relations and the Watson theorem. 3. Data
The present analysis used CLAS data5i6i7taken over an invariant mass W ranging from 1.10 GeV to 1.66 GeV. The combined data set included differential cross sections (do)and longitudinally polarized electron beam spin asymmetries ( A i T ) for T+ and TO electroproduction on the proton at Q2 = 0.4 and 0.65 GeV2. The and A i T ( r 0 )were taken from the 1999 run at 1.5 data for do(^+),
171 60
1
W= 1.23 Cosi%'=0.383
W= 1.22 C O S I Y ' = - O . ~ C
ZU4 0
-
0
0
100
200
300
0
100
200
300
-
0
0
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Figure 1. Typical single pion electroproduction cross section (du) and single spin beam asymmetry (AILT)in the center-of-mass frame. Curves show unitary isobar model fit.
GeV, while do(rO)was obtained from an earlier run period in 1998. For the Sll(1535) resonance, a separate analysis of p(e, e'p)q datag from CLAS was made at Q2 = 0.375 and 0.75 GeV2. Because of the large solid angle provided by CLAS, full angular coverage in the n r + center-of-mass was accessible for the first time in the second resonance region. 4. Results
Our fits to the CLAS data are summarized in Tables 1-4. It is seen that both UIM and DR approaches produce consistent results with acceptable x2 (Table
1). The relatively large value of x2 for the'r7 cross sections is caused by the very small statistical uncertainties connected with this data set5. Figure 1 shows the UIM fits compared to typical center-of-mass azimuthal angular distributions for the 7rN observables measured with CLAS. 4.1. p33(1232)
From Table 2 it is seen that the amplitudes obtained for the A(1232) in the two analyses are in good agreement with each other. The values of the ratios I m E ; p / I m M ? r , I m S ~ f / I m Mwhich ~ ~ ,measure the quadrupole strength of the N + A(1232) transition, are well determined, and are in good agreement with the results obtained from no cross sections using a truncated multipole expansion6. The W dependence of the real and imaginary parts of E;? and S;? obtained in our fits at Q2 = 0.4 GeV2 are shown in Fig. 2 compared to MAIDO3, which
172 Table 1. Summary of reduced x 2 of fits. Observable
Q2
Nfit
%(no) ---
0.4 0.6-0.65 0.4 0.6-0.65 0.4 0.65 0.4 0.65 0.375 0.75
3530 3818 2308 1716 956 805 918 812 172 412
%((..+, A ~ p (. n .' ) ~~
ALp(n+)
%(11)
X:lrM
1.22 1.22 1.62 1.48 1.14 1.07 1.18 1.18 1.32 1.42
x20r
1.21 1.39 1.97 1.75 1.25 1.3 1.63 1.15 1.33 1.45
Table 2. The results for the imaginary parts of M:?, E;? and S:? at W = 1.229 GeV. For each Q2, the values on the first and second rows are obtained in this work using UIM and DR, respectively. The other results are obtained using a truncated multipole expansion6. Q2 (GeV/c)2 0.4
IrnM:C ( p b 1 / 2 )
0.65
3.87 f 0.01 3.89 zk 0.01
4.93 f 0.01 4.97 f 0.01
-
-
REAL MAID03 - - - - IMAG MAID03 -----
ImE:c/ImM:r -2.4 f 0.2 -2.9 f 0.2
(%)
-3.4 f 0.4 f 0.4 -1.0 f 0.3 -2.0 f 0.3 -1.9 f 0.5 f 0.5 -2.0 f 0.4f0.4
IrnS;?/ImM:c -5.0 f 0.2 -5.9 f 0.2 -5.6 -6.2 -7.0 -6.9 -6.6
(%)
f 0.4 f 0.6 f 0.4 f 0.4 & 0.6 f 0.5 f 0.4 f 0.2
REAL UIM IMAG UIM
0
-0.1
-0.2
I 04
I l l l l l ( l l l l l l d l l l l l 1 .1
1.15
1.2
E,+(I=3/2) Figure 2.
1.25 W (GeV)
--
\-
l l l l l l l l l l l l l l
1.1
1.15
1.2
S,+(I=3/2)
1.25 W (GeV)
W dependence at Q2 = 0.4 GeV2 of real and imaginary parts of E;C, Sl+ 312 .
Dashed curve show UIM fit to CLAS data described in this work. Solid curve shows MAIDO3.
173 was fitted to all published nop electroproduction cross sections.' The largest differences are in Re(S1+) for W < 1.2 GeV and may reflect the absense of previous data in this region as well as the inclusion of n'n and polarization observables in the present fit. Table 3. Masses, widths and n N branching ratios for 41(1440), 013(1520) and 511(1535) used to obtain the photocoupling amplitudes. State I Mass 1 Full Width Pltf1440) 1 1.440 GeV I 0.350 GeV sIiii535j j 1.530 GeV j 0.150 GeV 013(1520) 1.520 GeV I 0.120 GeV
I
I aN BR I
i
I
0.6 0.4 0.5
4.2. Pii(1440) A new significant result using these data is discovery of a large sensitivity to the M:/" and S:L2 multipoles, which receive contributions from excitation of the Roper q1(1440). The fits to the combined data set which includes ALT and cross sections du taken in the second resonance region, significantly constrains the real and imaginary parts of these multipoles through their interference, based on the UIM analysis, with largely Born dominated non-resonant multipoles. The sensitivity of the quantity uiT z du . A i T to these multipoles is demonstrated in Fig. 3. Using the model fits we have extracted the Roper photocoupling amplitudes at two Q2 points, as shown in Fig. 4 and Table 4. We also show a recently published" point at Q2 = 1.0 GeV2 from Hall A. These new data can completely rule out some previous quark model calculations, such as most non-relativistic approaches, as well as the quark-gluon hybrid approach for which no zero crossing occurs in A' and Sf/2= 0. The strong longitudinal response seen in our data 1 /2 appears to revive the traditional 'breathing mode' interpretation of the Roper, possibly augmented by coupling to the qij cloud of the nucleon as suggested by the good agreement with the VMD model of Can0 and Gonzales''. Another controversy centers around the possible role of the Roper as a member of a pentaquark anti-decuplet in the JafTe-Wilczek diquazk model. Precise measurements of the Roper form factor may help decide this question.
4.3. S11(1535), 013(1520) Our results for the transverse helicity amplitudes of the S11(1535) and D13(1520) resonances are consistent with existing data, indicated by the gray bands in Figs. 5-6 which represent a Single Quark Transition Model (SQTM) parameterization of previous measurements.". For the S11(1535), our extraction of photocoupling amplitudes from T and 3 electroproduction channels give results
174
E = l 515 GeV P'=0.4 GeV'
1
1
c a d . = 0.125
E=1.515 GeV Q'=0.4 Ge\T
I
cosd:= 0375
6 -
........
._..
--.
.>""..............
...............4..
,LI' 1 . .
0
0
-1
I
.
I
cosd'. = 0.875
D
-
1.2 J*NR@J
..... - 0 5+M,.
........
Figure 3.
14
-0.5+8,-
16
12
1 4
p(e.e'Ti*)n
16
W(GeV)
Sensitivity of CLAS measurements of uiT to changes in multipoles M:/2
(dashed) and S:/" (dotted) for nn+ channel (left) and p r o channel (right). Solid line (JANR03) shows best fit using Unitary Isobar Model.
..........
0 HALLA A PDG
Q2 (GeV2) Figure 4.
Results for the q 1 ( 1 4 4 0 ) photocoupling amplitudes
Q' (GeV') and SF/2. CLAS
points include model errors. Hall A pointlo shows MAID03 fit model error. Bold, solid, dashed and dot-dashed lines are from various theoretical calculation^.^^^'^^^^^^^
in good agreement with each other (see Fig. 5 ) , unlike at Q2 = 0 where A' 1 / 2 from i~ production is smaller than for 7 production. amplitude of the y*p + We also obtain a more accurate value for the
175 150 125 100
2 0
75
-
50
0
25
'
0
05
1
15
2
25
3
Q2
(GeV')
9' (GeV')
Figure 5. Results for the sii(1535) photocoupling amplitudes A!l2 and S ~ 1 2Symbols . same as Fig. 4. Points at Q2 = 0 are from GWUi8(0), PDGig(0), and Aznauryan4(o). Table 4. Helicity amplitudes obtained in the analysis of CLAS .rr and q electroproduction data in second resonance region. Units are GeV-1/2. For each Q2 the two values listed are obtained from the UIM and DR fits, respectively. Resonance pii(1440)
Q2 0.40 0.65
013(1520)
0.40 0.65
Sii(1535) y'p t n N
0.40 0.65
sii(1535)
Y'P
--t
0.375
VP 0.75
PAl/2
-15 f 2 -452 4+4 23 f 4 -66f3 -68413 -67f3 -69f3 95f2 88 f4 98 f 4 93 f 4 92 f 1 91 f 1 89 f 1 93 1
+
PA3/2
71f4 75313 70f4 66f4
Ps1/2
44f2 41 f 2 44 f 4 37f4 -46f3 -41f3 -38f3 -38f3 -25 f2 -18 f2 -17 f2 -12 f 2 -12 f 3 -13 f 3 -12 & 3 -14 f3
D13(1520) transition than earlier results, due to the substantial influence of our more precise nx+ data on the I = 1 / 2 channel. The transverse amplitude A* 312
for this transition, which is dominant at Q2 = 0, falls very rapidly with increasing Q 2 ,and all quark models predict that at high Q2, AP will become the dominant 112 contribution t o y*p -+ 013(1520). Recent calculations, however, show no agree-
176 200
150
2
r:2
100
2
0
0-
-50-
50 -100-
0
05
0
Figure 6. S;,2.
1
15
2
25
3
Results for the 013(1520) photocoupling amplitudes A:l2,
and
Symbols same as Fig. 4. Solid, dashed and dot-dashed lines show theoretical
calculation^.'^^'^^'^ = ment on the value of Q 2 where nor can they consistently describe our results (Fig. 6). This is especially true for the longitudinal couplings, which are determined quite accurately from our fits to CLAS data.
Acknowledgments
This work was supported by the U.S. Department of Energy (DOE) and the National Science Foundation, the French Commissariat 8. 1'Energie Atomique, the Italian Instituto Nazionale di Fisica Nucleare, and the Korean Science and Engineering Foundation. The Southeastern Universities Research Association (SURA) operates the Thomas Jefferson National Accelerator Facility under DOE Contract No. DE-AC05-84ER40150. References
1. D. Drechsel, 0. Hanstein, S. S. Kamalov, and L. Tiator, Nucl.Phys. A645, 145 (1999). 2. W. Chiang, S.N. Yang, L.Tiator, and D.Drechse1, Nucl.Phys. A700, 429 (2002).
177 3. I.G. Aznauryan, Phys.Reu. C67, 015209 (2003). 4. I.G. Aznauryan, Phys.Reu. C68, 065204 (2003). 5. H. Egiyan, Ph.D thesis, William and Mary (2001). 6. K. Joo, CLAS Collaboration, Phys.Rev.Lett. 88, 122001 (2002). 7. K. Joo, CLAS Collaboration, Phys.Rev. C68, 032201 (2003). 8. L. Tiator etal., nucl-th/0310041. 9. R. Thompson, CLAS Collaboration, Phys.Rev.Lett. 86, 1702 (2001). 10. G. Laveissiere, JLAB Hall A Collaboration, Phys.Rev. C69, 045203 (2004). 11. V. Burkert etal., Phys.Rev. C67 035204 (2003). 12. Zh. Li, V. Burkert, Zh. Li, Phys.Rev. D46, 70 (1992). 13. S. Capstick and B. D. Keister, Phys.Reu. D51, 3598 (1995). 14. S. Simula, Proceedings of NSTAR 2001, Mainz. 15. F. Cardarelli and S. Simula, Phys.Rev.Lett, 62, 06520 (2000). 16. F. Cano, P. Gonzales, Phys.Lett. B431, 270 (1998). 17. M. Warns etal., Z.Phys. C45, 627 (1990). 18. R.A. Arndt etal. Phys.Rev. C53, 430 (1996). 19. K. Hagiwara etal., Phys.Rev. D66, 010001 (2002).
Experimental Review of Double Pion Electromagnetic Production M. RIPANI Istituto Nazionale d i Fisica Nucleare Via Dodecaneso 33, I-16146, Genova, Italy E-mail:ripani63ge.infn.d Two pion photo- and electroproduction has been the subject of intense experimental activity at different laboratories, mainly with the aim of improving our knowledge of baryon states in the second and third resonance region, as well as to look for new states, predicted by quark models but for which no experimental evidence is reported in the PDG listings. In this contribution I will report about several results covering two pion production from threshold up to the mass region above 2 GeV.
1. I n t r o d u c t i o n Successful models of baryonic excitations are typically based on three constituent quarks confined in a potential well and bound by forces whose unperturbed Hamiltonian obeys S U ( 6 ) x O(3) symrnetry1l2. Such models differ in the specific implementation of basic ingredients like confining potential, quark-quark spin/flavour interactions, etc. The baryon spectrum as well as the wave functions of various states are calculated, which leads to making experiments to measure resonance masses and form factors. In particular, a well known puzzle of baryon physics is that the number of observed baryon resonances is lower than predicted by theories, originating the so-called problem of ”missing states”. However, other models, with different symmetry properties and a reduced number of degrees of freedom, as e.g. in ref. predict fewer states. Therefore the question of how many and what states we do actually have in the spectrum is a crucial one and connected to fundamental symmetry aspects in our picture of baryons. In fact, most of the existing information on baryon resonances has been obtained in the past from experiments where a single pion is present either in the incoming or in the outgoing channel (nN-+ nN,y N -+ nN,etc.). On the other hand, many of the nucleon excited states in the mass region around and above 1.7 GeV tend to decouple from the single-pion and eta channels, while decaying predominantly in multipion channels, such as An or N p 4 , a situation that is also predicted in several model^^>^. A similarly weak or even absent pion-nucleon coupling is in fact expected also for the “missing state^"^'^, that therefore may have escaped detection in past experiments. What about their electromagnetic excitation ? It seems that at least in some cases it may be sizeable5.
178
179 By using an electromagnetic probe to produce multipion final states we have therefore both the possibility of enhancing poorly known states in the mass region above 1.5 GeV, and of discovering new states. At the same time, when using electron scattering we can study the transition form factors that are another essential piece of information in understanding the degrees of freedom and the symmetries involved116. Indeed high intensity and high quality continuous electron and photon beams have been and will be used in a variety of experiments aimed at a vast improvement of our understanding of the light quark baryon resonance properties in laboratories around the world. In this contribution, I will report some specific results about the measurement of baryon resonance properties in the double pion electromagnetic production channel. Before discussing the data, it may be useful to recall that two pion production typically proceeds through isobar quasi-two-body” states, in particular AT and p N , manifesting as bands in the Dalitz plot of the invariant masses M + and px MT+=-. An NTT “uncorrelated production” is also present, which uniformly populates the Dalitz plot. A total of five independent kinematic variables is necessary to completely describe the final state, which leads to many possible alternative choices. 2. Low energy region
The second resonance region has been explored at the MAMI facility in Mainz by using tagged photons from 400 to 800 MeV. Data have been collected using the DAPHNE and the TAPS detectors for all possible charge configurations in the final state, and also using polarized photons and a polarized target. DAPHNE has been the first to provide new data in this energy region7. A first theoretical analysis of these result^^^^ showed essentially that the reaction -yp + ~ T + T -is dominated by the non-resonant background, and that interference effects in particular due to the 013(1520) resonance are important and have to be properly taken into account. Using the GDH set-up for polarized measurements, by using the circularly polarized photon beam from MAMI together with a “frozen spin” solid butanol target”, also the polarized cross section for y p + p7r’nhas been measured” and compared with theoretical calculations9i12i13.This is a very important and continuing experimental program with the aim of determining with high precision the contributions to the GDH sum rule from different reactions. Such sum rule deals with a weighted integral over the photon energy of the helicity difference in the total cross section and is related to fundamental properties of the photon-nucleon interaction. Both a simple Regge parametrization12, as well as a more sophisticated model based on tree-level diagrams from a Lagrangian description and on the main resonances from the second N’ regiong provide a relatively good agreement. Still, the data are not completely understood, which leaves the questions open whether resonance parameters may still be varied to accomodate the observed discrepancy, and whether the treatment of the non-resonant background is satisfactory. Total cross sections for the reaction -yp + ~ T + T ’ ,already measured with DAPHNE, have been measured more recently with the TAPS set-up, particularly well-suited for detection of gammas
180
from decay of neutralmesons as well as with the GDH set-up". Experimental results as well as the comparison with models are reported in the two
400
500
600
700
800
E, (MeV) 60 50
-
40
13
3 30 d 20
10 0 400
500
600
700
800
v (MeV) Figure 1. Total cross sections for the reaction yp -+ n d 7 ~ ' .The top graph is comparing data from different experimental set-ups, while the bottom one is reporting only the data from the GDH set-up. In the top graph, the full curve is the Valencia model13, while the dashed curve is the Holvoet-Vanderhaeghen c a l ~ u l a t i o n ~The ~ . bottom graph reports a comparison of the data with the model by Hirata et a1.I6 (full curve), the Valencia model13 (long-dashed curve), and the Holvoet-Vanderhaeghen Regge parameterization12 (short-dashed curve).
panels of figure 1. While the Regge parametrization provides the ballpark12, the more sophisticated Valencia model is working quite well13. A different tree-level calculation16 points instead to the importance of the pseudoscalar T N N coupling, concluding that it is working better in describing the data. The difference in the +yp + n.rr+.rro cross sections corresponding to photon-proton with paral-
181 80 60
Y
40
v
E;
20 0
-20
400
500
600
700
800
v (MeV)
Figure 2. Helicity difference in the cross sections for the reaction ~p 3 nn+nOfrom the GDH set-up. The data are compared with the model by Hirata et a1.16 (full curve), the Valencia model13 (long-dashedcurve), and the Holvoet-Vanderhaeghen Regge parameterization" (short-dashed curve). lel and antiparallel helicities is reported in figure 2, where it is compared again with theoretical c a l c ~ l a t i o n s Again ~ ~ ~ ~the ~ ~Regge ~ ~ . parametrization provides the ballpark12. The Valencia c a l ~ u l a t i o n 'does ~ somewhat better and essentially finds that p meson production via sub-threshold resonance decay and &3(1700) contributions are essential to reproduce ~ 3 / 2 while , u112 turns out to be too small. The japanese group16 again stresses the importance of using the pseudoscalar r N N coupling to reproduce the data. Finally, the ~p + p r o r o reaction has been explored with the TAPS set-up15. The comparison of the threshold behavior17 with a calculation based on chiral perturbation theory18 has shown that in this reaction chiral loops provide the dominant contribution. The new TAPS data provide a high precision total cross section measurement for this important reaction (previous DAPHNE cross sections suffered from the big extrapolation) that covers the second resonance region and overlaps with GRAAL points, which assures that systematics are relatively under control. A comparison of the invariant mass distributions with calculations from the Valencia group13 and from Laget8>19raises the question whether the data are dominated by the &(1520) (Oset et al.) or by the q1(1440) (Laget). It would therefore be desirable that this issue be sorted out by using both single and double pion unpolarized and polarized data from MAMI. Only such a global comparison with the complete available reaction database in this energy region can provide a clue as to what the correct resonance parameters are.
The Valencia model'3, besides the above mentioned tree-level mechanisms, contains in its latest version contributions from the p33(1232), q1(1440), 013(1520), and 033(1700) states. The model by Laget and Murphy contains contributions from the p11(1440), 013(1520), 013(1700), 033(1i'oO), and p11(1710) states.
182
3. Double 7ro production at higher energies Recently, the GRAAL experiment produced completely new data for the reaction y p -+ p7r07ro, using linearly polarized photons from laser backscattering with energy from 0.65 t o 1.5 GeV, therefore covering part of the second resonance region, the full third resonance region and somewhat beyond2'. These are very important data as in this completely neutral channel the non-resonant background is expected to give a very limited contribution, while N* excitation should be the dominant production mechanism. Both total and differential cross sections, as W (MeV) 1300 1400 1500 1600 I700
1800
1900
Figure 3. Total cross section for yp --t p.rroxo from GRAAL (full points), together with previous d a t a from TAPS (open circles and squares). Data are compared t o theoretical calculations as presented in the picture legend.
well as some polarization observables have been derived and compared to the available theoretical calculationss~13~19. Figure 3 shows data and models for the total cross section. The Valencia model extends only up to about 900 MeV photon energy, corresponding to resonance masses of 1600 MeV, while the model by Laget and Murphy is extending beyond the resonance region and for this particular channel assumes production of the u meson as the main non-resonant contribution. Comparing the GRAAL data to both these models in the low energy region, in both cases it is found that interference effects are very important. However, again in the Valencia model the low energy data are explained by a dominance of the D13(1520) resonance, while in the calculation by Laget the dominant N* state is the Pll(1440). In this latter case, it is worth to notice that agreement with the data is found assigning a mass of 1500 MeV to the P11(1440), this value being the PDG extreme4. The analysis of the invariant mass distributions and the polarization observables does not allow a conclusion on these two different interpretations in terms of dominant &(1520) or P11(1440), as both models reproduce the general features of the data but with remaining discrepancies on the detailed shapes. It is clear here again that data on different observables from different laboratories should be rather fitted all together, by
183 identifying what parameters can be allowed to vary in the models and in what ranges. This is the only way to reach a better understanding of these new high quality data and hopefully extract resonance parameters with better accuracy. Double 7ro production is also the subject of intense investigation with the Crystal Barrel/TAPS detector set-up at the ELSA accelerator in Bonn2', where photons with energy between 750 MeV and 3 GeV are being used to explore the high-lying resonance region, looking for missing states and the parity doublets that should appear if chiral symmetry is restored at such a high mass scale. Preliminary data (see figure 4) clearly show the TOT' contribution as well as an interesting xoq production yield. Invariant mass plots indicate production of the strong AT intermediate channel as well as N * n production with higher mass N* isobars. In the near future, measurements with polarized beam and target are foreseen, as clearly more observables are needed to constrain the extraction of resonance contributions from the complicated chain of isobar production. A full Partial Wave Analysis (PWA) program is under way and is expected to lead to a better understanding of the densely populated high-mass resonance region, especially when the new polarized data will be available.
Figure 4. Total cross section for y p --t pro.rro from GRAAL (full points), together with previous data from TAPS (open circles and squares). Data are compared to theoretical calculations as presented in the picture legend.
4. prr+rr-
production at higher energies
A vast program for N* investigation is under way with the CLAS detector in Hall B at Jefferson Laboratory". In particular the reaction -yp + p7r'n- has been measured with CLAS and a PWA based on the extended Maximum Likelihood method has been performed with the purpose of extracting P W in an almost model-independent way, then fitting the resonance contributions in each PWZ3. An example of the results obtained is shown in figure 5 . In this case, the task is clearly more difficult due to the well-known dominance of the non-resonant background. In this approachz3, no specific dynamical model has been assumed,
184
explicitly expanding cross sections in a geometrical basis of waves with definite angular momentum and parity. Some t-channel contributions were added empirically to account for strong forward production that would require too many P W in the geometrical basis. In this PWA of CLAS data, it was demonstrated that high-quality acceptance-corrected cross sections (independent of physics assumptions) can be derived both for the overall 2n production and for the isobar partial channels. This is a very good feature in this kind of analysis, as everybody will be able to use these experimental cross sections to perform a comparison with any specific dynamical model. However, there are certainly some limitations to this approach, in particular one should establish whether the freedom assigned to the P W is compatible with explicit dynamical models, and whether the limited detector acceptance is still permitting a fully sensible P W extraction. From this analysis, a large strength is seen for J p = -+ pp, which seems to confirm the
;+
;
strong coupling of the known P l ~ ( 1 7 2 0resonance ) to pp. Some indication of a resonant wave with decay t o An may be present, but with smaller strength. Although this may sound in contradiction with the indication for a new $+ decaying to An seen in e l e c t r o p r ~ d u c t i o nthe ~ ~ ,different couplings seen by the real photon with respect to the virtual one, as well as the strong non-resonant background together with sizeable interference effects may explain the difference in the two observations (see section 5). Clearly, more needs to be done to understand the reliability of the extracted partial waves, in particular comparing the obtained resonance parameters with the PDG ranges. Also, a better understanding of the non-resonant background in terms of indications from dynamical models may help in assessing the physical meaning of the extracted PW.
F
n- cos(8) C.M.
Figure 5. PWA of CLAS data for y p t pa+a-. The points with error bars are the data reported here as a function of the a- CM angle 8. The full curve is a PWA fit with a limited number of waves, while the dashed curve, obtained with a larger set of P W , provides a very good description of the data.
In CLAS, a sizeable part of the data for y p
+ pn+n-
were taken with circu-
185 larly polarized photons, produced by bremsstrahlung from the polarized electron beam. Preliminary cross sections have been derived on asymmetries corresponding to left-handed and right-handed photons, for particular kinematic^^^. Results have been compared to model calculation^^^'^^, obtaining a surprising agreement for some value of the invariant hadronic mass W and substant,ial disagreement in other cases. Clearly this work in progress will provide more constraints on the N* extraction and will greatly benefit from the approved future program of measurements with a frozen spin target28. A parallel analysis work is in progress on a sizeable database of measurements in CLAS with linearly polarized photons obtained by bremsstrahlung on a diamond crystal, with focus on vector meson photoproduction as a tool to access resonance excitation at high masses and therefore to look in particular for missing states2g. Linear polarization is providing complementary information to the measurements with circularly polarized photons, giving access to different interferences among complex production amplitudes, which will enrich the comparison with dynamical models, and can provide further strength to the full PWA. Interesting results are coming out of the analysis of yp + ~T'T- from previous measurements with the SAPHIR detector at ELSA3'. Beautiful mass plots with clear separation of AT and p contributions have been obtained, which will be an important complement to the existing body of data on this reaction. electroproduction and combined analysis w i t h photoproduction f r o m CLAS
5 . prr+rr-
~~ The new high statistics data from CLAS for ~ T + T -e l e c t r o p r o d u ~ t i o nshowed that using the phenomenological INFN-JLab-Moscow mode131 with known resonance i n p ~ t does ~ ~not > ~ allow ~ to explain the prominent bump seen around 1700 MeV of mass, neither using this approach as a model prediction nor using it to fit the data by varying resonance parameters within limits accepted in the literature. A more recent, refined version of the dynamical model that includes a larger number of reaction mechanisms according to empirical observations from the CLAS data34 attributes more strength in that region to non-resonant mechanisms, but still finds that substantial new resonant strength appears necessary in the AT intermediate isobar channel. This is in contradiction with existing knowledge on the established p13(1720) resonant state, for which 80-90 % p N branching ratio and no AT decay is reported in the l i t e r a t ~ r e ~It~ ?may ~ ~ be . possible that, due to the intrinsic difficulty of fitting many overlapping states, the results from this previous analyses of hadronic data have an intrinsic systematic error leading to a reversal of the two branches36. Independently of any consideration on the branching rations and their precision, it does not seem to be possible to reproduce the overall strength in the 1700 MeV mass region without increasing the known states in that region beyond reasonable limits set by previous analyses or quark model calculations. In fact, when we performed same phenomenological calculation taking the electromagnetic amplitudes from the Hypercentral Quark Model', still no agreement was found for the total virtual photon cross section as a function of W .
186 30
E
:
g25 20
-
-
15 -
10
-
S -
ot
" " "
" " " '
1.4
1.5
1.6
1.7
" " " " " '
1.8
1.9
2
I
Figure 6. Comparison of the CLAS data to a calculation based on resonant electromagnetic amplitudes from the HQM6. The data are from CLAS at the three different momentum transfers, < Qz >=0.65, 0.95, 1.3 GeV2/cz. The dot-dashed line is the calculation within the INFN-JLab-Moscow mode131 using resonance electromagnetic amplitudes (including longitudinal ones) from the HQM. The solid line is the calculation within the INFN-JLab-Moscow model using resonance electromagnetic amplitudes (including longitudinal ones) from the HQM except for the Roper, which is taken from previous fits of CLAS dataz4. For comparison, we report as the dashed line our final fitz4 starting from the amplitudes from reference3z.
A combined analysis of the real and virtual photon cross sections for pn+nfrom CLAS has been performed using the recent extension of the INFN-JLabMoscow model The need for a new state around 1720 MeV of mass, with J p = $+ and 41 f 13 % branching ratio into AT is confirmed. This state was found to contribute also to the real photon cross sections, but its presence turned out to be masked by very strong interference effects with the dominant non-resonant background. The presence of a new resonance in the CLAS data remains therefore a hot topic. Hopefully further confirmation will come from the undergoing CLAS analyses exploiting the real photon polarization. Future experiments with a polarized target in CLAS may provide an even richer set of spin observables to work with. Finally, other experiments measuring the same or different channels, possibly with the help of spin observables, like the current or upcoming measurements with the Crystal Barrel at ELSA may also shed light on this particular subject. In summary, a whole wealth of new data about double pion production, with real and virtual photons, for different final channels and including spin observables, is or will be soon available to the community. This poses a challenge to the theorists, requiring a support both in the direction of developing specific dynamical models, as well as in the direction of establishing firm PWA results.
187
Acknowledgments I wish to express my deep gratitude to all who provided material, pictures in particular, that helped me a lot in preparing the presentation and the writeup. References 1. M.M. Giannini, Rep. Prog. Phys. 54, 453 (1990) 2. S. Capstick, W. Roberts, Prog. Part. Nucl. Phys. 45, S241 (2000) 3. M. Kirchbach, Mod. Phys. Lett. A12, 3177 (1997) 4. K. Hagiwara et al., Phys. Rev. D66, 010001 (2002) 5. S. Capstick, contribution to this Workshop 6. M. Aiello et al., Phys.Lett. B387, 215 (1996) 7. A. Braghieri et al., Phys. Lett. B363, 46 (1995) 8. L.Y. Murphy, J.M. Laget, DAPNIA-SPHN-96-10, March 1996 9. J.A. Gomez Tejedor and E. Oset, Nucl. Phys. A571, 667 (1994) 10. H.J. Ahrends, contribution to this Workshop 11. Michael Lang, PhD Thesis, University of Mainz, to be published 12. H. Holvoet, PhD Thesis, University of Gent, in collaboration with M. Vanderhaeghen 13. J.C. Nacher et al., Nucl. Phys. A695, 295 (2001); J.C. Nacher, E. Oset, Nucl. Phys. A697, 372 (2002) 14. J. Ahrens et al. Phys. Lett. B551, 49 (2003) 15. M. Kotulla, contribution to this Workshop 16. M. Hirata et al., Phys. Rev. C67, 034601 (2003) 17. M. Kotulla et el. Phys. Lett. B578, 63 (2004) 18. V. Bernard et al., Phys. Lett. B382, 19 (1996) 19. J.M. Laget, unpublished 20. Y. Assafiri et al. , Phys. Rev. Lett. 90, 222001 (2003) 21. U. Thoma, Proceedings of the NSTAR 2002 Workshop on the Physics of Excited Nucleons, Pittsburgh, Pennsylvania, October 9-12, 2002, World Scientific 22. V. D. Burkert, Proceedings of the 7th Workshop on Electron Nucleus Scattering, Isola d’Elba, Italy, 24-28 Jun 2002, Eur. Phys. J . A17, 303 (2003) 23. M. Bellis, PhD Thesis, Rensselaer Polytechnic Institute, 2003, and contribution to this Workshop 24. M. Ripani et al., Phys. Rev. Lett. 91, 022002 (2003) 25. S. Strauch, contribution to this Workshop 26. W. Roberts and A. Rakotovao, hep-ph/9708236 27. V.I. Mokeev et al., Phys. Atom. Nucl. 66, 1282 (2003) 28. C.D. Keith et al., Proceedings of the 2nd International Symposium on the Gerasimov-Drell-Hearn Sum Rule and the Spin Structure of the Nucleon (GDH 2002), Genova, Italy, 3-6 Jul 2002, World Scientific 29. P.L. Cole et al., Proceedings of the International Symposium on Electromagnetic Interactions in Nuclear and Hadron Physics (EM1 2001), Osaka, Ibaraki, Japan, 4-7 Dec 2001, World Scientific; P.L. Cole et al., Proceedings of the 2nd International Symposium on the Gerasimov-Drell-Hearn Sum Rule and
188 the Spin Structure of the Nucleon (GDH 2002), Genova, Italy, 3-6 Jul 2002, World Scientific; P.L. Cole, Proceedings of the 2nd Conference On Nuclear And Particle Physics With CEBAF At Jlab (NAPP 2003), 26-31 May 2003, Dubrovnik, Croatia, to appear in Fizika B C. Gordon, ibidem 30. F. Klein and K.H. Glander, private communication 31. V. Mokeev et al., Phys. Atom. Nucl. 64, 1292 (2001) 32. V. D. Burkert et al., Phys. Rev. C67, 035204 (2003) 33. D.M. Manley, E.M. Saleski, Phys. Rev. D45, 4002 (1992) 34. V.I. Mokeev et al., contribution to this Workshop 35. T.P. Vrana et al., Phys. Rept. 328, 181 (2000) 36. S. Dytman, private communication; M. Manley, private communication; see also the ongoing discussion in the Baryon Resonance Analysis Group
A Partial Wave Decomposition of y p + p 7r+7rM. BELLIS Rensselaer Polytechnic Institute Department of Physics 110 g h St, Troy 12180, USA E-mail:
[email protected] THE CLAS COLLABORATION 12000 Jefferson Avenue Newport News, V A 23606, USA We perform a partial wave decomposition on the reaction y p -+ p . r r f r - for photon energies of 0.5-2.4 GeV (W = , h = 1.35 - 2.35 GeV/c2). The data was collected using the CLAS detector located at Jefferson Laboratory in Newport News, VA. We are searching for baryon states produced in y p + B and decaying by B --t p7r+nthrough quasi-two body intermediate states such as An and p p . Our partial wave decomposition allows us to accurately calculate the total and differential cross section. We also calculate the cross section for y p --t A++r-, y p + nor+, and 7 P -+ PP.
1. Introduction The goal of this analysis is t o answer the missing baryon problem: that the constituent quark model predicts states which have not been experimentally observed. One explanation is the diquark model12. Table 1 shows the non-strange baryons as listed in the PDG13 with the baryons predicted by the diquark model are shown in bold-face. It is interesting to note that these states correspond almost entirely to the well known 3- and 4-star resonances. Later calculations138i11 suggest that these missing states may not couple strongly t o N T and may be more easily observed in yN scattering where N m final states are analyzed. We perform a partial wave decomposition (PWD) on the reaction y p -+ p ~ + n - . By extracting the partial wave amplitudes it is hoped that any missing baryon states can be identified. In this stage of the analysis, we use the results of the PWD to acceptance correct the data and calculate total and differential cross sections, as well as calculate the cross sections for the various isobars through which the decays proceed.
189
190 Table 1. Non-strange baryons as listed in the PDG. The states predicted by the diquark model are shown in bold face. Status
**** **** **** ****
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2. The experiment and data selection
The data was collected at the CLAS (CEBAF Large Acceptance Spectrometer) at Jefferson Lab in Newport News, VA. This sample of data is taken from the "glc" running period which ran from 0ct.-Nov. 1999. About 15% of the total run period is analyzed. A bremsstrahlung photon beam is produced corresponding to a center-of-mass W from 1.35 to 2.35 GeV/c2. Details of the CLAS detector can be found in the reference^'^. A GEANT-based program, gsim, was used for Monte carlo simulation. A detailed study of the acceptance was performed to check the agreement between the simulation and real-world data. The full description of the method is given in the references4, but we provide a summary. We determine the detector efficiency for a given final state particle by calculating how often a particle had some momentum, and then looking to see how often we detected that particle. For example, let me determine the efficiency of the CLAS to detect a proton. We look at events where a n+ and n- are detected, regardless of whether or not a proton has been detected. The missing mass off the pions is calculated and it is determined if there was a proton in the final state. At this point we look if the CLAS saw a proton, and if its momentum corresponds to the missing momentum off the pions. With this information we calculate an efficiency and bin in each particle's momentum. We calculate this efficiency independently for both the real world data and the Monte Carlo simulation. Examples of the efficiency plots are shown in Fig. 1. We use this diagnostic tool to identify our fiducial cuts. In the end, we have a very clean sample of 775,553 exclusive data events. Because of questions regarding acceptance, we only show results above W = 1.55 Gev/c2.
191
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3. Features of the data
Even before we perform any sort of PWD or acceptance correction, there are some obvious features in the data. The two-body plots in Fig. 2 demonstrate the primary isobars in the W M 1.75 GeV/c2 range. The A++ is the dominant isobar through which the decay proceeds, though some Aok are clearly visible. Fig. 3 shows the same quantities for W M 2.15 GeV/c2. The p is now the strongest signal, though the A's are still visible. There may also be N*'s in the region 1.5 and 1.7 GeV/c2 in the p7r- spectrum.
4. Partial wave decomposition 4.1. Method
The basis of our PWD is to take the transition amplitude for the reaction, and expand in some basis determined by the intermediate states ( a ) .
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=
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We do not know what the coupling may be for some state to decay to our isobars,
193 and so this term will get wrapped up into the production amplitude in the fit. We fit the intensity using the maximum likelihood method. The waves we included can be found in the reference^.^>^ 4.2. Results
4.2.1. Description of data distributions
From the results of a fit in some bin, we weight the accepted Monte Carlo data and compare the kinematic distributions to the CLAS data as a check of how well we are modeling the data. In Fig. 4 we show the CLAS data for the 7rpolar angle in the center-of-mass compared with accepted phase space and the accepted phase space weighted by the results of a fit. The fits pulls the Monte Carlo away from a flat distribution in an effort to describe the data.
p cos(8) C.M
p cos(8) C.M.
Figure 4. 1.69 < W < 1.71 GeV/c2. The first plot shows the T- cos(8) in the center of mass for CLAS data in the filled plot, and the thick line represents accepted Monte Carlo data. The second plot shows the same variable with the same CLAS data, but the solid line represents the accepted Monte Carlo data weighted by the results of some fit.
Figure 5 . Differential cross sections for center-of-mass angle for r- and proton. 1.69 < W < 1.71 GeV/c2.
194
120 100
40
O
1.4
1.6
1.8
2
2.2
2.4
W GeV/c2 Figure 6. Total cross section. 4.2.2. Differential and total cross sections
We take the results of a fit and weight the raw Monte Car10 data to calculate differential and total cross sections as shown in Fig. 5 and Fig. 6. Total cross section is compared with two earlier bubble chamber experiments'". 4.2.3. Cross section for isobars
Our PWD method also allows us to calculate the cross section for our three isobars as shown in Fig. 7. The A++ and p cross sections are compared with the previous measurements''2. 5. Conclusions
We have greatly improved previous measurements for the total and differential cross sections and started providing these quantities to the community for comparison with more model dependant analysis. We are in the process of understanding the cross sections for the individual waves and the best way to incorporate this into a more involved coupled-channel resonance analysis. References 1. Aachen-Berlin-Bonn-Hamburg-Hedielberg-MunichCollaboration, Photoproduction of meson and baryon resonances at energies up to 5.8-GeV, Phys. Rev., 175:1669-1696, 1968 2. Cambridge Bubble Chamber Group, Production of the N*(1238) Nucleon Isobar by Photons of Energy up to 6 BeV, Phys. Rev., 163:1510-1522, 1967 3. Bellis, Matthew, A search for missing baryon states, UMI-31-13552 4. Bellis, Matthew, Reliability and liabilities of GSIM, CLAS-NOTE 2002-016, 2002 5. Bellis, Matthew and the CLAS collaboration,' An analysis of yp -+ PT'Tusing the CLAS detector, AIP Conf. Proc., 698:535-538, 2004
195
70
.,
I
.
. .
A-
n
W GeVIc'
2.4
W GeV/c2
Figure 7.
Calculated cross sections for photoproduction of A++, Ao and p.
6. Capstick, Simon and Roberts, Winston, NT decays of baryons in a relativized model, Phys. Rev., D47:1994-2010, 1993 7. Chung, Suh Urk, Spin formalisms, Lectures given an Academic Training Program of CERN, 1969-1970 8. Forsyth, C.P. and Cutkosky, R. E., A quark model of baryons with natural flavor, 2. Phys., C18:219, 1983 9. Hagiwara, K. et. al., Review of particle physics, Phys. Rev., D66, 2002 10. Jacob, M. and Wick, G. C., On the general theory of collisions for particles with spin, Ann. Phys., 7:404-428, 1959 11. Koniuk, Roman and Isgur, Nathan, Baryon decays in a quark model with chromodynamics, Phys. Rev., D21:1868, 1980
196
12. Lichtenberg, D. B., Baryon supermultiplets of SU(G)x0(3) in a quark-diquark model, Phys. Rev., 17:2197-2200, 1969 13. Mecking, B. A. et. al., The CEBAF Large Acceptance Spectrometer (CLAS), Nucl. Instrum. Meth., A503513-553, 2003
7 Photoproduction Off the Neutron at GRAAL: Evidence for a Resonant Structure at W = 1.67 GeV Viacheslav KUZNETSOV FOR THE GRAAL COLLABORATION Institute for Nuclear Research, 117312 Moscow, Russiaa E-mail:
[email protected],
[email protected] New data on q photoproduction off the neutron are presented. These data reveal a resonant structure at W = 1.67 GeV.
Meson photoproduction on the neutron may provide essentially new information regarding the spectrum of baryons. An example is given by a model' which exploits the SU(6) symmetry and assumes single-quark transitions from ground nucleons to the [70,1-] supermultiplet. The model predicts only weak photoexcitation of the D15(1675) resonance from the proton target. Conversely, photonneutron couplings of D15(1675) calculated in the framework of this approach are not small. Measurements of the relative strength of photoneutron/photoproton interaction are therefore an important testing ground for this (and others) theoretical approaches. Another example is possible photoexcitation of the non-strange pentaquark state, which is associated with the second member of an antidecuplet of exotic baryons273. Evidence for the lightest member of the antidecuplet, the O'(1540) baryon, is now being widely discussed4. It can be produced, in particular, by ~ forbid the prophotoexcitation of the nucleon. However, exact S u ( 3 ) would ton photoexcitation into the proton-like antidecuplet member. The chiral soliton model predicts that photoexcitation of the non-strange pentaquark has to be suppressed on the proton and should occur mainly on the neutron, even after accounting for s U ( 3 ) violation5. ~ Estimates of the mass and width of the nonstrange pentaquark are ambiguous. As initial input, the mass was used to be 1.71 GeV2, with the width estimated 40 MeV. More recent evaluation of the chiral soliton approach led to the range of 1.65 - 1.69 GeV'. In the di-quarks approach3, the mass of the pentaquark with hidden strangeness is quoted about 1.7 GeV. Modified partial wave analysis of the n N scattering7 suggests two possible candidates, at 1.68 GeV and/or at 1.73 GeV, with the total width about 10 MeV and the partial width for nN decay mode less than 0.5 MeV. Thus, photo-neutron excitation data, and their comparison with photo-proton excitation, may be important both in establishing existence of pentaquarks and in discriminating between different theoretical concepts. Among other reactions, 1
-
&Present temporal address is Thomas Jefferson National Accelerator Facility, 12000 Jefferson Av., Newport News, VA23606 USA.
197
198 photoproduction has been suggested as particularly sensitive to the manifestation of the non-strange p e n t a q ~ a r k ~ ~ ~ , ~ ~ ~ . Up to now, q photoproduction on the neutron has been explored only in the region of the &1(1535) resonance from threshold up to W = 1.6 GeV'7gi10. Some of the previous experiments' were limited to inclusive measurements detecting only the outgoing 17. In exclusive experimentsgi10, both the q and the recoil nucleon are detected. This makes it possible to discriminate between qn and q p final states and to select events corresponding to quasi-free kinematics. A new exclusive measurement has been performed at GRAAL11712using a deuteron target. Both quasi-free yn + qn and y p + q p reactions were explored simultaneously in the same experimental run under the same conditions and solid angle. Two photons from q + 2y decay were detected in the BGO crystal ball13. Recoil neutrons and protons emitted at @ l a b = 3 - 23', were detected in an assembly of forward detectors, which includes two planar multiwire chambers, a time-of-flight (TOF) wall made of thin scintillator strips, and a lead-scintillator sandwich TOF waIll4. The latter detector adds the option of neutron detection with an efficiency of 22%. The momenta of the q and recoil nucleons were reconstructed from measured energies, TOFs and angles of outgoing particles.
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Recoil neutron, proton farget
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Figure 1. Bi-dimensional plots of invariant mass of two photons versus missing mass calculated from momenta of recoil nucleons for proton and deuteron targets.
As a first step, the identification of the qn and q p final states was achieved in a way similar to that used in the previous measurements12 on the free proton. The q was identified by means of the invariant mass of two photons and its momentum was reconstructed from measured photon energies and angles. Then measured parameters of the recoil nucleon were compared with ones expected assuming quasi-free kinematics. Fig. 1 shows bi-dimensional plots of 27 invariant mass
199 versus q missing mass obtained in experimental runs with proton and deuteron targets. A good q p signal was obtained with the proton target, while only few qn events were detected in this run. Signals of both final states clearly appear with the deuteron target. In case of a photon interaction with the nucleon bound in a deuteron target, event kinematics is “peaked” around that one on the free nucleon. Fermi motion of the target nucleon changes the effective energy of photon-nucleon interaction and affects parameters of outgoing particles. Part of events may suffer from re-scattering and final-state interaction15. The goal of the second-level selection was to reduce re-scattering events, the remaining background (mostly from yd + q r N N ) , and those events whose kinematics are strongly distorted by Fermi motion. Additional cuts on the recoil nucleon missing mass M ( y N ,q ) and ATOF have been applied. Those events in which the detection of two photons and the recoil nucleon was accompanied by the detection of any low-energy particle(s) in the 4r GRAAL detector, have been eliminated from the analysis. The strategy at this stage was to study the dependence of spectra of selected events on cuts. Two criteria of quality of the selection procedure have been exploited: (i) distribution of Fermi momentum of the target neutron reconstructed as “missing momentum” with small correction on binding energy; (ii) difference of the center-of-mass energy W calculated from the momentum of the initial-state photon and assuming the target nucleon at rest, and the center-of-mass energy deduced as the invariant mass of the final-state q and the neutron. The first quantity includes uncertainties due to Fermi motion and is “peaked” around the real center-of-mass energy of photon-nucleon interaction. The qn invariant mass is not affected by Fermi motion but includes large uncertanties (50 - 80 MeV, FWHM) due to detector resolution. In the upper row of Fig. 2, the final-state (first column) and initial-state (second column) W spectra obtained with the first-level cut are shown. Both of them indicate a wide bump in the region 1.6 - 1.7 GeV. The Fermi momentum (third column) exhibits a broad distribution. Plots in the lower row correspond to final cuts. Both final and initial-state spectra are similar and show an enhancement of the s11(1535) resonance below 1.6 GeV. The bump near 1.67 GeV observed in the previous spectra, becomes more narrow and well-pronounced. The Fermimomentum spectrum is more compressed and has its maximum near 0.05 GeV/c, as expected for quasi-free events. Evolution of spectra in Fig. 2 suggests that most of events rejected by the second-level cuts either originate from re-scattering and final-state interaction or strongly suffer from Fermi motion. On the contrary, events shown in lower-row plots, are more “clean”. They correspond to quasi-free photoproduction, and the distortion due to Fermi motion is reduced. The latter fact makes it possible to clearly reveal the structure at 1.67 GeV. These events were found suitable for the further analysis. Preliminary quasi-free qn and q p photoproduction cross sections are shown in Fig. 3. The normalization has been done by comparing quasi-free proton data and the E429 solution of the SAID yp + q p partial wave analysis17 for q photoproduction on the proton which was obtained from the fit to all available data includ-
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ing recent data from GRAAL11312,JLab18, and SAPHIR”. Such normalization made it possible to avoid ambiguities related to the fact that some of the events are lost due to the re-scattering and final-state interaction. Above 1.55 GeV, a reasonable coincidence in the shape of the cross sections has been obtained. At lower energies, re-scattering and final-state interaction become more significant and play a dominant role near threshold15. Error bars shown in Fig. 3 correspond to statistical uncertainties only. The present normalization uncertainty of 12% originates mostly from the quality of simulations of quasi-free processes and from uncertainties in the neutron detection efficiency. At W below 1.6 GeV, both cross sections exhibit bumps due to the S11(1535) resonance. At higher W, an additional structure clearly appears for the neutron and is not seen on the proton. Remarkably, beam asymmetry C (Fig. 4) shows pecularities at the same energies. In the region of S11(1535) resonance, C ranges around 0.2 and is nearly the same for the neutron and the proton. In the region 1.65 - 1.73 GeV, there are step-like changes. The trends of these changes are opposite: for the proton, the asymmetry becomes almost 0, while for the neutron it rises up to 0.4. It is worth noting that beam asymmetry is more sensitive to the non-dominant contributions than cross section since it is given by the interference of helicity amplitudes Hi16 corresponding to four possible helicity states of the target and recoil nucleon:
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GeV.
Both the observed peak in the cross section on the neutron and corresponding changes in beam asymmetry might be an indication that one of the nucleon resonances has much stronger photocoupling to the neutron than to the proton. In Fig. 3, the simulated contribution of a narrow (10 MeV) resonance state with a mass of 1.675 GeV is shown. Such a state appears in the cross section as a 40 MeV wide peak due to Fermi motion of the target nucleon. The shape of the simulated peak fits quite well the shape of the peak observed in the cross section on the neutron. Therefore, this peak may be a signal of a relatively narrow state. Potentially, this state looks promising as a candidate for the non-strange pentaquark. The feature of strong photocoupling to the neutron agrees with the prediction of the chiral soliton model'. On the other hand, one cannot exclude that the ob-
202
Figure 4. Beam asymmetry C for Vn(1eft) and Vp(right) photoproduction
served peak is a manifestation of one of the known resonances, in particular, the 015(1675), as is suggested by the single-quark transition model'. A crucial task is to "unfold" the cross-section and beam-asymmetry data from Fermi motion, in order to achieve a reliable estimate of the width of this state. As a further step, a partial wave analysis will be needed to fix its quantum numbers. It is worth to add that the kaon photoproduction has been quoted as well to be particularly sensitive to the signal of the non-strange p e n t a q ~ a r k ~as~ well. Very preliminary indications on a state at 1.72 GeV have been obtained in yn t KfA and y n + K+C- reactions2', in production of K f h final state in Au Au collision21, and in p p -+ K + Ap reaction22. This work was supported by the Universiti di Catania and Laboratori Nazionale del Zud, INFN Sezione di Catania (Italy). Discussions with Ya. Azimov, W. Briscoe, V. Burkert, D. Diakonov, M. Kotulla, B. Krusche, A. Kudryavtsev, V. Mokeev, E. Pasyuk, M. Polyakov, A. Sibirtsev, I. Strakovsky, and R. Workman were very helpful.
+
References
1. V. Burkert et al., Phys. Rev. C67, 035205 (2003). 2. D. Diakonov, V. Petrov, and M. Polyakov, 2. Phys. A 359,305 (1997).
3. R. JaEe and F. Wilczek, Phys. Rev. Lett. 91, 232003 (2003); arXiv:hepph/0307341. 4. T. Nakano, to be published in Proceedings of Workshop on Physics of Excited Nucleons NSTAR2004, Grenoble, March 24 - 27, 2004; V. Burkert, to be published in the same Proceedings. 5. M. Polaykov and A. Rathke Eur. Phys. J A 18, 691 (2003); arXiv:hepph/0303138. 6. D. Diakonov and V. Petrov, Phys. Rev. D 69, 094011 (2004); arXiv:hepph/0310212 7. R. Arndt et al., Phys. Rev. C 69,0352008 (2004); arXiv:nucl-th/0312126. 297 (1997); 8. B. Krushe et al., Phys. Lett. B358,40 (1995).
203 9. V. Heiny et al., Eur. Phys. J. A 6,83 (2000);J. Weil3 et al., Eur. Phys. J. A 16,275 (2003), arXiv:nucl-ex/0210003. 10. P. Hoffman-Rothe et al., Phys. Rev. Lett. 78,4697 (1997). 11. F. Renard et al., Phys. Lett. B528,215, 2002. 12. J. Ajaka et al., Phys. Rev. Lett. 81,1797, 1998. 13. F. Ghio et al., Nucl. Inst. and Meth. A 404,71, 1998. 14. V. Kouznetsov et al., Nucl. Inst. and Meth. A 487,128, 2002. 15. A. Baru, A.Kudryavtsev, and V. Tarasov, Phys. Atom. Nucl. 67 743, 2004, a.rXiv:nucl-th/0301021; A. Sibirtsev, S. Schneider, and C. Elster, Phys. Rev. C 65,067002 (2002), arXiv:nucl-th/0203039; A. Fix and H. Arenhovel, Phys. Rev. C 68,44002 (2003), arXiv:nucl-th/0203039; and references therein. 16. Definitions of helicity amplitudes are available in W.-T. Chiang and F. Tabakin, Phys. Rev. C 55, 2054 (1997); R. A. Arndt et al., Phys. Rev. C 42,1853 (1990). 17. R. A. Arndt, W. J . Briscoe, I. I. Strakovsky, and R. L. Workman, in progress, http://gwdac.phys.gwu.edu. 18. M. Dugger et al., Phys. Rev. Lett. 89,222002 (2002). 19. V. Crede et al., arXiv:hep-ex/0311045. 20. V. Kuznetsov for the GRAAL Collaboration. Talk at Workshop “Pentaquark states: structure and properties”, Trento, Italy, February 10 - 12, 2004. http: //www.tp2.ruhr-uni-bochum.de/talks/trentoO4/index.html. 21. S. Kabana for the STAR Collaboration. Talk at 20th Winter Workshop on Nuclear Dynamics, Jamaica, March 15 - 20, 2004. arXiv:hep-ex/0406032. 22. W. Eyrich for the COSY-TOF Collaboration. Talk at the International Workshop ‘LPentaquark04”,Spring-8, Japan, July 20 - 23, 2004. http://www.rcnp.osaka-u.ac.jp/penta04/.
Excited Baryons and Pentaquarks on the Lattice F. X. LEE Center for Nuclear Studies, Physics Department, The George Washington University, Washington, DC.20052, USA I review recent progress in computing the mass spectrum of excited baryons and pentaquarks in lattice QCD.
1. QCD primer Quantum Chromodynamics (QCD) is widely accepted as the fundamental theory of the strong interaction. The QCD Lagrangian density can be written down simply in one line (in Euclidean space)
+
where F,, = aA, - dA, g[A,, A,] is the gluon field strength tensor and D, = a, gA, is the covariant derivative which provides the interaction between the gluon and quark terms. The action of QCD is the integral of the Lagrangian ~ X is . a highly non-linear density over space-time: SQCD = ~ L Q C D ~QCD relativistic quantum field theory. It is well-known that the theory has chiral symmetry in the mq = 0 limit and the symmetry is spontaneously broken in the vacuum. At high energies, it exhibits asymptotic freedom, while at low energies it has confinement. At the present, the only tool that provides a solution t o QCD with controlled systematic errors is lattice QCD which solves the theory on a discrete space-time lattice using numerical simulations. The basic building block for computing the spectrum is the fully-interacting quark propagator defined via the path integral
+
+
where M = y p D, mq is the quark matrix. In the last step the quark fields have been exactly integrated, resulting in a path integral over only the gluon fields. The expression resembles a statistical system with the weighting factor detMe-SG for which Monte-Carlo methods can be employed. In this sense the quark propagator is simply the inverse quark matrix in the background of detMe-'". The determinant detM proves costly to simulate so it is usually set t o a constant, leading to savings of up to a factor of 100. This is called the quenched approximation which amounts to ignoring the quark-antiquark bubbles in the QCD vacuum.
204
205 Fig. 1 is a picture of the proton in QCD. Three valence QCD quarks propagate in time continuously from one point to another in the QCD vacuum with the quantum numbers of the proton. They can back in both space and time. Quarkantiquark bubbles pop up from the vacuum. The quark lines are dressed by any number of gluons. It's the interactions such as these that are responsible for most of proton's mass. The quark themselves (5 MeV) contribute less than 1 percent to the proton mass. This is in contrast to the quark model where most of the proton mass comes from the constituent quarks (330 MeV) with only weak pair-wise interactions via one-gluon-exchange.
U L
d -
-U Figure 1. Proton in QCD (left) vs. proton in quark model (right).
2. Baryon resonances
The rich structure of the excited baryon spectrum, as documented by the particle data group ', provides a fertile ground for exploring the nature of quark-quark interactions. Most of the spectrum, however, is poorly known. Traditionally quark models have led the way in making sense of the spectrum. But many puzzles remain. What is the nature of the Roper resonance, and the A(1405)? How to explain the inverted ordering of the lowest-lying states which has the order of positive and negative-parity excitations inverted between N , A and A channels? Two contrasting views have emerged about the nature of the hyperfine splittings in the baryons. One is from the constituent quark model 3 3 4 which has the interaction dominated by one-gluon-change type, ie., color-spin A: . A;& . 52. The other is based on Goldstone-boson-exchange which has flavor-color Af . X i 5 1 . 52 as the dominant part. Lattice QCD is perhaps the most desirable tool to adjudicate the theoretical controversy surrounding these issues. Evidence from valence QCD favors the flavor-color picture. Lattice QCD has evolved to the point that the best quenched calculation, of the ground-state hadron spectrum, shown in Fig. 2, has reproduced the observed values to within 7%, with the remaining discrepancy attributed to the quenched approximation. This bodes well for the exploration of the excited sectors of the spectrum, even in the quenched approximation.
206
1.8 1.6 1.4
c
% 1.2
IY R
a
2
K* 1.0
N
P
0.8
0.6
rH
K
IP
I A
K input
Q input experiment
0
c
0.4
Figure 2. Light hadron spectrum from quenched lattice QCD by the CP-PACS Collaboration '.
2.1. Roper and
S11
There exist a number of lattice studies of the excited baryon spectrum using a variety of actions 7,8,9,10,11,12113,14. The nucleon channel is the most-studied, focusing on two independent local fields:
x 1 is the standard nucleon operator, while x 2 , which has a vanishing nonrelativistic limit, is sometimes referred to as the 'bad' nucleon operator. Note that baryon interpolating fields couple to both positive and negative-parity states, which can be separated by well-established parity-projection techniques. There are two problems facing these studies. First, they have not been a h k to probe the relevant low quark mass region while preserving chiral symmetry at finite lattice spacing (except Ref. l 2 which uses the Domain Wall fermion). Since the controversy about the nature of Roper hinges on chiral symmetry, it is essential to have a fermion action which explicitly exhibits the correct spontaneously broken chiral symmetry. Another difficulty of the calculation of the excited states in lattice QCD is that the conventional two-exponential fits are not reliable. Facing the uncertainty of the fitting procedure for the excited state, it has been suggested to use the non-standard nucleon interpolating field x 2 , in the hope that it may have negligible overlap with the nucleon so that the Roper state can be seen more readily. However, the lowest state calculated with this interpolation field (2.2 GeV) is much higher than the Roper state. Employing the
207 maximum entropy method allows one to study the nucleon and its radial excitation with the standard nucleon interpolation field 15. However, with the pion mass at 600 MeV, the nucleon radial excitation is still too high (- 2 GeV). So the ordering of the nucleon, Sll(1535) and the Roper in these studies remains the same as that from quark models. Our results below are obtained on two lattices, 123 x 28, and 163 x 28, using the Iwasaki gauge action l6 and the overlap fermion action 17. The lattice spacing of a = 0.200(3) fm was determined from fir l8 for both lattices, so the box size is L=2.4 fm and L=3.2 fm, respectively. Our quenched quark propagators cover a wide range of quark masses: 26 masses ranging from pion mass of 916 MeV to 181 MeV. Our strange quark mass is set by the 4 meson, corresponding to a pseudoscalar meson mass m p 762 MeV. The Iwasaki gauge action is an O ( a 2 ) renormalization-group improved action which allows the use of relatively coarse lattices without suffering from large discretization errors. The standard Wilson gauge action, on the other hand, has O ( a ) discretization errors, so one has to work at relatively fine lattice spacings to achieve comparable accuracy. The overlap fermion action preserves exact chiral symmetry on the lattice, thus it does not have O ( a ) error. One further finds that O ( a2) errors are small for the meson masses 18. Owing to the the relatively gentle critical slowing down, it allows us to push to unprecedented small quark masses. The relatively large box size ensures that the finite-volume errors are under control. At our lowest pion mass, the finite-volume error is estimated to be 2.7%. We have used the combination of Iwasaki gauge action and overlap fermion action in a number of recent studies, including chiral logs l9 and baryon excited states 20. We use a constrained-fitting algorithm called the sequential empirical B a y e s method 21 that we developed to handle excited states and unconventional fitting models, especially in the light quark region. We analyzed 80 gauge configurations. Our final result is shown in Fig. 3. We see that for heavy quarks ( m , 2 800 MeV), the Roper, ,911, and nucleon splittings are like those of the heavy quarkonium. When the quark mass becomes lighter, the Roper and S11 have a tendency to coincide and cross over around m, = 220MeV. More statistics are needed to clarify this point. However, from the insert in the figure, we can see that the ratio of Roper to nucleon has a smaller error (by 40%) than the Roper mass itself. It shows that the Roper is consistent with the experimental value near the physical pion mass. We use the form CO C112ma C l m z to extrapolate the Roper and ,911 to the physical pion mass. The resultant nucleon mass of 928(56))MeV, Roper at 1462(157) MeV, and Sll at 1554(65) MeV are consistent with the experimental values. Our result confirms the notion that the order reversal between the Roper and Sll(1535) compared to the heavy quark system is caused by the flavor-spin interaction between the quarks due to Goldstone boson exchanges '. It serves to verify that the Roper (1440) is a radial excitation of the nucleon with three valence quarks. It also cast doubts on the viability of using the non-standard interpolation field for the Roper. We further support the notion that there is a transition from heavy quarks (where the SU(6) symmetry supplemented with color-spin interaction for the valence quarks gives a reasonable description) to light quarks (where the dynamics is dictated by chiral symmetry).
-
-
-
-
+
+
208
t
2 h
3
$
v
rn ran rn
m (1535)
S:l
0
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1
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0
1.7 1.5
cd
0.5
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I
I
I
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0.2
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Q~( GeV2 )
Figure 3. Nucleon, Roper, and Sll masses as a function of m:, using the standard nucleon interpolating field XI. The insert is the ratio of Roper t o nucleon mass. The experimental values are indicated by the corresponding open symbols.
It is suggested that this transition occurs at m,
N
400 MeV for the nucleon.
2.2. The 17’ ghost
The above result is obtained only after the special effects of the so-called 7’ghost are removed. In full QCD, the 7’meson contributes t o the proton via vacuum polarizations, as shown in Fig. 4. Being a relatively heavy meson, its contribution is much smaller than that of the pion. However, in quenched QCD, the vacuum loops are suppressed, as shown in Fig. 5 (hairpin diagram), resulting in the following peculiar properties. First, it becomes a light degree of freedom, with a mass degenerate with that of the pion. Second, it is present in all hadron correlators. Third, it gives a negative-metric contribution t o the correlation function. For these reasons, it is termed the 7’ghost: it is an unphysical state, and a pathology of the quenched approximation. The effects of 7’ghost were first observed in the a0 meson channel 2 2 , where the ghost S-wave q ’ state ~ lies lower than a0 for small quark mass. The situation here is similar with the excited state of the nucleon where the P-wave q’N appears in the vicinity of the Roper. Since this is not clearly exhibited in the nucleon correlator where the nucleon is the lowest state in the channel and dominates the long-time behavior of the correlator, we can look at the parity partner of
209
the nucleon ( N i p or S11) with I = 1/2. There, the lowest S-wave q’N state with a mass close to the sum of the pion and nucleon masses can be lower than ,911 for sufficiently low quark mass. Due to the negative-metric contribution of the hairpin diagram, one expects that the S11 correlator will turn negative at larger time separations as is in the case of the a0 22. In Fig. 6, we show the S11 correlators for 6 low quark cases with pion mass from m, = 181(8)MeV to m, = 342(6) MeV. We see that for pion mass lower than 248(7) MeV, the Sll correlator starts to develop a negative dip at time slices beyond 4, and it is progressively more negative for smaller quark masses. This is a clear indication that the ghost 7’N state in the S-wave is dominating the correlator over the physical S11 which lies higher in mass. This is the first evidence of 17’ ghost in a baryon channel.
P
U
Figure 4. Quark-line diagram for the Q’ contribution to the proton in full QCD (left) and its hadronic representation (right). Any number of gluon lines can be present in the quark-line diagram.
U
*
d
*
$ ghost P
i
_..-__ _. ..
P
P
U
Figure 5.
The 7’contribution to the proton in quenched QCD.
Using our constrained curve fitting algorithm, we are able to distinguish the physical Roper and ,911 from the ghost two-particle intermediate states (17”) by checking their volume dependence and their weights as a function of the pion mass. For details, see 20. Our results demonstrate that the effects of 7’ghost must be reckoned with in the chiral region (below m, MeV ) in all hadron channels in quenched QCD. Another progress is the separation of the two nearby state in the 1/2- nucleon channel: N ( 1535)1/2- and N ( 1620)1/2-. Conventional techniques have difficulty in separating the two on the lattice. This has been achieved in a recent study 23 by using multiple operators and variational analysis, as shown in Fig. 7.
-
210 3e-06 2e-06 le-06
0 -1e-06 3e-06
t
t
t
2e-06 le-06
0 -1e-06 I
II
I
I 1
I
I
I
2
4
6
8 101214
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6
8 101214
I
I
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I
2
4 6
8 10121416
I
I
I
Time-Slices (t) Figure 6 . Evidence for the 7’ ghost in the Sll correlators for six low pion masses (in GeV) .
It would be interesting t o see if this can b e pushed t o smaller quark masses after the ghost states are taken out.
2.5
aM
0.5
163 x 32 full curve I lz3 x 24 : dashed curve
0.00
I
0.05
I
I
0.10
,
I
0.15
I
-
Nucleon
I
0.20
I
am
0.25
4
Figure 7. Results in the nucleon channel in lattice units. The two nearby states N(1535)1/2- and N(1620)1/2- are clearly separated. Figure taken from 23.
211 2.3. Hyperon Resonances
Fig. 8 show the results in A channel. The lowest negative-parity state is the flavorsinglet A(1405)1/2-. The correct ordering between it and the lowest two octet A states is reproduced on the lattice. There is no level-crossing in this channel. An interesting puzzle is the ordering between N(1535)1/2- and A(1405)1/2-. A(1405)1/2- has the same spin-parity, but a heavier s quark its quark content (uds) than N(1535)1/2- which has quark content (uud). Yet it lies lower than N(1535)1/2-. This is correctly reproduced on the lattice, as shown in Fig. 8. The reason it can happen has to do with the different flavor structure of the A(1405)1/2-. This example shows the importance of flavor-spin interact ins in the baryon spectrum. 2.5 I
I
I
I
I
2.5
I
I
I
I
I
I
h
5
2.0
0
v v)
1.5
5 2 m 1.0
m
0.0
0.2 '0.4 0.6 m n (GeV')
0.8
1.0
0.5
I
I
I
I
I
0.0
0.2
t.4
0.6
0.8
mn (GeV')
1.0
Figure 8. Left: Preliminary results for the level-ordering in the A($*) channel. Right: Preliminary results for the level-ordering between N(1535)1/2- and h(1405)1/2-.
2.4. Chiral Dynamics
To understand the chiral dynamics taking place in the small quark mass region, we show quark-line diagrams that contribute to the meson cloud surrounding the nucleon. In the quenched approximation, the last two disconnected diagrams are suppressed, but the connected Z-type diagrams survives. Similar diagrams can be drawn for the A(1405) and others. These connected diagrams are responsible for the non-linear behavior (curvature) in the chiral region. Effective theories that incorporate these diagrams are likely to capture the chiral degrees of freedom of
QCD. 3. Pentaquarks Since the report on the discovery two years ago of an exotic pentaquark, named as O+(uuddS), with a mass of about 1540 MeV and a narrow width of less than 20
212
.
*
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,...
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Figure 9. Quark skeleton diagrams that constitute the meson cloud in the nucleon channel. Any number of gluons can contribute in these diagrams.
MeV 24, there has been an explosive growth of interest in the subject 2 5 . Here I focus on an overview of developments on the lattice. So far, there are four lattice calculations 26,27,28,29,30 Here we use 26130 to recap the essential elements of a lattice calculation of the pentaquark. Pentaquarks do not have a unique color structure aside from being a color singlet. For a pentaquark of the type uudd5, we consider both isospin 1=0 and 1=1 states with the following interpolating field
where the minus sign is for 1=0 and the plus sign for I=l. The explicit spinparity of this interpolating field is +-, but it couples to both parities. Under the anti-periodic boundary condition used in this work, the positive-parity state propagates in the forward time direction in the lower component of the correlation function, while the negative-parity state propagates backward in the same lower component. The correlation function using the interpolating field in Eq. ( 5 ) has four terms. Due to isospin symmetry in the u and d quarks, the two diagonal terms are equal, and so are the two cross terms. The master formula, after contracting out all
21 3 possible quark pairs, reads
( X b )x ( 0 ) ) = 2EabcEa'b'c'
{ s:a'CySS:b'TS,"f*s;f
TCY5Scf
+sp'Tr (s i b ' Cy5sr' cy5sys," - 1 bb' -%pin, col (Sd st )s:"' CY5S d CY5 sc' -Trspin,color (Sd s,t1s:"' w : b ' CY5 sr' CY5 1 F2EabcEa'b'c' { -s;f s,"f * Ts?'n ( S p C"15s:b' CY5 1 - s i b ' (CY5s2'Tcyg)s:f s:f*Ts?' T
f
OT
-s;f Sif' T s ~ " ' ( c ^ / ~ s ~ b ' T C ^ / B ) s ~ ' - S ~ ~ ' C ~ 5 S ~ T S : f ' s} ~ f T C ~ ~ s ~
(6)
where the minus sign is for 1=1 and the plus sign for I=O. In the above expression, S, (z, 0 ) is the fully-interacting quark propagator; summation over all color indices is assumed; the transpose and trace are on the spin unless otherwise noted. The first four terms are the diagonal correlations, and the last four terms are cross correlations. The left half of Fig. 10 shows the results in the I ( J p ) = 1 (1/2-) channel as a function of mz. Also plotted is the KN threshold energy in the S-wave EKN(P= 0) = mK r n which ~ is the same on both lattices. There is no need to consider ghost states in this channel, which is supported by the fact that the correlation function is positive throughout. The calculated ground state is plotted in the figure for the two lattices. The energy on the smaller lattice (L=2.4 fm) is consistently higher than that on the larger one (L=3.2 fm). This is the expected volume dependence for two particles in a box with a negative scattering length for medium and heavier quark masses. At the lowest mass, the energy coincides with the S-wave threshold, meaning that there is little interaction, consistent with the experimental fact of zero scattering length. The first excited state in this channel is much higher than 1.54 GeV near the physical pion mass, and we identify it as the p = l KN scattering state. There is no candidate for a pentaquark. As far as the ground state is concerned, our results more or less agree with those of Ref. 27 and 28, but disagree with those of Ref. 2 9 . It is noted in Ref. '7 and 28 that they have seen an low-lying excited state above the K N mass threshold and they interpret it as the pentaquark state. We tried but could not accommodate an 100 MeV above the K N threshold in extra low-lying pentaquark state within our one-channel calculation. In the I ( J p ) = 1 (1/2+) channel shown in the the right half of Fig. 10 the NKq' ghost state, pentaquark, and K N p-wave scattering state are the lowest states. We found a ghost state and KN scattering state, but not a pentaquark state near 1.54 GeV. We have tried to see if our data could accommodate three states, but the X2/dof would simply reject it. The energy of the K N scattering
+
-
214 state lies higher on the smaller lattice (L=2.4 fm) than that on the larger lattice (L = 3.2 fm). This mainly reflects the fact that p l is larger on the L = 2.4 fm lattice than the one on the L = 3.2 fm lattice. At the lowest mass, the energies almost coincide with the P-wave thresholds, meaning that the K N interaction is weak, consistent with experiment.
35
a
J
3
a
Y m
2.5
.
u,
N
d
0 H I1
J
3
0 d
2.5
\ N
2
1.5
L=3.2im: P-wave (3.2 im) :
4
-
2
0 I1 H
-
1.5
4
0
0.2
04
0.6
08
1.2
1
%* (GeV')
1.4
0
0.2
0.6
0.4
%2
0.8
1
1.2
4
(GeV2)
Figure 10. Left: the computed mass in the I ( J p ) = 1 (1/2-) channel as a function of rn; for the two lattices L=2.4 fm and L=3.2 fm. The curve is the K N threshold energy in the S-wave E K N (=~0) = m K m N . Right: same, but for I ( J P ) = 1 (1/2+) channel. The two lower curves are the K N threshold energies in the P-wave E K N (=~ 1). The two higher curves are for the non-interacting ghost states.
+
Fig. 11 shows the 1=0 result on the smaller lattice (L=2.4 fm), which lies higher than that for 1=1 on the same lattice. This result agrees with that in Ref. 27 where the 1=0 state is also lower than the I=l. Our conclusion of not observing a pentaquark state below the K N P-wave threshold again agrees with those of Ref. 27 and 28 and disagrees with that of Ref. 2 9 . There is one relatively easy test that can check whether a state is a genuine pentaquark or a KN scattering state. It is the volume dependence of spectral weight w as in G ( t ) = we-mt. For a one-particle state, there is almost not volume dependence for w . But for a two-particle state, there is an inverse volume 1/V. Fig. 12 shows our results in the 1 (1/2*) channels. The dependence w results in the 0 (1/2*) are similar. Some comments are in order concerning other recent lattice studies of the pentaquark. The work in 27 considered two kinds of operators, one given in Eq. 5 and one with a mixed color contraction between the N and K states, and employed a 2x2 correlation matrix to separate the lowest two states. In the 0- channel, they isolated two states, one with a ratio of 0.994 which they identify as the S-wave scattering state, one with 1.074 which they identify as the pentaquark state. The result in the 0' channel has a rather high ratio of about 2 which is ruled out as a candidate. The work has reasonable statistics, has finite-size effects under control by exploring several lattices with varying spacing and volume, and
-
215 3.5 I
;f 111
$
3
f f
f
u 0 N
-P2
2.5
m
0
-II
i=o:
2
I=1:
-
1.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Figure 11. The computed mass in the J p = 1/2+ channel as a function of rn; for the I = 0 and I = 1 channels.
Figure 12. Volume dependence of the spectral weight in the 1 (1/2-) channel (left) and 1 (1/2+) channel (right). The line at 2.37 is the expected volume dependence of the spectral weight.
performs a continuum extrapolation. The main concern here is the separation of two nearby states, the S-wave scattering state and the pentaquark state, that lie within 150 MeV of each other. It relies on the two operators and the use of the variational method of the 2x2 correlator matrix. We know from variational principle that the larger the basis, the more reliable the prediction for lowest-lying states. It is expected that to make reliable predictions for the two lowest states requires the use of at least three independent operators, especially when the two states are close to each other. Their analysis method also relies on the sharp cancellation in the lowest state which maybe another source of contamination. In 2 8 , three new operators axe proposed for the pentaquark which are inspired by diquark-diquark-antiquarkpicture. The main claim is that two states
216
are observed in the same correlation function in the 1/2- channel, one of which is identified as the S-wave scattering state, the other as the candidate for pentaquark. The two states are fairly close to each other (on the order of 100 MeV) with the 2nd state having a larger amplitude than the first state. Our experience with fitting excited states is that it requires extraordinary statistics and lattice resolution to isolate two close-by states with the parameters given in the work. It is stressed by the author that it has to do with special nature of the operator having a large overlap with the pentaquark state. This operator, however, can be shown to be partially related to the KN operator (Eq. 5) by a Fiertz transform, which means that both interpolation fields couple to the same physical states, albeit with different but no-zero strengths. In Ref. 2 9 , a pentaquark of positive parity near 1.54 GeV is claimed, exactly as that from experiment. The puzzling point is that this calculation uses the exact same operator as that in 2 8 , yet the the results from the two calculations axe qualitatively different. This is an issue that must be reconciled. 4. Conclusion
It appears that the ordering of low-lying baryons can be reproduced on the lattice with standard interpolating fields built from three quarks. We observed the crossover of the Roper and S11 in the region of pion mass 300 MeV. This shows the importance of pushing into the light quark region mass where chiral dynamics dominates. Our results support the notion that there is a transition from colorspin to flavor-spin in the hyperfine interaction from heavy to light quark masses. However, additional complications arise due to the v1 ghost states in the light mass region in the quenched approximation. This was clearly exposed in the S11 channel. More advanced fitting algorithm that incorporates these ghost states has to be used. As long as the ghost states are properly dealt with, our results show that the quenched approximation can be used to explore the baryon spectrum deep in the chiral region. As for the pentaquarks, there is no consistent picture emerging on the lattice. Our results based on the overlap fermion and pion mass as low as 180 MeV seem to reveal no evidence for a pentaquark state of the type uuddS with the quantum numbers I ( J p ) = near a mass of 1540 MeV. Instead, the correlation functions are dominated by KN scattering states and the ghost KNq’ states in the 1/2+ channel at low quark mass (pion mass less than 300 MeV). Our results are consistent with the known features of the KN scattering phase-shifts analysis 3 1 ) . We have checked that the K N states exhibit the expected volume dependence in the spectral weight for two-particle scattering. Our conclusion is in contradiction with the other lattice calculations which has claimed a pentaquark signal of either negative parity 27y28, or positive parity 2 9 , in the vicinity of 1.54 GeV. These claims should be taken with caution. The central issue is how to reliably separate a genuine pentaquark from the KN scattering states. We propose a simple test, namely volume dependence in the spectral weight, that can distinguish one from the other. We advocate this volume dependence to test the character of extracted states.
-
O(i*)
217 This work is supported in part by U.S. Department of Energy under grants DE-FG02-95ER40907 and DE-FG05-84ER40154. The computing resources at NERSC (operated by DOE under DE-AC03-76SF00098) are also acknowledged. Collaboration with N. Mathur, K.F. Liu, C. Bennhold, Y. Chen, S.J. Dong, T. Draper, Horvath and J.B. Zhang is gratefully acknowledged. References 1. Particle Data Group, Eur. Phys. J. C 15, 1 (2000).
2. 3. 4. 5.
Phys. Rev. Lett. 84, 238 (2000) N. Isgur and G. Karl, Phys. Rev. D 18,4187 (1978). S. Capstick and N. Isgur, Phys. Rev. D 34,2809 (1986). L. Ya. Glozman and D.O. Riska, Phys. Rep. 268,263 (1996); L. Ya. Glozman et al., Phys. Rev. D 5 8 , 0903 (1998). 6. K.F. Liu et al., Phys. Rev. D 59,112001 (1999). 7. D.B. Leinweber, Phys. Rev. D 51,6383 (1995). 8. F.X. Lee, D.B. Leinweber, Nucl. Phys. B (Proc. Suppl.) 73,258 (1999); F.X. Lee, Nucl. Phys. B (Proc. Suppl.) 94,251 (2001); F.X. Lee et al., Nucl. Phys. B (Proc. Suppl.) 106,248 (2002) 9. S. Sasaki, Nucl. Phys. B (Proc. Suppl.) 83, 206 (2000); hep-ph/0004252; T. Blum, S. Sasaki, hep-lat/0002019; S. Sasaki, T. Blum, S. Ohta, heplat/0102010. 10. D. Richards, Nucl. Phys. B (Proc. Suppl.) 94,269 (2001); M. Grokeler et al., hep-lat/0106022. 11. W. Melnitchouk et al., heplat/0202022. 12. S. Sasaki, T. Blum, and S. Ohta, Phys. Rev. D65, 074503 (2002). 13. D.G. Richards et al., Nucl. Phys. (Proc. Suppl.) B109, 89 (2002). 14. R. Edwards, U. Heller, D. Richards, hep-lat/0304. 15. S. Sasaki, K. Sasaki, T. Hatsuda, and M. Asakawa, hep-lat/0209059; S. Sasaki, nucl-th/0305014. 16. Y. Iwasaki, Nucl. Phys. B 258,141 (1985). 17. H. Neuberger, Phys. Lett. B 417,141 (1998). 18. S.J. Dong, F.X. Lee, K.F. Liu, and J.B. Zhang, Phys. Rev. Lett. 85, 5051 (2000). 19. S.J. Dong, T. Draper, I. HorvAth, F.X. Lee, K.F. Liu, N. Mathur, J.B. Zhang, Phys. Rev. D (in print); hep-lat/0304005. 20. S.J. Dong, T. Draper, I. Horvdth, F.X. Lee, K.F. Liu, N. Mathur and J.B. Zhang, hep-ph/0306199. 21. Y. Chen, S.J. Dong, T. Draper, I. Horvdth, F.X. Lee, K.F. Liu, N. Mathur, C. Srinivasan, S. Tamhankar, J.B. Zhang, hep-lat/0405001. 22. W. Bardeen, A. Duncan, E. Eichten, N. Isgur, H. Thacker, Phys. Rev. D65, 014509 (2002). 23. BGR [Bern-Graz-Regensburg] Collaboration, hep-lat/0309036. 24. T. Nakano et al. (LEPS Collaboration), Phys. Rev. Lett. 91,012002(2003). 25. See these proceedings on the subject of pentaquarks. A search at SPIRES (http://www.slac.stanford.edu/spires/find)or the e-print archive
218
(http://arxiv.org) would reveal more than 300 papers so far. Or more than 6000 entries on google. 26. F.X. Lee eta all “A search for pentaquarks on the lattice”, (unpublished), presented at Lattice03 and Cairns Workshop in summer 2003. 27. F. Csikor, Z. Fodor, S.D. Katz and T.G. KOVBCS,JHEP 0311,070 (2003), hep-lat /0309090. 28. S. Sasaki, hep-lat/0310014. 29. T.W. Chiu and T.H. Hsieh, hep-ph/0403020, hep-ph/0404007. 30. N. Mathur, F.X. Lee, C. Bennhold, Y. Chen, S.J. Dong, T. Draper, I. Horvath, K.F. Liu, J.B. Zhang, “A lattice study of pentaquarks with overlap fermions”, (to be published). 31. J.S. Hyslop, R.A. Arndt, L.D. Roper, and R.L. Workman, Phys. Rev. D 46, 961 (1992).
N* Properties from the l/Nc Expansion (An Update) CARLOS SCHATa Department of Physics Comisi6n Nacaonal de Energia Atdmica Avenida Libertador 8250 (1429) Buenos Aires, Argentina E-mail:
[email protected] Recent results for excited baryons from the l/Nc expansion are discussed. The tower structure that follows from the contracted SU(4), symmetry and the m a s relations for L = 2 and exotic states are examples that show the importance of excited baryons as non-trivial probes of low energy QCD.
1. Introduction The l / N c expansion of QCD has turned out to be a fruitful approach to its nonperturbative regime, as is shown by many examples of successful applications to the study of ground state baryons. The excited baryons are very interesting because they provide a wider testing ground for the l / N c expansion. The situation as by January 2003 is summarized in Rich Lebed's contribution' to the proceedings of the NStar2OU2. I will comment here on some more recent results. There are very good reviews of the l / N c expansion as applied to baryon phenomenology where a detailed exposition of the technical details can be found2. However, it is still useful to recall a few general facts that make the large number of colors limit interesting and useful: Although in the large Nc limit the degrees of freedom increase, the physics simplifies. The l / N c expansion is the only candidate for a perturbative expansion of QCD at all energies. In the Nc + 00 limit baryons fall into irreducible representations (irreps) of the contracted spin-flavor algebra S U ( 2 n f ) , . The S U ( 2 n f ) ,symmetry relates properties of states in different multiplets of the approximate flavor symmetry. The breaking of spin-flavor symmetry can be studied order by order in l / N c as an operator expansion. aWork supported by CONICET, Argentina.
219
220 For Nc = 3 the l / N c corrections are comparable to the SU(3)flavoTbreaking corrections parametrized by E M 1 / 3 , which allows to make a double expansion in l / N c and E . At the fundamental level of QCD diagrams can be classified3 according to their scaling with N c . Planar diagrams are the leading order, non-planar diagrams and quark loops are subleading in l / N c . In order to obtain finite amplitudes the quark-gluon coupling constant must scale as g 0; Nc-"2. An m -body operator requires at least the exchange of m - 1 gluons which gives a suppression factor of N:-m. However, the matrix elements of an operator can eventually be enhanced by coherence effects, as is the case of GZadefined belowb. Different hadronic operators like the masses, magnetic moments, axial currents, etc., can be e ~ p a n d e d ~in>l~/ N ' ~c . For the mass operator we have schematically
with ( 3 k a k-body operator. Both the coefficients Ck (which correspond to reduced matrix elements of QCD operators) and the matrix elements of the quark operators on baryon states (ok)have power expansions in l / N c with coefficients determined by nonperturbative dynamics. The basic building blocks to construct the 01, are the generators of S U ( 2 n f ) ,where nf is the number of flavors'
%
In the large Nc limit we can define X,Oa limNC+, , because the matrix elements of Gi, scale like Nc for the states of interest, which is the coherence effect mentioned before. In this way we obtain the contracted algebra SU(4),
[si,sj] = i E i j k S k ,
[Si,$a]
= i c i j k x k0a
[Ta,Tb] = ifabcTc ,
p a , x:b]
= iEabcXtc ,
,
bwhen resticted to the subspace of states with spin and isospin of order N o , which are the ones that will correspond to the Nc = 3 physical states =for the orbitally excited baryons we will also include the orbital angular momentum as a generator of O(3) and it will be convenient to split G = Gc g in two parts, one that only acts on the excited quark (g) and another one that acts on the Nc - 1 unexcited "core" quarks (G,)
+
221 The last commutation relations can also be obtained in a purely hadronic ianguage. They are known as consistency relations7 and are necessary to obtain finite amplitudes for pion-nucleon scattering, as shown in Fig.1. The pion-nucleon coupling scales like which makes each diagram separately to scale like Nc. To obtain a finite amplitude for the physical process we need a cancellation to happen. This requires X otarX 361 o = U ( l / N c ) ,which in the large Nc limit gives
a, [
Eq. (4).
Figure 1. Consistency relations for pion nucleon scattering.
2. L = l baryons
For Nc = 3 we have five well established nucleon states and two A states. These seven states are the non-strange members of the [70,1-] studied in 8i9,10,11. The physical spectrum is shown on the left side in Fig.2 and compared with the large Nc spectrum12 on the right, where states fall into irreps of SU(4)c and are labeled by T . At leading order the only three operators that contribute to the (3/2, 5/2)
(U2, 3/2)
Figure 2.
T=2
T=I
Mass spectrum illustrating assignment No.1 in Table 1
222 mass matrix, Eq. (1), are
where l(’)Zj is the symmetric and traceless tensor constructed from the orbital angular momentum li and sz is the spin of the excited quark. The diagonalization of the mass matrix gives the mass eigenstates in the large Nc limit as linear combinations of the quark model states
The naive expectation is that these mass operators would yield five different eigenvalues. However, the explicit calculation shows that they only yield three different eigenvalues13
The N5/2 state does not mix and has the m s s M i o ) . The mixing angles are fixed by Eqs. (6) and ( 7 ) . Cohen and Lebed also found similar results analyzing excited baryons as resonances in meson-nucleon scattering14. Thes_eresults make the tower structure explicit. The label T corfesp_ondsto T = L P , where @ = f for mixed symmetric spin-flavor irreps and P,= 0 :or tke syfnme_tricfrrep12. The baryon spin J is related to its isospin I by J = L I P = I T . Note that in the case of the ground state baryons we just have one tower with T=O and to leading order the mass spectrum is the same as with the usual SU(4) spin-flavor symmetry of the quark model.
+
+ +
+
Table 1. The four possible assignments of the ed baryons.
223 There is a discrete ambiguity in the assignment of the five observed N * excited nucleons into the large Nc irreps of SU(4)c. The four possible ways of grouping them into multiplets are shown in Table 1. In the large Nc limit the favored assignment is No.1, and it is shown as an illustrative example in Fig.1. However, l/Nc corrections change this picture and also allow for other pos~ibilities'~.In addition to constraining the masses of the tower states, the contracted SU(4)c symmetry relates also their strong decay widths". T = I : r(Nr
--t
2
[N+)
:r ( N g 2
--f
[nTls)= I
:1
(8)
+ [AT],): r(Nq --f "TI,) : r ( N g + [AT],)= 2 : 1 : 1 T = 2 : r(Nq + : r(Nq --f [An],) : r ( N $ + "TI,) : r(N! --t
T = 1: r ( N 1
[ATID)
- 1 1 2 7 2 ' 2 ' 9 ' 9 '
States that belong to the same tower have equal widths to leading order which implies sum rules such as (for the T = 2 states) r ( N 3 / z --f [ N T I D )-k r(N3/a +
= r(N5/z --f "a],)
-tr ( N 5 / 2 --$ [ A r l o ) . (9)
These relations are broken by l/Nc terms in the expansion of the N* N axial current, and by kinematical phase space effects. The l/Nc scaling of the widths has been recently discussed in l6,l7. The decays to leading order have also been discussed treating the excited baryons as resonances. To that order the T=O state decays exclusively to v N , which suggests that the N(1535) should be assigned to the T=O tower14. This disfavors the assignment No.1 suggested by the mass spectrum. The resolution of this ambiguity might require the analysis of the decays to order l/Nc.
3. L=2 baryons The [56,2+] multiplet is completely symmetric in spin-flavor and its non-strange members belong to a T = 2 tower. The predictions" for the mass spectrum of orbitally excited baryons with L = 2 are summarized in Fig.3. It is interesting to note that the spin-orbit operator 2,s that contributed to the rich O(1) structure in the L = 1 case now turns out to be of order l/Nc, the reason being that the operator identity si = Si/Nc holds within the symmetric representation. The mass operator to order O ( l / N 2 ) is
where E % 1/3 for Nc = 3 is the strength of the SU(3) breaking. Solving for ci, bi leads to the mass relations shown in Table 2. 4. Pentaquarks
The recently discovered2' exotic pentaquark 0+(1540) is believed to belong to a -
10 irrep of flavor SU(3). Higher dimensional SU(3) multiplets also contain exotics with the same quantum numbers. Similar to the case of the L = 2 baryons, the
N N
A
Table 2. Mass relations for [56,L = 2+] orbitally excited baryons. GMO and EQS stand for GellMan-Okubo and for the equal spacing rule respectively. (1)
A5/2 - A 3 / 2
=
N5/2
(2)
5(A7/2 - A 5 / 2 ) A7/2 - A1/2 22(A5/2 - N 5 / 2 ) 3(&/2 - c 3 / 2 )
=
7(N5/2 - N 3 / 2 ) 3(N5/2 - N 3 / 2 ) 15(c5/2 - A 5 / 2 ) 4(N5/2 - N 3 / 2 )
(3) (4) (5) (6) (7)
8(A3/2 - N 3 / 2 )
+
- A3/2 + A5/2 - A3/2 c 5 / 2 - c 3 / 2 7 c$/2 5 c7/2
A5/2
(8)
+
cl/2
(GMO) (EQS)
e7/2
2(N+2) Z-A
= = = =
- N3/2
- '8/2)
(';/2
= =
12 c;,2
=
3A+C ;-C=R-2
=
+ 30(&/2
- A7/2)
Accuracy 0.6 % 1.8 % 1.5 % o.4 % 1.7 % 0.5 % 0.5 %
c$/2
-
Note: In order to compare to what extent the empirical accuracies of the mass relations match the theoretical expectations, each of the mass relations is cast in the form LHS = RHS with the left hand side (LHS) and right hand side (RHS) possessing only terms with positive coefficients. The accuracy of the mass relations is then defined as ILHS - RHSI/[(LHS RHS)/2]. These ratios are 0 ( t 2 N P 2 )for T ~ )0 ( e N F 3 ) for the others. For Nc = 3 , the GMO and EQS relations, and 0 ( N c 3 ) ,~ ( E ~ Nand/or and E 1/3, the ratios associated with the relations (1) to (8) in the present table are estimated to be of the order of 4%. The ratios obtained with the physical masses are listed in the last column and they are within that estimated theoretical range.
+
N
225
2400
ZJOO
i t
i
2500
4
Figure 3. Mass spectrum of L=2 baryons. The shaded boxes correspond to the experimental data4 and the hatched boxes are the l / N c results18 .
l/Nc analysis uncovers relations between exotic states21i22. Assuming that the Nc + 1 light quarks are in a completely symmetric spin-flavor representation the mass operator is
where Jq and Jq are the spin of the quarks and antiquarks respectively. The exoticness E of a state is the number of antiquarks, which is E=l for the pen-
226
taquarks. In the SU(3) symmetric limit Eq (11) yields
where the brackets denote the spin-averaged masses. These relations lead to the predictions (27) = 1735 MeV and (35) = 2126 MeV to an accuracy of 1/Nz, which corresponds to approximately 30 MeV. The strong decays of these states have also been studied22 to leading order. 5. Concluding remarks
The N* baryons are a good testing ground for the contracted SU(4)c symmetry which is a non-trivial prediction of QCD in the large Nc limit. A better understanding of the strong decays is needed to obtain a consistent picture23. The mass spectra of [70,1-] and [56,2+] are well reproduced and the double l/Nc and E expansion gives many new mass relations among the L = 2 states. The first pentaquark studies also lead to mass relations between different flavor multiplets in the SU(3) symmetric limit. Finally, the l/Nc expansion also provides a unifying framework for quark model and Skyrme model calculation^^^, giving the spinflavor structure in a model independent way. This together with the expected observation of more members of the new family of exotics that started with the O'(1540) sets the ground for many more applications of the l/Nc expansion in the near future. Acknowledgements I am very grateful to the organizers of the Conference for the invitation and for their generous support. This work was funded in part by DOE grant DE-FG0296ER.40945. References 1. R. F. Lebed, hep-ph/0301279. 2. E. Witten, Nucl. Phys. B160, 57 (1979). R. F. Lebed, Czech. J. Phys. 49, 1273 (1999) [nucl-th/9810080]. A. V. Manohar, hep-ph/9802419. E. Jenkins, Ann. Rev. Nucl. Part. Sci. 48, 81 (1998) [hep-ph/9803349]. Jenkins, E., [hepph/Oll1338].
227 3. G. 't Hooft, Nucl. Phys. B 72,461 (1974). 4. Jenkins, E., Phys. Lett., B 315, 441 (1993). R.F. Dashen, E. Jenkins, and A.V. Manohar, Phys. Rev. 51,3697 (1995). 5. M.A. Luty and J. March-Russell, Nucl. Phys. B42, 71 (1994). 6. C.D. Carone, H. Georgi, and S. Osofsky, Phys. Lett. 322B, 227 (1994). 7. J.-L. Gervais and B. Sakita, Phys. Rev. Lett. 52,87 (1984); Phys. Rev. D 30, 1795 (1984). R.F. Dashen and A.V. Manohar, Phys. Lett. 315B,425 (1993); 438 (1993). R. F. Dashen, E. J., and Manohar, A. V., Phys. Rev., D 49,4713 (1994). 8. C.D. Carone, H. Georgi, L. Kaplan, and D. Morin, Phys. Rev. D 50, 5793 (1994). 9. J.L. Goity, Phys. Lett. 414B, 140 (1997). 10. C.E. Carlson, C.D. Carone, J.L. Goity, and R.F. Lebed, Phys. Lett. 438B, 327 (1998); Phys. Rev. D 59, 114008 (1999). 11. J.L. Goity, C. Schat, and N. Scoccola, Phys. Rev. Lett. 88, 102002 (2002); Phys. Rev. D 66,114014 (2002). 12. Pirjol, D., and Yan, T. M., Phys. Rev., D 57, 1449 (1998). Pirjol, D., and Yan, T. M., Phys. Rev., D 57,5434 (1998). 13. Pirjol, D., and Schat, C., Phys. Rev., D 67,096009 (2003). 14. T. D. Cohen and R. F. Lebed, Phys. Rev. Lett. 91, 012001 (2003); Phys. Rev. D 67,096008 (2003); Phys. Rev. D 68,056003 (2003). 15. D. Pirjol and C. Schat, AIP Conf. Proc. 698,548 (2004) [hep-ph/0308125]. 16. T. D. Cohen, D. C. Dakin, A. Nellore and R. F. Lebed, Phys. Rev. D 69, 056001 (2004) [hep-ph/0310120]. 17. J. L. Goity, hep-ph/0405304. 18. J. L. Goity, C. Schat and N. N. Scoccola, Phys. Lett. B 564,83 (2003) 19. K. Hagiwara et al. [Particle Data Group Collaboration], Phys. Rev. D 66, 010001 (2002). 20. T. Nakano et al. [LEPS Collaboration], Phys. Rev. Lett. 91, 012002 (2003) [hep-ex/0301020]. V. V. Barmin et al. [DIANA Collaboration], Phys. Atom. Nucl. 66, 1715 (2003) [Yad. Fiz. 66, 1763 (2003)] [hepex/0304040]. S. Stepanyan et al. [CLAS Collaboration], Phys. Rev. Lett. 91, 252001 (2003) [hep-ex/0307018]. J. Barth et al. [SAPHIR Collaboration], hep-ex/0307083. A. Aleev et al. [SVD Collaboration], hep-ex/0401024. A. Airapetian et al. [HERMES Collaboration], Phys. Lett. B 585,213 (2004) [hep-ex/0312044]. M. Abdel-Bary et al. [COSY-TOF Collaboration], hepex/0403011. S. Chekanov et al. [ZEUS Collaboration], Phys. Lett. B 591, 7 (2004) [hep-ex/0403051]. 21. T. D. Cohen and R. F. Lebed, Phys. Lett. B 578, 150 (2004) [hepph/0309150]. 22. E. Jenkins and A. V. Manohar, hep-ph/0402024. 23. J. L. Goity, C. Schat and N. N. Scoccola, in preparation. 24. E. Jenkins and A. V. Manohar, hep-ph/0402150 ; hep-ph/0401190.
Dynamical Baryon Resonances from Chiral Unitarity A. RAMOS Departament d'Estructura i Constituents d e la Mattria, Universitat de Barcelona, E-08028 Barcelona, Spain C. BENNHOLD Center f o r Nuclear Studies, Department of Physics, The George Washington University, Washington D. C. 20052 A. HOSAKA, T. HYODO Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-004 7, Japan ECT", Villa Tambosi, Strada delle Tabarelle 286, I-38050 Villazzano, Italy
U.-G. MEISSNER HISKP, University of Bonn, Nuj3alle 14-1 6, D-53115 Bonn, Germany J.A. OLLER Departamento d e Fisica, Universidad de Murcia, 30071 Murcia, Spain
E. OSET, M. J. VICENTE-VACAS Departamento d e Fisica Tedrica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Apartado 22085, E-46071 Valencia, Spain We report on the latests developments in the field of baryonic resonances generated from the meson-baryon interaction in coupled channels using a chiral unitary approach. The collection of resonances found in different strangeness and isospin sectors can be classified into SU(3) multiplets. The R(1405) emerges as containing the effect of two poles of the scattering amplitude and various reactions that might preferentially select one or the other pole are discussed.
1. Introduction
Establishing the nature of hadronic resonances is one of the primary goals in the field of hadronic physics. The interest lies in understanding whether they behave as genuine three quark states or they are dynamically generated through the iteration of appropriate non-polar terms of the hadron-hadron interaction, not being preexistent states that remain in the large N , limit where the multiple scattering is suppressed. In the last decade, chiral perturbation theory (xPT) has emerged as a powerful scheme to describe low-energy meson-meson and mesonbaryon dynamics. In recent years, the introduction of unitarity constraints has
228
229 allowed the extension of the chiral description to much higher energies and, in addition, it has lead to the generation of many hadron resonances both in the mesonic and the baryonic sectors. The A(1405) resonance is a clear example of a dynamically generated state appearing naturally from the multiple scattering of coupled meson-baryon channels with strangeness S = -1 [l-51. Recently, the interest in studying its properties has been revived by the observation in the chiral models that the nominal A(1405) is in fact built up from two poles of the T-matrix in the complex plane [5-71 both contributing to the invariant .rrC mass distribution, as it was the case within the cloudy bag model [8]. The fact that these two poles have different widths and partial decay widths into .rrE and K N states opens the possibility that they might be experimentally observed in hadronic or electromagnetic reactions. The unitary chiral dynamical models have been extended by various groups [5,7,9-161, covering an energy range of about 1.4-1.7 GeV and giving rise to a series of resonant states in all isospin and strangeness sectors. All these observations have finally merged into the classification of the dynamical generated baryon resonances into SU(3) multiplets [17], as seen also in Ref. [18]. In this contribution we present a summary of our latest developments in the field of baryon resonances generated from chiral unitary dynamics. 2. Meson-baryon scattering model
The search for dynamically generated resonances proceeds by first constructing the meson-baryon coupled states from the octet of ground state positive-parity baryons ( B ) and the octet of pseudoscalar mesons (@) for a given strangeness channel. Next, from the lowest order lagrangian
one derives the driving kernel in s-wave
where the constants Cij are SU(3) coefficients encoded in the chiral lagragian and f is the meson decay constant, which we take to have an average value of f = 1.123fT, where fr = 92.4 MeV is the pion decay constant. While at lowest order in the chiral expansion all the baryon mases are equal to the chiral mass M o , the physical masses are used in Eq. (2) as done in Refs. [4,12]. We recall that, in addition to the Weinberg-Tomozawa or seagull term of Eq. (2), one also has at the same order of the chiral expansion the direct and exchange diagrams considered in Ref. [ 5 ] . Their contribution increases with energy and represents around 20% of that from the seagull term at 6 N 1.5 GeV. The scattering matrix amplitudes between the various meson-baryon states are obtained by solving the coupled channel equation
230 Table 1. Branching ratios at K - p threshold. Experimental values taken from Refs. [21, 221. Ratio r(K-p+?r+r)
7=
r(K-p+?r-x+)
c-
Rn
Model
2.36 f 0.04
2.32
* 0.011 0.1’9 * 0.015
r(K-p+charged particles) r(K-p--tall)
r(K -
Exp.
0.664
p - d A)
= r(K-p--talI neutral states)
0.627 0.213
Table 2. Pole positions and couplings to meson-baryon states of the dynamically generated resonances in the S = -1 sector [12]. ZR
A(1405)
(MeV)
A(1670)
1390-i66 1426-i16 1680-i20
C11620’1
1579-i274
I SEN
I9?rC
8.4 2.3 0.01
I 9?rA 4.2
I9sC
7.2
4.5 7.4 0.61
1‘
I SEN 2.6
I9aA
0.59 2.0 1.1
I gqC 3.5
I9KE
0.38 0.12 12 IgKE
12
where i , j , 1 are channel indices and the Vil and Tlj amplitudes are taken on-shell. This is a particular case of the N/D unitarization method when the unphysical cuts are ignored [19,20]. Under these conditions the diagonal matrix Gl is simply built from the convolution of a meson and a baryon propagator and can be regularized either by a cut-off (qkax),as in Ref. [4], or alternatively by dimensional regularization depending on a subtraction constant ( a l ) coming from a subtracted dispersion relation [5,12]. 3. Strangeness S = -1 In the case of K - p scattering, we consider the complete basis of meson-baryon states, namely K - p , Eon, 7rA, qA, qCo, 7r+C-, r-C+,7r0Co,K+E- and KO=’, thus preserving SU(3) symmetry in the limit of equal baryon and meson masses. Taking a cut-off of 630 MeV, the scattering observables, threshold branching ratios and properties of the A(1405) resonance were well reproduced [4,11], as shown in Table 1 and Figs. 1 and 2. The inclusion of the qA,qC channels was found crucial to obtain a good agreement with experimental data in terms of the lowest order chiral lagrangian. Our model extrapolated smoothly to high energies 1121 by using the dimensional regularization scheme. The subtraction constants resulted to have a “natural” size [5] which permits qualifying the generated resonances as being dynamical. While the I = 0 components of the E N + E N and E N + 7rC amplitudes displayed a clear signal from the h(1670) resonance, the I = 1 amplitudes showed to be smooth and featureless without any trace of resonant behavior, in line with the experimental observation. In Table 2 we display the value of the poles of the
231 150 125 100 75 50 25 0 80
60 v
&
40 20
0 50 40 30 20 10
75 50 25 0
Figure 1. Total cross sections of the K - p elastic and inelastic scatterings. The solid line denotes our results including both s-wave and p-wave. The dashed line shows our results without the p-wave amplitudes. The data are taken from Ref. [23]. scattering amplitude in the second Riemann sheet, ZR = M R - iI'f2, together with the corresponding couplings to the various meson-baryon states, obtained from identifying the amplitudes Tij with g i g j / ( z - ZR) in the limit z + z ~ Two . poles define the A(1405) resonance. The pole at lower energy is wider and couples mostly to 7rC states, while that at higher energy is narrower and couples mostly to K N states. The consequences of this two-pole nature of the h(1405) are discussed in detail in Refs. [17,25]. We also find poles corresponding to the A(1670) and C(1620) resonances. The large coupling of the h(1670) to KZ states allows one to identify this resonance as a "quasibound" KE state. The large width associated t o the C(1620) resonance, rated as 1-star by the Particle Data Group (PDG) [13], explains why there is no trace of this state in the scattering amplitudes. 4. Strangeness S = -2
The unitariy chiral meson-baryon approach has also been extended to the S = -2 sector [13] to investigate the nature of the lowest possible s-wave Z states, the
232
m m 22
1350
1400
1450
C.M. Energy (MeV)
Figure 2. The sC invariant mass distribution around the A(1405) resonance. Results in particle basis (solid line), isospin basis (short-dashed line) or omitting the qA, qCo channels. Experimental histogram taken from Ref. [24].
z(1620) and =(1690), rated 1- and 3-star1 respectively, and quoted with unknown spin and parity by the PDG [13]. Allowing the subtraction constants to vary around a natural size of -2, a pole is found at ZR = 1605 - i66, the real part showing a strong stability against the change of parameters. The imaginary part would apparently give a too large width of 132 MeV compared to the experimental ones reported t o be of 50 MeV or less. However, due a threshold effect, the actual -. 7r= invariant m a s distribution, displayed in Fig. 3, shows a much narrower width and resembles the peaks observed experimentally.
1.2 1 0.0
E 2
0.6
L
a, a ln
0.4
ln
0.2
u)
3
0 '
1500
1600
1700
I 1800
d'*[MeV] Figure 3. The aZ invariant mass distribution as a function of the center-of-mass energy, for several sets of subtraction constants. Solid line: a x 5 = -3.1 and a B A = -1.0; Dashed line: aT= = -2.5 and a ~ , ,= -1.6; Dotted line: a,z = -2.0 and a~~ = -2.0. The value of the two other subtraction constants, a~~ and aq=, is fixed to -2.0 in all curves.
233 The couplings obtained are I gnE 12= 5.9, I g K A 12= 7.0, I g K c 12= 0.93 and 1 g q 8 12= 0.23. The particular large values for final 7rE and K A states rule out identifying this resonance with the E(1690), which is found to decay predominantly to K C states. Therefore, the dynamically generated S = -2 state can be safely identified with the E(1620) resonance and this also allows us to assign the values J p = 1/2- to its unmeasured spin and parity. The model of Ref. [18] finds this state at ZR = 1565 - i124, together with another pole at ZR = 1663 - i2, identified with the E(l690) because of its strong coupling to K C states. 5 . Strangeness S
=0
For completeness, we briefly mention here the work done in the S = 0 sector [9,10] where the N(1535) was generated dynamically within the same approach. In order to reproduce the phase shifts and inelasticities, four subtraction constants were adjusted to the data leading to a N(1535) state with a total decay width of r N 110 MeV, divided into rX N 43 MeV and rq T 67 MeV, compatible with present data within errors. The dynamical N(1535) is found to have strong couplings to the KC and q N final states. 6. SU(3) multiplets of resonant states The SU(3) symmetry encoded in the chiral lagrangian permits classifying all these resonances into SU(3) multiplets. We first recall that the meson-baryon states built from the octet of pseudoscalar mesons and the octet of ground state baryons can be classified into the irreducible representations: 8 8 8 = 1 @ 8s CE 8a CE 10 @ f 0 CE 27
(4)
Taking a common meson mass and a common baryon mass, the lowest-order meson-baryon chiral lagrangian is exactly SU(3) invariant. If, in addition, all the subtraction constants a1 are equal to a common value, the scattering problem decouples into each of the SU(3) sectors. Using SU(3) Clebsh-Gordan coefficients, the matrix elements of the transition potential V in a basis of SU(3) states are
V,,
0: -
1
1
.
- ~ ( i , a ) C ~ ~ ( j =, ~~ d) i a g ( - 6 , - 3 , - 3 , 0 , 0 , 2 ) 4 f 2 i,j
4f
,
(5)
taking the following order for the irreducible representations: 1& ,S,,lO,l% and 27. The attraction in the singlet and the two octet channels gives rise to bound states in the unitarized amplitude, with the two octet poles being degenerate [17]. By breaking the SU(3) symmetry gradually, allowing the masses and subtraction constants to evolve to their physical values, the degeneracy is lost and the poles move along trajectories in the complex plane as shown in Fig. 4, which collects the behavior of the S = -1 states. As discussed further in Refs. [17,25], two poles in the I = 0 sector appear very close in energy and they will manifest themselves as a single resonance, the A(1405), in invariant 7rC mass distributions.
234
t
200
F z N "
-E
'
150 100 50 0
1300
1400
p
1
1500
j
\
1600
1700 Rez,
[MeV]
Figure 4. Trajectories of the poles in the scattering amplitudes obtained by changing the SU(3) breaking parameter x gradually. At the SU(3) symmetric limit (x = 0 ) , only two poles appear, one is for the singlet and the other (two-times degenerate) for the octets. The symbols correspond to the step size 6x = 0.1. The results are from Ref. [17].
7. The two-pole nature of the A(1405) The A(1405) is seen through the invariant mass distributions of .rrC states given bY
with i standing for any of the coupled channels ( K N , TC,qA, K Z ) and C; being coefficients that determine the strength for the excitation of channel i, which eventually evolves into a TC state through the multiple scattering. As the two A(1405) poles couple differently to TC and K N states, the amplitudes t , ~ - + ~ x , tRN+nC are dominated by one or the other pole, respectively, thus making the invariant mass distribution sensitive to the coefficients CTc,C R ~ i,e . to the reaction used to generate the A(1405). An interesting example is found in the radiative production reaction K - p -+ yA(1405). In order to access the subthreshold region, the photon must be radiated from the initial K - p state, ensuring that the A(1405) resonance is initiated from K - p states, hence selecting the pole that couples more strongly to EN which is narrower and appears at a higher energy. The calculated invariant mass .rrE distribution [27] appears indeed displaced to higher energies (- 1420 MeV) and it is narrower (35 MeV) than what one obtains from other reactions. The A(1405) can also be produced from the reaction (7,K') on protons, recently implemented at LEPS of SPring8/RCNP [28]. In this case, the invariant mass distribution of the final meson-baryon state obtained in Ref. [29] shows a width of around 50 MeV. Due to the particular isospin decomposition of the .rrE states, the T-C and .rr+C- cross sections differ in the sign of the interference
235
I
KO .. _ - - -
Figure 5. Diagrams entering the production of the A(1405) in the reaction x-p t K'A(1405) --t Ko7rC.
Figure 6.
Resonant mechanisms for A(1405) production in the x - p
--t
K'xC reaction.
between I = 0 and I = 1 amplitudes (omitting the negligible I = 2 contribution). This difference has been observed in the experiment performed at SPring8/RCNP [28] and provides some information on the I = 1 amplitude. The dynamics that goes into the 7r-p + K'TC reaction, from which the experimental data of the A(1405) resonance have been extracted [30], has recently been investigated [31]. As shown in Fig. 1, the process is separated into a part which involves tree level 7r-p + K ' M B amplitudes (hatched blob), and a second part which involves the final state interaction M B + 7rC. The initial process is described following the model for the TN + TTN reaction close to threshold, which contains a pion pole term and a contact term, both of them calculated from the chiral lagrangians. Since in this reaction 6 1900 MeV, one must also consider resonance excitation in the 7rN collision leading to the decay of the resonance in M M B , as seen in Fig. 6. We select the N*(1710) since, in the energy region of interest, it is the only S = 0 P11 resonance with the same quantum numbers of the nucleon having a very large branching ratio to 7r7rN (40-90%) [13]. The contribution of the chiral and resonant mechanisms to the invariant mass distribution are shown in Fig. 7 by the dotted and dashed lines, respectively. Both contributions are of similar size and their coherent sum (solid line) produces a
-
236
Figure 7. Invariant mass distribution of aC obtained by averaging a+C- and v C + . The histogram shows the experimental data taken from Ref. [30].Resonance parameters: M R = 1740, = 200 MeV, rxN = 30 MeV and rxxN= 120 MeV.
distribution more in agreement with the experimental histogram. The chiral tree amplitude 7r-p -+ K'MiBi for the case MiBi = E N involves the combinations 3 F - D and D F, which are large compared to the D - F combination that one finds for Mi& F 7rC (we take F = 0.51 and D = 0.75). Therefore, the chiral distribution gives a larger weight to the tgN-txc amplitude, which is dominated by the narrower pole at higher energy. On the contrary, the the N* -+ B M l M 2 vertex in the resonant mechanism goes like the difference of energies of the outgoing mesons prior to final state interaction effects, which is practically zero for N K K o and 300 MeV for %KO. Therefore, the resonant contribution is strongly dominated by the ~ , c - + amplitude, ~c which couples more strongly to the wider pole at lower energy. Recently, the production of the A(1405) through K* vector meson photoproduction, -yp + K*A(1405) + T K T C , using linearly polarized photons has been studied 1321. Selecting the events in which the polarization of the incident photon and that of the produced K* are perpendicular, the mass distribution of the A(1405) peaks at 1420 MeV, since in this case the process is dominated by t-channel K-meson exchange, hence selecting preferentially the ~ K ~ ampli+ R ~ tude.
+
8. Summary and Conclusions
By implementing unitarity in the study of meson-baryon scattering using the lowest order chiral lagrangian, a series of resonant states have been dynamically generated in all strangeness and isospin sectors.
237 In the SU(3) limit, all these resonances belong to a singlet or to either of the t,wo (degenerate) octets of dynamically generated poles of the SU(3) symmetric scattering amplitude. In the physical limit, there are two I = 0 poles representing the A(1405), the one at lower energy having a larger imaginary part than the one at higher energy. These poles couple differently to TC and K N states and, as a consequence, the properties of the A(1405) will depend on the particular reaction used to produce it. Various processes that might preferentially select the contribution from one or the other pole have been discussed. Acknowledgments
This work is supported by DGICYT (Spain) projects BFM2000-1326, BFM200201868 and FPA2002-03265, the EU network EUR.IDICE contract HPRN-CT2002-00311, and the Generalitat de Catalunya project 2001SGR00064. References
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1. 2. 3. 4. 5. 6.
238 al., Phys. Rev. 139 (1965) B719 ; T. S. Mast et al., Phys. Rev. D 11 (1975) 3078 ; P. Nordin, J r , Phys. Rev. 123 (1961) 2168 ; D. Berley et al., Phys. Rev. D 1 (1970) 1996 ; M. Ferro-Luzzi, R. D. Tripp, and M. B. Watson, Phys. Rev. Lett. 8 (1962) 28 ; M. B. Watson, M. Ferro-Luzzi, and R. D. Tripp, Phys. Rev. 131 (1963) 2248 ; P. Eberhard et al. Phys. Rev. Lett. 2 (1959) 312 ; J.K. Kim, Phys. Rev. Lett. 21 (1965) 719 24. R. J. Hemingway, Nucl. Phys. B253,742 (1985). 25. D. Jido, J. A. Oller, E. Oset, A. Ramos and U. G. Meissner, these proceedings. 26. Particle Data Group, K. Hagiwara e t al., Phys. Rev. D66, 010001 (2002). 27. J. C. Nacher, E. Oset, H. Toki and A. Ramos, Phys. Lett. B461,299 (1999). 28. J. K. Ahn, for the LEPS collaboration, Nucl. Phys. A721, 715c (2003). 29. J. C. Nacher, E. Oset, H. Toki and A. Ramos, Phys. Lett. B455, 55 (1999). 30. D. W. Thomas, A. Engler, H. E. Fisk, and R. W. Kraemer, Nucl. Phys. B56, 15 (1973). 31. T. Hyodo, A. Hosaka, E. Oset, A. Ramos and M. J. Vicente-Vacas, Phys. Rev. C 68,065203 (2003). 32. T. Hyodo, A. Hosaka, M. J. Vicente-Vacas and E. Oset, Phys. Lett. B593, 75 (2004).
Form Factors of Hadronic Systems in Various Forms of Relativistic Quantum Mechanics B. DESPLANQUES Laboratoire d e Physique Subatornique et d e Cosmologie (UMR CNRS/IN2P3- UJF-INPG), F-38026 Grenoble Cedex7 France The form factor of hadronic systems in various forms of relativistic quantum mechanics is considered. Motivated by the agreement of the nucleon “point-form’’ results with experiment, results for a toy model corresponding to the simplest Feynman diagram are first presented. These ones include t h e results for this diagram, which plays the role of an experiment, for the front-form and instant-form in standard kinematics (q+ = 0 and Breit frame), but also in unconventional kinematics and finally a Dirac’s point-form inspired approach. Results for an earlier “point-form”approach are reminded. Results are also presented for the pion charge form factor. Conclusions as for the efficiency of various approaches are given.
1. Introduction The primary goal for studying baryon physics is to get insight on how QCD is realized in the non-perturbative regime. This includes for instance the structure of baryons in terms of constituent quarks and the properties of these ones. In this respect, form factors represent an important source of information since their momentum dependence allows one to probe baryons at different scales. To fully exploit the experimental data however, a safe implementation of relativity is required. There are various ways to implement relativity. Ultimately, they should converge to unique predictions by incorporating two- or many-body currents beside the one-body current generally retained in calculations. In the frame of relativistic quantum mechanics, different forms have been proposed, following the work by Dirac They can be classified according to the symmetries of the hyperfurface which physics is described on, determining at the same time the dynamical or kinematical character of the Poincarb-group generators For applications to baryons, some approaches do well by giving the constituent quarks some form factor Other ones do without 4,6. This obviously calls for an independent check of the reliability of the underlying formalisms. A system that can provide a useful testing ground consists of two scalar particles of mass m exchanging a scalar particle of mass p. In the two extremes, p = 0 (Wick-Cutkosky model) and p = 03 (vertex function), the Bethe-Salpeter equation can be solved and solutions can be used to calculate form factors that are exact ones and can thus play the role of an “experiment”. It has also been
239
240 shown that the mass spectrum provided by the first model is reasonably described by a simple mass operator whose solutions can be employed for the calculation of form factors in different forms of relativistic quantum mechanics. In the second case, the uncertainty due to the range of the interaction is reduced to a minimum and the solution is essentially known. The comparison of the results obtained in both ways (Bethe-Salpeter equation and mass operator) offers many advantages. The dynamics of the interaction is the simplest one that can be imagined and the uncertainty arising from that one on the effective interaction entering the mass operator is limited. Spin effects are absent, allowing one to check possibly large effects like those due t o the Lorentz contraction or the “point-form” spectator approximation at high Q2 Finally, the intrinsic form factors of the constituents, if any, cancel in the comparison while they have to be accounted for when an experiment is involved, which could actually contribute to their determination. In this paper, we concentrate on the above schematic model in the case p = oc). Beside the “experiment”,we consider form factors in various forms and, for some of them, with different kinematics. The forms of interest here include the instant and front ones as well as a Dirac’s inspired point form An earlier “pointform” implementation 1 0 7 1 1 > 1 2 which , differs from the Dirac’s one by the fact it involves a hyperplane perpendicular to the velocity of the system l o (and not a hyperboloid), is also considered. Some results similar to the above ones will be considered for the pion charge form factor. Apart from the fact that the pion represents a physical system, there are real data but, as already mentioned, one has then to worry about constituent form factors. The plan of the paper is as follows. After reminding the relation of the constituent momenta t o the total momentum of the system in different forms, we present and discuss results for the charge form factor in the schematic model. The emphasis is put on the differences and the similarities beween various approaches. This is followed by a presentation of results for the pion charge form factor. Their discussion and a conclusion are finally given.
2. Form factors i n a schematic model
%fP Figure 1. Kinematics relative to the photon absorption on a two-body system.
241 The interaction of a two-body system with an external probe is represented in Fig. 1 in the single-particle current approximation. In the frame of relativistic quantum mechanics, which we are workin in here, the particles in the intermediate state are on mass shell (e = In order to calculate the corresponding form factor, two ingredients are needed: 1) the relation of the constitupt momenta to the total momentum of the system (respectively $1 and $2, and P ) . This one characterizes the form under consideration and is closely related to the symmetries of the hypersurface which physics is described on. 2) a solution of the mass operator which can be taken as form-independent. In all cases we consider, the relation of the constituent momenta to the total momentum can be cast into the form:
d d ) .
where [I” is specific of each approach. This relation is fulfilled by a Lorentz-type transformation that _allows one to express the constituent momenta in terms of an internal variable, k , which enters the mass operator, and the total momentum, @. This transformation, which underlies the Bakamjian-Thomas construction of the PoincarC algebra in the instant form 13, reads:
with
G and wo
=
d
m given by:
The 4-vector t Pappearing in the above expression multiplies a term (4 e i - M 2 ) that can be transformed into an interaction one. This is in accordance with the expectation that changing the surface pertinent to each approach implies the dynamics. Apart from these features, it can be seen that the above expression is independent of the scale of the 4-vector [ I . Thus, up to an irrelevant scale, the 4-vector [ p is given as follows:
to= 1, f = 0, t o= 1, f = Z,(161 = 1, fixed direction), - Dirac’s point form: = 1, $= C,(ICI= 1, from (PI + p 2 - P ) 2 = 0). In the last case, C can point to any direction, consistently with the absence of any
- instant form: -front form:
orientation on a hyperboloid The boost transformation introduced in an earlier “point-form” approach l 2 is recovered from Eq. (1) by taking t P0: P P . Thus, the calculation of a form factor in this last approach implies initial and final states that are described on different hyperplanes, contrary to all other cases where a unique hypersurface is involved. The second ingredient needed for the calculation of form factors is the solution of a mass operator. For the interaction model considered here (exchange of an
242 m0.3 GeV, M=0.14GeV
m=O 3 GeV, M=0.14GeV
/-----Exact + F.F. (perp.) ........ I.F. (Emit frame)
D.P.F. I S + F.F. (parallel) 'P.F.'
\\ ,\ \
'\\
' Exact+ F.F. (pep.) . .... I.F. (Enrllrama)
\. '\
\~ \
\.
\
0.-
0
0.05
\. --_
0.1
.
D.P.F. I.F. + F.F. (parallel) 'P.F.'
\
0.15
Q"2 [(GeV/c)"2]
0.2
0
20
40 60 Q"2 [(GeV/c)"2]
80
100
Figure 2. Charge form factor in various forms of relativistic quantum mechanics: left for low Q 2 and right for high Q2 (multiplied by Q 2 in the last case).
infinitely-massive boson), the solution can be taken as q$(i) 0: ( A( 4 4 M 2 ) ) - l '. The constituent and total masses entering this expression, m = 0.3 GeV and M = 0.14 GeV, are chosen in accordance with those used for the pion results presented in the following section. Two form factors can be considered for the system under consideration, a charge one, F l ( Q 2 ) ,and a Lorentz-scalar one, Fo(Q2).Their expressions for different forms, which can be cast into a unique one in terms of the 4-vector, t p , can be found in most cases in Ref. 7. Due to the lack of space, results are presented here for F l ( Q 2 ) . Two aspects of charge form factors are of interest, the charge radius and the asymptotic behavior, which are determined by the low and high Q2 parts respectively. The form factors are presented accordingly in the left and right parts of Fig. 2. They contain: - the exact form factor (continuous line), - the standard front-form one (q+ = 0), identical to the exact result, - the instant-form one (dotted line, I.F. ( Breit frame)), - a Dirac's inspired point-form one (short-dashed line, D.P.F.), corresponding to a fully Lorentz-covariant result ', - a fr_ont-form one in the configuration where the initial and final momenta, $i and Pf are parallel to the front orientation (dashed line, F.F. (parallel)), - an instant-form one in the parallel kinematics, @i 11 @f, with an average momentum going to 00 (I.F. (parallel)) (coincides with the previous curve), - and an earlier "point-form" one (dash-dot line, "P.F."). As form factors scale in most cases like Q-2 (up to log terms), the quantities
243
displayed in the right part of Fig. 2 are multiplied by the factor Q2. Form factors clearly fall into two sets: close or even identical to the "experiment'' and far apart. The difference in the behavior can be ascribed to the dependence on the total mass of the system, M 1 4 . Rather weak in the former case, it becomes important in the latter one. Actually, results in this last case depend on the momentum transfer Q through the combination Q/2M. This produces a charge radius that scales like the inverse of the mass of the system, hence the steep slope of the corresponding form factors at small Q 2 . This feature is also responsible for the suppression of the form factors at high Q2 (a factor 21 ( M / 2 ~ n ) ~ In) .the "P.F." case, further suppression occurs, the dependence on Q2 involving an extra factor (1 Q2/4M2)at high Q2 8, hence the approximate asymptotics QP4 of the corresponding form factor in the present case. Results very similar qualitatively to the above ones are obtained for the Lorentz-scalar form factors. The same conclusion holds to a lesser degree for interaction models involving the exchange of a zero-mass boson (Wick-Cutkosky model) '. In this case, some uncertainty affects the determination of the effective interaction entering the mass operator. With the simplest possible interaction, the discrepancy does not however exceed a factor 2 in the cases where an identity was previously obtained. The discrepancy between the two sets of results mentioned above is considerably increased, in relation with a different asymptotic behavior, QP4 instead of QP2.
+
3. Pion charge form factor
1oo
. % 0
-FJ
0.6
- \\
\' \'<
a
......... I.F. (Ereit frame)
F.F. @erp.)
li 0.4 -
I
I.F. + F.F. (parallel)
(3 u
-
lo4
a li
\ \
F.F. (perp.) I.F. (Ereit frame) I.F. + F.F. (parallel) "P.F."
N
b 0.2
0.0
lod
-
0.0
0 Q"*2 [(GeV/c)"2]
2.0
4.0 6.0 8.0 Q"2 [(GeV/c)"2]
Figure 3. Same as Fig. 2 but for the pion charge form factor.
10.0
244 In this section, we consider the pion charge form factor for which experimental data are known. Calculations similar t o those of the previous section are presented. There are however two main differences that make worthwhile to consider this system. The pion consists of two quarks that carry a 1/2-spin. The interaction has a finite range and is dominated by a one-gluon exchange at small distances. Moreover, there are predictions concerning both the charge radius and . of the asymptotic behavior that should be ultimately recovered l 5 > l 6Expressions form factors in the single-particle current approximation, which have to account for the quark spin, can be obtained from Ref. 17. As for the interaction entering the mass operator, it is taken as the sum of a confining potential with a standard string tension (1 GeV/fm) and a gluon exchange with strength as = 0.35. No attempt is made in the present work t o optimize the results which are presented in Fig. 3. Their examination shows they are very similar to the scalar-particle ones, confirming those obtained in works with a different scope 18,19,20. We however notice that, in the best case, the &-2 QCD asymptotic behavior is not recovered and that relatively standard two-body currents are needed in this order. As the discrepancy with experiment evidenced by the other approaches we considered reaches orders of magnitude, one can safely discard them as efficient ways to implement relativity. 4. Discussion and conclusion
In this paper, we compared different forms of relativistic quantum mechanics t o calculate form factors. We first considered a schematic interaction model. The very good or complete agreement with an exact calculation in some cases, the disagreement in other ones leaves no doubt about which approach is appropriate or inappropriate to get the bulk contribution of form factors. A similar conclusion can be inferred from considering the pion form factor. Thus, front- and instantform approaches with standard kinematics (g+ = 0 and Breit frame respectively) appear as quite convenient t o calculate the dominant contribution to form factors. The same approaches with unconventional kinematics or the point-form approach require a large contribution from non-standard two-body currents (of the type
OD).
One may wonder why approaches based on a single-particle current work well while other ones, fully covariant in some cases, don’t. Taking into account that front- aDd instant-form approaches with unconventional kinematics or a Dirac’s point-form inspired approach give relatively similar results (same asymptotic behavior and dependence on Q through the factor Q/2M), we are tempted to consider that the approaches that work are an exception. A simple argument explaining the above observation would be helpful. One often has advantage to break some symmetry t o get closer to the properties of a physical system (think to a deformed mean field for calculating the binding energy of a nucleus with J = 0). Thus, among the different approaches considered here, the Lorentz-covariant one (point form) may not be necessarily the best one. This approach has been advocated because the corresponding kinematical character of boosts makes easy t o get wave functions of states with momenta different from the rest-frame one.
245 However, one also has to relate the transferred momentum to the momenta carried by the struck particle. In the point-form approach, this relation involves the dynamics, while it has a kinematical character in the field-theory models underlying physics of interest here. With this respect, using the point-form approach represents a bad strategy as interaction effects introduced in the above relation will have to be removed later on, under the form of two-body contributions. Instead, the standard front- and instant-form approaches are those which better fulfill the kinematical character of the above momentum relation in field theory. This is perhaps the reason why they are more appropriate for the calculation of form factors. We began this presentation by reminding that the goal for studying form factors is to learn about hadronic physics. Present results for the pion charge form factor are still prematurate. However, taking into account that only the standard front- and instant-form approaches provide a reliable implementation of relativity when a single-particle current is considered, it is found that the corresponding form factors can a priori accommodate a reasonable constituent form factor. Its precise nature has to be determined.
Acknowledgments We are very grateful to A. Amghar, S. Noguera and L. Theul for their collaboration at the early stage of the development of this work. References 1. P. A. M. Dirac, Rev. Mod. Phys. 21, 392 (1949). 2. B. Keister and W. Polyzou, Adv. Nucl. Phys. 20, 225 (199 1. 3. F. Cardarelli et al., Phys. Lett. B357, 267 (1995). 4. D. Merten et al., Phys. Eur. J. A14, 477 (2002). 5. R. F. Wagenbrunn et al., Phys. Lett. B511, 33 (2001). 6. A. Amghar et al., Nucl. Phys. A694, 439 (2001). 7. A. Amghar et al., Nucl. Phys. A714, 213 (2003). 8. T. W. Allen et al., Phys. Rev. C63, 034002 (2001). 9. B. Desplanques, nucl-th/0405059, to be submitted. 10. S. N. Sokolov, Theor. Math. Phys. 62, 140 (1985). 11. F. M. Lev, Rivista del Nuovo Camento 16, 1 (1993). 12. W. H. Klink, Phys. Rev. C58, 3587 (1998). 13. B. Bakamjian and L. H. Thomas, Phys. Rev. 92, 1300 (1953). 14. B. Desplanques et al., Phys. Rev. C65, 038202 (2002). 15. V. Bernard and U. G. Meissner, Phys. Rev. Lett. 61, 2296 (1988). 16. G. R. Farrar and D. R. Jackson, Phys. Rev. Lett. 43, 246 (1979). 17. A. Amghar et al., Phys. Lett. B574, 201 (2003). 18. S. Simula, Phys. Rev. C66, 035201 (2002). 19. B. L. G. Bakker et al., Phys. Rev. D63, 074014 (2001). 20. J. P. B. C. de Melo et al., Nucl. Phys. A707, 399 (2002).
Hadron Structure from the Salpeter Equation BERNARD METSCH Helmholtz-Institut fur Strahlen- und Kernphysak (Abteilung Theorie) der Universitat Bonn, Nuflallee 14-16, 0-53115 Bonn, Germany E-mail:
[email protected] The major features of light-flavoured hadronic excitation spectra, from the ground state up to resonances with high total angular momentum at high mass x 3 GeV, can be accounted for in a relativistically covariant quark model, formulated within a field-theoretical framework on the basis of the Bethe-Salpeter equation with instantaneous interaction kernels, containing a confinement potential rising linearly with inter-quark distances and a spin-flavour dependent interaction motivated by instanton effects, that accounts for the most prominent spin-dependent mass splittings observed. It is indicated how this treatment is related to both traditional non-relativistic constituent quark models and other field theoretical approaches.
The ultimate goal of any approach to the structure of hadrons is a unified description of the mass spectra of e.g. light-flavoured mesons and baryons up to masses of 3 GeV and high angular momenta -accounting for all such features as Regge trajectories, low-lying scalar excitations, parity doublets etc. - together with reliable calculation of electro-weak properties, such as electromagnetic form factors, radiative decays and transitions, semi-leptonic decays etc. In principle the most fundamental approach is doubtless lattice gauge theory, which in the present unquenched form is a simulation of QCD itself. In spite of enormous progress in the past decade, unfortunately, as far as the hadronic excitation spectrum is concerned, the results are restricted t o the lowest state in each channel only; some results on first excited states, addressing e.g. the position of the Roper resonance, are emerging now. Therefore constituent quark model approaches, where it is assumed that the majority of mesonic and haryonic excitations can be understood in terms of 44and q3- bound states of (constituent) quarks, respectively, and assuming that the coupling to strong decay channels can be treated perturhatively, constitute an indispensable tool to correlate a wealth of spectroscopic data and thus a reliable framework to judge what is to be considered exotic. However, since even with constituent quark masses of a few hundred MeV quarks are not really slow inside a hadron, moreover, hadron masses differ appreciably from the sum of its constituents and many observables involve processes at larger momentum transfers, a relativistic treatment seems to imperative. A field-theoretical approach, which respects relativistic covariance, is based on (coupled) Dyson-Schwinger / Bethe-Salpeter equations, and indeed very in-
246
247 teresting results on ground state meson properties have been obtained on the A basis of a suitable parametrisation of the gluon propagator, see e.g. Ref. more practical approach in the framework of quantum field theory is based on the Salpeter equation (see below), using free-form fermion propagators with constituent masses and instantaneous interaction kernels to model confinement by linearly rising potentials and to explain the remaining spin dependent splittings by instanton effects. In this manner the complete hadronic excitation spectrum can be addressed. This of course is also the usual scope of the more traditional non-relativistic constituent quark models 2 , which are essentially based on the Schrodinger equation] possibly improved by using relativistic kinematics and some parametrisation of relativistic effects in the quark dynamics. Recently it has been shown, how in the framework of Dirac’s relativistic quantum mechanics, especially in its point form, one can obtain a reliable calculation of electromagnetic properties in such a setup, see e.g Ref. In the framework of quantum field theory composite bound states are described by the homogeneous Bethe-Salpeter equation, which involves the full propagators, irreducible interaction kernels and interaction vertices, which in the skeleton expansion in turn fulfil (an infinite set of (inhomogeneous)) integral equations, such as e.g. the Dyson-Schwinger equation for the fermion propagator. In practise one truncates this expansion] makes an Ansatz for some n-point function and solves the equations (e.g. the Bethe-Salpeter-equation for two-particle bound states or the Dyson-Schwinger-equation for the self-energy) of lower order. At this point we refer to results from a renormalisation-group-improved rainbow-ladder approach (DSE) based on an effective gluon propagator with a specific infrared behaviour see also 4 . A simplified Ansatz is to assume that the fermion propagator has the free form S ( p ) z i [yppp - m ic1-l and accordingly, that all the self-energy contributions can be suitably accounted for by introducing a constituent mass m. If in addition one assumes that (as the Coulomb-potential in Coulomb-gauge QED) all interactions can be taken to be instantaneous (i.e. neglecting retardation) in the form of potentials V ( @ ] $ one ) , can define the Salpeter amplitude in terms of
+
the Bethe-Salpeter amplitude x for a qq-system by
a(p3 =
Jgx ( p o , $ l
P=(M,6)
which fulfils the homogeneous Salpeter equation:
f(3 := u i ( p ’ ) f H i ( p 3, are the projectors on positive and negative energy where Ri 2ui (6) solutions with H i ( 8 = -yo ( ( 7 . 3+mi) the usual DIRAC-one-particle hamilto-
J T +T
nian and wi($ = m . Id2. This equation constitutes the basis of virtually all constituent quark models: In the extreme non-relativistic limit one ignores the first term on the r.h.s. of this equation; the remaining component of the Salpeter
248 amplitude can then be interpreted as a Schrodinger wave function, which fulfils a Schrodinger-type equation with a relativistic kinetic energy and relativistic corrections to the potentials, and as such was exploited very successfully both for For the application of the full Salpeter equamesons, see and for baryons
0.0
1.0
3.0
4.0
5.0
Figure 1. Comparison of the w r y - and K’Ky- transition form factor of the results obtained from the Dyson-Schwinger (DSE) approach of and from the instantaneous Salpeter equation, (BSE) . Figure adapted from l .
tion to mesons, which accounts for confinement by an instantaneous string-like potential and for the major mass splittings by an effective instanton-induced interaction, in particular the meson mass spectra and a multitude of electroweak observables, we refer to 6,7. In spite of the instantaneous approximation involved here, it seems that one can reliably calculate form factors, see Fig. 1 for a comparison to the result of . With the very same assumptions, i.e. effective constituent quark propagators and instantaneous (three-body) interaction kernels, the Salpeter equation for @,+n depending on relative internal momenta $<,p;7 for baryons as q3-states can likewise be written as an eigenvalue equation
249
where the two-body interactions have been accounted for by an effective instantaneous kernel constructed in lowest order 8. Although the Salpeter hamiltonian given above is not positive definite, it can be shown that the negative energy solutions of the eigenvalue equation can via CPT-symmetry be related to positive energy solutions of opposite parity. Thus as is the case for mesons the number of states is in instantaneous approximation the same as for the non-relativistic constituent quark-model, but in the relativistic treatment states of opposite parity are coupled. For results on mass spectra, where V ( 3 )was taken to be a three) body linear confinement potential with a suitable spin-dependence and V ( 2 takes into account the effective instanton-induced interaction, we refer to the results of the (parameter-free) calculation of electroweak (transition) form factors can be found in l o , electromagnetic form factors for strange mesons in l 2 and some results on strong decays are indicated in ll. Here we merely present a representative result for the N - A-magnetic transition form factor, which clearly shows,
1
.8 .6 .4 * 20 .2
7h
V
0
0 0.5 1 1.2 2 2.i) 3 3.5 4 Q [GeV
I
Figure 2. Comparison of the calculated N - A - transition form factor (normalised to a dipole form factor) with the experimental data 13.
that the covariant quark model calculations accounts for the high momentum transfer data quite well. For smaller momentum transfers pionic contributions, not included in the present calculation, might explain the discrepancy.
250 We also like to point out a novel approach to calculate magnetic mo( Q ~ J = J I ~ ~ I Q = J = J
2M ) , with ments directly in terms of Salpeter amplitudes: p = (@$I@$) = 2 M , where the relativistic form of the magnetic moment operator acting on Salpeter amplitudes is given by:
1
3
which in the non-relativistic limit where w + m has an obvious interpretation. The last subtracted term reflects the relativistic total orbital angular momentum, which of course does not contribute to the intrinsic magnetic moment. The result for the magnetic moments of the octet and decuplet ground state baryons is given in Table 1. The results of Eq.(1) and those of Ref. 3 , which completely Table 1. Magnetic moments (in p ~ of) ground state octet and decuplet baryons; The experimental data l4 are compared t o the results calculated with the Salpeter amplitudes (BSE) , according t o Eq.(l), see also Ref. l 2 and the results (GBE) 3, obtained by calculating the currents in Dirac's point form of relativistic quantum mechanics on the basis of a constituent quark model with Goldstone Boson Exchange. Baryon
BSE 2.77
P
A
-0.61
c+ EO
2.51 -1.33 4.14
A++ 0-
-1.66
Exp. 2.793 -0.613 2.458 -1.250 3.7- 7.5 -2.020
GBE 2.70 -0.59 2.34 -1.27 4.17
Baryon
n Co
BSE -1.71
Exp. -1.913
0.75
-
GBE -1.70 0.70
C-
-1.02
-1.160
-0.94
E-
-0.56
-0.651
-0.67
A+
2.07
2.7 f 1.5
* 1.3
2.08
-1.59
differ concerning the dynamical equation solved and the origin of the effective spin-flavour dependent interaction, but which both use a relativistically covariant description for calculating electromagnetic currents, are strikingly similar, indicating that such a prescription itself is even more crucial than the details on the quark dynamics. We conclude that the constituent quark models, provided they respect relativistic covariance, provide indeed a very powerful tool to arrive at unified description of the complete light-flavoured mass spectra, electroweak properties and (to some extend) strong decay amplitudes. This seems important in view of some recent indications for exotic states and the possible classification of (non-exotic) baryons to exotic multiplets. References
1. P. Maris, C.D. Roberts, Int. J. Mod. Phys. E l 2 297 (2003). 2. S. Capstick, W. Roberts, Prog. Part. Nucl. Phys. 45, S241 (2000).
25 1
3. W. Plessas: Baryons as relativistic three quark states in: CFIF Fall Workshop 2002, Nuclear Dynamics, Eds. T. M. Pena, A. Stadler, A. M. Eiro, J. Adam, Few Body Syst. Suppl. 15, Springer, 139 (2003). 4. M. Pichowsky: Recent Advances in Dyson-Schwinger Studies in: Proceedings of the Workshop on the Physics of Excited Nucleons, NSTAR 2002, Eds. S. A. Dytman, E. S. Swanson, World Scientific, 83 (2003). 5. S. Godfrey, N. Isgur, Phys. Rev. 32 189 (1985). 6. M. Koll et al., Eur. Phys. J . A9, 73 (2000). 7. R. Ricken et al., EUT.Phys. J . A9, 221 (2000). 8. U. Loring et al., Eur. Phys. J . A10, 309 (2001). 9. U. Loring et al., E ~ TPhys. . J. A10, 395 (2001); ibid., 447. 10. D. Merten et al., Eur. Phys. J . A14, 477 (2002). 11. B. Metsch: Evidence for Instantons in the Baryons in: Proceedings of the Workshop on the Physics of Excited Nucleons, NSTAR 2002, Eds. S. A. Dytman, E. S. Swanson, World Scientific, 152 (2003). 12. T. van Cauteren et al., Ew. Phys. J . A20 283 (2004). 13. W. Bartel et al., Phys. Lett., 28B 148 (1968); F. Foster et al., Rep. P T O ~ . Phys., 46 1445 (1983); S. Stein et al., Phys. Rev., D 12 1884 (1975); V. V. Rolov et al., Phys. Rev. Lett, 82 45 (1999). 14. K. Hagiwara et al. (Particle Data Group), Phys. Rev. D66, 010001 (2002).
Point-Form Approach to Baryon Structure W. PLESSAS Theoretische Physik, Institut fur Physik Universitat Graz, Universitiitsplatz 5, A-8010 Graz, Austria E-mail:
[email protected] A critical discussion is given of the results for baryon electromagnetic and axial form factors obtained from relativistic constituent quark models in the framework of PoincarB-invariant quantum mechanics. The primary emphasis lies on the point-form approach. First we summarize the predictions of the Goldstone-bosonexchange constituent quark model for the electroweak nucleon structure when using a spectator-model current in point form. Then the influences of different dynamics inherent in various kinds of constituent quark models (Goldstone-boson-exchange, one-gluon-exchange, instanton-induced interactions) are discussed. Finally the point-form results are compared to analogous predictions calculated in instant form. Relativistic effects are always of sizeable magnitude. A nonrelativistic approach is ruled out. The instant-form results are afflicted with severe shortcomings. In the spectator-model approximation for the current, only the point-form results appear t o be reasonable a-priori. In fact, the corresponding quark model predictions provide a surprisingly good description of all elastic electroweak observables in close agreement with existing experimental data, specifically for the Goldstoneboson-exchange constituent quark model.
1. Introduction Constituent quark models (CQMs) have become a reliable concept for t h e description of hadron spectroscopy. Specifically the low-lying spectra of t h e light a n d strange baryons have experienced a reasonable explanation by respecting t h e spontaneous breaking of chiral symmetry of quantum chromodynamics (QCD) i n t h e dynamics employed for t h e effective interaction between constituent quarks. In this respect, t h e so-called Goldstone-boson-exchange (GBE) CQM'l has proven especially adequate2. Consequently it appears essential t o include t h e relevant symmetries of low-energy QCD in t h e construction of any CQM. It is of similar importance t o observe t h e symmetry requirements of special relativity. In order t o obtain relativistic predictions for observables, any CQM must be based on a dynamical concept (e.g., a relativistic mass operator or a n equivalent Hamiltonian) invariant under t h e transformations of t h e PoincarC group. In following a relativistic quantum-mechanical treatment of few-quark systems one must make a choice of t h e formalism t o b e applied. T h e different approaches are distinguished by t h e specific stability subgroups of t h e PoincarC group in case of a n interacting system718. T h e point form is characterized by four generators
252
253 dependent on interactions, namely, the components of the four-momentum. The stability subgroup of the instant form has the same dimension (with the Hamiltonian and the three generators of the Lorents boosts dependent on interactions). In case of the front form, only three generators are interaction-dependent. Until a few years ago the point form had been the approach least frequently followed, even though it has specific advantages. For instance, one can easily and accurately apply Lorentz boosts, since their generators remain purely kinematical. Following the works by Klink et al.5, the Graz-Pavia collaboration has applied the point form to the calculation of electromagnetic and axial form factors of the n~cleon~> One ~ >has ~ . obtained very remarkable results. The direct predictions of the GBE CQM, calculated with the nucleon wave functions just as obtained from the quark model, have been found in close agreement with experimental data in all instances. The behaviour of these results is therefore rather distinct from corresponding results obtained before in other approaches such as the front form (see, for example, ref^.^). There, one needed quark form factors in order to bring the theoretical predictions into the vicinity of the experimental data. Below I fist summarize the characteristics of the point-form results for the electroweak structure of the nucleons. Then I compare the covariant results with the nonrelativistic ones, consider different CQMs (wave functions), and contrast the point form to the instant form. In the discussion a few observations are made also with regard t o relativistic invariance (frame independence) and current conservation. 2. Point-Form Results
Let us first have a look at the predictions of the GBE CQM'l for the nucleon electromagnetic form factors in figs. 1 and 2 and for the axial as well as induced pseudoscalar form factors in fig. 3. There the covariant results obtained in pointform spectator approximation (PFSA) are displayed. The direct predictions of the GBE CQM are immediately found in reasonable agreement with the available experimental data up to momentum transfers of Q2 4 GeV2. On the other hand, the results calculated in nonrelativistic impulse approximation (NRIA) fall short in every respect. In order t o demonstrate the boost effects we also show the results that come out if one uses a nonrelativistic current but includes the boosts according t o the point form (PFSA-NRC). For the axial form factor, instead, we give the results for the case when a relativistic current is employed but no boosts are included (RC/no boosts). With regard to the induced pseudoscalar form factor a comparison is given to the case when the pion pole is neglected; evidently, one then misses contributions of more than an order of magnitude. From all of these results one learns that relativity is of utmost importance and the pion degrees of freedom play an essential role. How important are the specific dynamics prevailing in a certain CQM? In figs. 4 and 5 we give a comparison of the PFSA predictions of the GBE CQM", of the one-gluon-exchange (OGE) CQM after Bhaduri-Cohler-Nogamil' in the relativistic parametrization by Theual et and of the instanton-induced (11) CQM by the Bonn group12, which is treated in a Bethe-Salpeter approach; in
-
254
1.o
0.5
0.0
0
1
2 0' [(GeV/c)']
3
4
I " " " " ' I " " " " ' I " " " " ' I " " " " ' I
Eden Meyerhoff
0
+
~
.-
x I
~
PFSA NRlA PFSA-NRC
Q2
[(GeV/c)']
Figure 1. Proton and neutron electric form factors as predicted by the GBE CQM'l.
addition the case with the confinement interaction only is shown. One sees that the dynamical influences are rather weak once a realistic nucleon wave function is produced. In particular, the kind of hyperfine interaction (GBE or OGE or 11) is not so decisive, at least not for the nucleon ground state. If only the confinement interaction is present, however, one faces severe shortcomings especially with respect to the neutron form factors. Above all the neutron electric form factor (fig. 4) is dependent on a small mixed-symmetry spatial component in the wave
255
0
Andivahis
2.5
-- -
-..
0.5
0.0
0
1 Q2
-"(
2 [(GeV/c)']
" rx,
t
d
z
f
3
0 0 A
v
,"
X
+
4
Markowitz Rock Bruins Gao Ankh 98 Anklin 94
a Kubon PFSA
"--- NRlA
Y
-2.0
- - _ PFSA-NRC
~ " " " " ' ~ " " " ~ " ~ " " " " " " " ~ " " ~
0
1
Q2
Figure 2.
2 [(GeV/c)']
3
4
Proton and neutron magnetic form factors as predicted by the GBE CQMl1.
function. If it is absent, like in the case with the confinement interaction only, one practically gets a zero result. In this context we have not shown a comparison for the induced pseudoscalar form factor. As explained above it requires the pion-pole contributions, which cannot consistently be implemented neither for the OGE nor the I1 CQMs. We have not addressed the electric radii and the magnetic moments here.
256
Figure 3. Nucleon axial and induced pseudoscalar form factors as predicted by the GBE CQM'~.
They follow from the electric and magnetic form factors in the limit Q2 -+ 0. The corresponding results have already been calculated not only for the nucleons but also for all other octet and decuplet baryon ground stated3. Again the direct predictions (of the GBE CQM) in PFSA are immediately found to be reasonable and in good agreement with experiment in all cases whenever data exist. Relativistic effects are of considerable importance also for the electric radii
257 1 .o
0
Andivahis
0.5
0.0
0
1
2
3
4
Q2 [(GeWc)']
Figure 4. Comparison of proton and neutron electric form factors as predicted by the GBE1', OGE4, and III2 CQMs and the case with the confinement potential only.
and magnetic moments. This may appear strange at first sight, since we deal here with observables in the limit of zero momentum transfer. Nevertheless boost effects bring about sizeable contributions, and a nonrelativistic theory is bound to fail even for these quantities13.
258
0
Andivahis Walker
A
Hoehler Bartel GBE OGE
v
0 -
--- COG.
.-.-
......
II
1
1.o
0.0
0
1
2 Q2
0 0 0 A
t
-1.5
I -!1
4
3
[(GeV/c)']
v X
+ G,"
4 ---
.-.......
Lung Markowitz Rock Bruins Gao Anklin 98 Anklin 94 Kubon GBE OGE Conf.
II
Figure 5 . Comparison of proton and neutron magnetic form factors as predicted by the GBE1', OGE4, and 11'' CQMs and the case with the confinement potential only.
3. Comparison of Point-Form and Instant-Form Results In view of the solid performance of the relativistic approach along the point form one has t o ask why these surprising results come out (whenever a realistic wave function is employed). One has to bear in mind that the theory is by no means complete, since only a model current is used, namely, the so-called PFSA current. Of course, this model current is certainly not a one-body current but still
259
0
1.5
0 A
Pion world data Pion Mainz Neutrino world data
1 .o
0.5
0.0
0
1
2
3
4
5
Q2 [(GeV/cf]
Figure 6. Comparison of axial form factors as predicted by the GBE", OGE4, and CQMs and the case with the confinement potential only.
III2
the corresponding calculation may lack sizeable contributions from further types of few-body currents. In order to elucidate the properties of the point form in the spectator model, we have performed a completely analogous study in instant form. In figs. 7 and 8 we present a comparison of the results obtained with the GBE CQM in PFSA and in instant-form spectator approximation (IFSA); in addition the NRIA (from figs. 1 and 2) is repeated. It is seen that the IFSA results remain far away from a reasonable description of the nucleon electromagnetic form factors. In fact, the IFSA results fall closer to the NRIA than to the PFSA (and thus to the experimental data), especially for the electric form factors. While this comparison is given for the Breit-frame calculations, one has to note that the instant-form results in the spectator-model approximation are frame-dependent. This makes them particularly questionable. A serious requirement of a relativistic theory is thus violated. In contrast, the point-form results are frame-independent. They are manifestly covariant even in the spectator-model approximation for the current. Another criterion for a reliable theoretical approach to electromagnetic form factors is current conservation. We have checked the fulfillment of the continuity equation in case of the PFSA. In the range of momentum transfers considered here, the violation of current conservation remains below 1 %! This is a satisfying observation though it does not definitely tell that two- and three-body currents would ultimately be small.
260
1 .o
0.5
0 .o
0
1
C' 'I' a
" " "
I '
'
Q2 " "
2 [(GeV/cf]
'
I " '
3
' ' """ Eden Meyerhoff Luno Herberg Rohe Ostrick Becker (corr. Golak) Passchier
" " "
0
+
0 A
v 0
x b
4 ' I -
r
0.05
-,-._.-.-.-.-._.
0.00
0
2
1 Q2
3
4
[(GeV/cf]
Figure 7. Comparison of proton and neutron electric form factors of the GBE CQM calculated in PFSA and IFSA as well as in NRIA.
4. Conclusions
From the present studies one can learn several important lessons. First of all it is evident that a nonrelativistic CQM is by no means adequate to describe the properties of hadrons, not even in the domain of low energies or momentum transfers. Second, an approach following relativistic (Poincark-invariant) quantum mechanics turns out to be justified and convenient. It allows to implement the symmetry requirements of special relativity and is not confronted with the problems of a field-theoretic approach (such as truncations of infinite series, discretizations of integrations, etc.). Specifically the point-form approach seems to
261
.-.
___.-,
.
/
,'
0
Markowitz
0 A
Bruins
V X
*+ 4
G,"
Anklin 98 Anklin 94
xu
- Kubon PFSA IFSA -2.0 i " " " " ' i " " ' ~
0
1
" ' i " " " " " " " " " "
2
Q2
3
4
[(GeV/cf]
Figure 8. Comparison of proton and neutron magnetic form factors of the GBE CQM calculated in PFSA and IFSA as well as in NRIA.
bring about a number of advantages. It guarantees a-priori for covariance, allows to solve the dynamical equations rigorously, and keeps the violation of current conservation very small; in practice, it is negligible in the domain of momentum transfers considered here. The IFSA, on the other hand, is affected by severe theoretical shortcomings. Most embarrassing is the frame dependence. It makes the instant-form approach in the spectator approximation very questionable if not completely inadequate. Certainly, at this instance, we are also left with a number of open problems. Even though the PFSA results provide a consistent description of all aspects of the electroweak structure of the light and strange baryon ground states, one
262 must not forget that the approach relies on simplifying assumptions and is by no means complete. It is also distinct from a field-theoretic treatment. Obviously, one may ask for the contributions of two- and three-body currents. The approximate fulfillment of current conservation in the PFSA may be taken as a hint that these contributions might indeed be small. However, this must still be proven by performing calculations with a more elaborate or even the complete current operator. Until this problem is settled one can also not definitely conclude on a possible structure of constituent quarks and/or a finite extension of the interaction vertices. It is also clear that due to their unitary equivalence14 all forms of relativistic quantum mechanics must lead to the same results once a full calculation is performed. The contributions missing beyond the present spectator-model calculations should then turn out of different magnitudes in the point and instant forms (and, of course, also in the front form). Beyond the elastic form factors a number of further observables remain to be studied. The framework of Poincark-invariant quantum mechanics is also applicable to inelastic processes such as transition form factors etc. Further important insights in the performance of relativistic CQMs and the adequacy of the relativistic quantum-mechanical approach may thus be obtained. Acknowledgment
The results discussed in this paper rely on essential contributions by my colleagues W. Klink (Iowa), S. Boffi and M. Radici (Pavia), as well as K. Berger, L. Glozman and especially R. Wagenbrunn (Graz). This work was supported by the Austrian Science Fund (Projects P14806 and P16945). References
1. L. Y. Glozman, W. Plessas, K. Varga, and R. F. Wagenbrunn, Phys. Rev. D 58,094030 (1998). 2. L. Y. Glozman, 2. Papp, W. Plessas, K. Varga, and R. F. Wagenbrunn, Phys. Rev. C 57,3406 (1998). 3. P.A.M. Dirac, Rev. Mod. Phys. 21,392 (1949). 4. B. D. Keister and W. N. Polyzou, Adv. Nucl. Phys. 20,225 (1991). 5. W. H. Klink, Phys. Rev. C58, 3587 (1998); T. W. Allen and W. H. Klink, Phys. Rev. C58,3670 (1998); T. W. Allen, W. H. Klink, and W. N. Polyzou, Phys. Rev. C 63, 034002 (2001). 6. R. F. Wagenbrunn, S. Boffi, W. Klink, W. Plessas, and M. Radici, Phys. Lett. B511, 33 (2001). 7. L. Y. Glozman, M. Radici, R. F. Wagenbrunn, S. Boffi, W. Klink, and W. Plessas, Phys. Lett. B516, 183 (2001). 8. S. Boffi, L. Y. Glozman, W. Klink, W. Plessas, M. Radici, and R. F. Wagenbrunn, Eur. Phys. J. A14, 17 (2001). 9. F. Cardarelli, E. Pace, G. Salmh, and S. Simula, Phys. Lett. B357, 267 (1995); Few-Body Syst. Suppl. 8, 345 (1995); E. Pace, G. Salmk, and A. Molochkov, Nucl. Phys. A699, 156c (2002); Few-Body Syst. Suppl. 14,339 (2003). 10. R. K. Bhaduri, L. E. Cohler, and Y. Nogami, Nuovo Cim. A65, 376 (1981).
263 11. L. Theussl, R. F. Wagenbrunn, B. Desplanques, and W. Plessas, Eur. Phys. J. A l 2 , 91 (2001). 12. U. Loring, B. C. Metsch, and H. R. Petry, Eur. Phys. J. A10, 395 (2001); ibid. A10, 447 (2001). 13. K. Berger, R. F. Wagenbrunn, and W. Plessas, nucl-th/0407009. 14. S. N. Sokolov and A. N. Shatnii, Teor. Mat. Fzz. 37,291 (1978).
Generalized Parton Distributions in the Light-Front Constituent Quark Model SILVANO SIMULA Istituto Nazionale d i Fisica Nudeare, Sezione d i Roma 111, Via della Vasca Navale 84, I-00146 Roma (Italy) E-mail:
[email protected] The Generalized Parton Distributions ( G P D s )of the nucleon are analyzed within the relativistic constituent quark model formulated on the light-front. It is shown that the matrix elements of the plus component of the one-body vector current are plagued by spurious effects related to the dependence on the hyperplane where the nucleon wave function is defined in terms of its constituents. The physical G P D s can be extracted only from the matrix elements of a transverse component of the one-body current. The loss of the polinomiality property is then related to the neglect of the pair creation process for non-vanishing values of the skewness. The need of implementing effective many-body currents corresponding to the 2-graph is stressed and a possible approach to achieve such a goal is proposed.
1. Introduction The physics issue of Generalized Parton Distributions (GPDs) is attracting a lot of theoretical interest and its experimental investigation is now included in the plans of various laboratories in the world. The importance of GPDs relies on the fact that they represent a unified theoretical picture of various inclusive and exclusive (both polarized and unpolarized) processes off hadrons in the Deep Inelastic Scattering ( D I S ) regime. The GPDs provide information of the longitudinal and transverse distributions of paxtons inside the hadrons, because they are offforward matrix elements of quark and gluon operators The GPDs depend on three variables: the internal light-front ( L F )fraction z, the squared 4-momentum transfer A2 and the skewness I , which is the relative change of the L F fraction of the hadron momentum. In the forward limit (I = A2 = 0) the GPDs reduce to the usual Parton Distribution Functions ( P D F s ) ,while their integrals over z provide the elastic form factors of the hadron under investigation. Using deeply virtual Compton scattering processes as well as hard exclusive production of vector mesons, information on the GPDs may be extracted from data (see 2 ) . Therefore various calculations of GPDs have been already performed using different models of the hadronic structure, like the bag model 4 , the chiral quark-soliton model and the Constituent Quark (CQ) model 5 1 6 . We should mention also phenomenological estimates of the GPDs, obtained using parameterizations of the usual PDFs and factorizing the A2-dependence according
'.
264
265 to the elastic form factors In this contribution we consider the estimate of the nucleon GPDs within the relativistic CQ model formulated on the light-front. Our aim is to extend to the case of GPDs some of the results of the analysis made in Refs. on elastic hadron form factors. It will be shown that the matrix elements of the plus component of the one-body vector current are plagued by spurious effects related to the dependence on the hyperplane where the nucleon wave function is defined in terms of its constituents. The physical GPDs can be extracted only from the matrix elements of a transverse component of the one-body current. The loss of the polinomiality property is then related to the neglect of the pair creation process (2-graph lo) for non-vanishing values of I . The need of implementing effective many-body currents corresponding to the 2-graph will be stressed, and a possible approach to achieve such a goal will be proposed. 2. Definition of nucleon G P D s and link with the CQ model
In what follows we limit ourselves to the case of the nucleon GPDs related to the vector current, adopting the so-called symmetric frame. According t o Ref. l 1 the nucleon off-forward, twist-two parton distributions are defined in terms of light-cone correlation functions in the gauge A . w = 0 as
where w is a null vector, v (v’)is the initial (final) helicity of the nucleon, the dots denote higher-twist terms and
with A E P’ - P being a space-like 4-vector (A2 5 0), [ f -w . A/(2w P = (P’ P)/2. The physical support of the GPDs is 1x1 5 1 (see
+
’ p )and
The nucleon GPDs, H ( z , E ,A2) and E ( z , ( ,A2), can be extracted from the matrix elements of the plus component of the vector current. Denoting [ ~ ( P ’ v I”l ’ ) u ( P v ) / 2 p + ] by I,”,,,, one has
where u2 is a Pauli matrix and A;
G
-4M212/(1 - I 2 ) . In Eq. (3) the transverse
d
m
.
vector is assumed to be (A1,O) with A, = In the forward limit Ap -+ 0 one has H ( z ,0,O) = q ( z B = z) for z > 0 and H ( z ,0,O) = - q ( z ~= -z) for z < 0, where zg is the Bjorken variable and q ( z B ) is the ordinary P D F , while
266 where Fl (F2) is the Dirac (Pauli) elastic form factor of the nucleon. Note that the 1.h.s. of Eq. (4)is independent on the skewness [. An estimate of the nucleon GPDs has been recently proposed in Ref. using the relativistic C Q model formulated on the light-front, at least for large values of z where valence quark degrees of freedom dominate the behavior of D I S structure functions. In the expansion of the nucleon state in terms of N-parton LF wave functions, derived in Ref. 12, was used to argue a correspondence (or link) between the nucleon wave function pertinent to relativistic C Q models and the lowest Fock-space component of the nucleon, i.e. the valence-quark LF wave function. As a result the valence-quark contribution to the GPDs was explicitly obtained in terms of the three-CQ wave function of the nucleon arising in quark potential models. The calculated GPDs have however a restricted physical support, z 2 [, and, moreover, their first moments (4)do depend upon 6.
3. Spurious effects in the L F CQ model Two are the main criticisms that we make to the link proposed in ‘. The first one is that the CQs are not expected at all to be in a one-to-one correspondence with current quarks, like the valence quarks, at least because of the different mass. Moreover, the hypothesis of a compositeness of the CQs has a very long history, and we limit ourselves just to mention the recent analysis made in 1 3 , where an almost model-independent evidence for extended substructures in the proton was found in the low-A’ data on the structure function F2 of the proton. As pointed out in the assumption that CQs have their own partonic content, allows to generate GPDs with a physical support not restricted to x 2 [, but corresponding at least to z 2 -[. This is not a trivial point, but in order to better focus on the second criticism the C Q compositeness will be neglected hereafter. The second criticism arises from the fact that, following the link proposed in 6 , one is led to estimate the valence-quark contribution to the GPDs using the one-body approximation for the vector current operator. While in field theory current operators are one-body, in relativistic quantum models, like the L F one adopted in ‘, the restriction to a finite number of degrees of freedom and the requirement of Poincark covariance introduce unavoidably many-body terms in the current operators (see 1 4 ) . Therefore, the GQ estimates of the GPDs should be extracted from the matrix elements of a complicated many-body operator, which we denote by
where d L Fdenoted ) the L F (three-CQ) wave function of the nucleon as described in and = Cj e j -f 6[x [ - (1 [) zj] ( m a n y - body terms), with x i being the L F fraction of the struck CQ. The matrix elements ( 5 ) have the same Lorentz decomposition as in Eq. (2), viz. ‘16,
v’”
+
+
+
267 where I? and E are the CQ estimates of the nucleon GPDs. Thus the latter can -+ be extracted from the matrix elements of the plus component, I,~,, as in Eq. (3). Note that if the Lorentz decomposition (6) holds, then the same G P D s can be extracted also from the-transverse matrix elements with p = y, where y is the direction transverse to A, in the I-plane. The critical point occurs when the full current is replaced by its one-body approximation
v’
As firstly pointed out by Karmanov and Smirnov l5 in case of form factors and subsequently derived from the analysis of the Feymann triangle diagram in Ref. 16, the Lorentz decomposition of the matrix elements of an approximate current includes spurious structures depending on the null 4-vector w’, which identifies the orientation of the hyperplane where LF wave functions are defined. The particular direction defined by w’ is irrelevant in the possible Lorentz structures only when the full current is used. In other words, in full analogy with the case of the elastic nucleon form factors analyzed in Refs. one has
v’
1718,
-
I $ , + (T(l))l,v = u(P‘v’)
{q)+ETl)} u ( P v ) / 2P+ ,
z(ll,
where ??(l) and D(l) are spurious GPDs, while z(lland E(l) are the physical G P D s in the one-body approximation; moreover, 77 c -A2/4M2. Note that 0: I, so that gauge-invariance is lost for [ # 0. The presence of the w-dependent structures in Eq. (8) does not allow any more to extract the physical GPDs from the matrix elements of the plus component of the vector current. Indeed one has
Note that fi(,)(z, 0,O) = H(l)(z,O, 0), i.e. forward parton distributions are free from spurious effects, as it should be in the Bjorken regime.
268 The matrix elements of the y component of the vector current are free from spurious effects and the physical GPDs can be obtained from
d(1
with A, = - r2)(A; - A n ) . Similar results holds as well in case of the helicity dependent GPDs related to the axial current. We do not report here the final formulae for lack of spa_ce. Any difference between H(l) (E(1))and fT(1) (F(l)) is the signature of spurious effects, which can therefore affect the dependence of the model GPDs on 2, [ and A2. The numerical impact in case of the explicit calculations of Ref. is left to future works. We just mention that in case of the magnetic form factors of the nucleon the very existence and relevance of spurious effects have been already demonstrated in Ref. (see there Fig. 5). Another interesting case, in which the role of spurious effects shows up dramatically, is represented by the nucleon axial charge, g A . In Ref. l8 it is claimed that the difference between the experimental value ( g i r p . )= 1.26) and the non-relativistic CQ result (gaNR)= 1.67) can be explained by relativistic effects due to Melosh rotations. However, the L F calculation of Ref. l8 is plagued by spurious effects and therefore it is not correct. Once the spurious effects are properly subtracted and the same values of the relevant CQ parameters used in l8 are adopted, the L F estimate becomes g A = 1.63, i.e. quite close to the non-relativistic result !
4. Pair creation process from the vacuum The use of the y component of the vector current allows to obtain nucleon GPDs free from spurious effects. However, an important drawback of the one-body approximation (7) still remains, namely the loss of the polinomiality property or, simply, the fact that the first moments of the model GPDs do depend upon 6. Such a dependence is nothing else than the frame-dependence of the form factors calculated within the one-body current. In this respect an extensive investigation of the elastic form factors of pseudoscalar and vector two-fermion systems has been carried out in Ref. ', adopting the L F Hamiltonian formalism both at [ = 0 and [ # 0. Huge numerical differences in the form factors have been found between the frame in which [ = 0 and the one where [ = Emax = d A 2f (A2 - 4 M 2 ) . The origin of such differences is entirely due to the pair creation process from the vacuum (2-graph), as shown in Ref. using the results of the analysis of the Feynman triangle diagram obtained in Ref. 16. The 2-graph is a process beyond the one-body approximation and represents a many-body current, which vanishes at [ = 0 and becomes more and more important as [ increases. Its evaluation is mandatory to obtain the appropriate [-dependence of the GPDs, so that the form factors obtained by integration of the GPDs become truly frame independent.
'
Since the contribution of the 2-graph is vanishing when 6 = 0, the form factors obtained using the one-body current plus the 2-graph at E # 0 should coincide with the ones calculated directly at ( = 0 with the one-body term only. Thus, within the LF formalism the evaluation of the 2-graph is not strictly necessary to calculate the form factors. These can be obtained by choosing ( = 0, which kills the 2-graph and minimizes therefore the impact of many-body currents (see The vanishing of the 2-graph at E = 0 is peculiar of the LF formalism. Indeed, in other Dirac forms of the dynamics, like the point-form, it is not possible to find a frame where the 2-graph is vanishing. Thus the impact of many-body currents may become quite important in the point form, as it has been extensively investigated by Desplanques (see Ref. and references therein). The explicit construction of an effective many-body current corresponding to the 2-graph is important for two reasons: i) to obtain form factors which are independent (at least to a large extent) of the particular choice of the form of the dynamics; ii) to estimate the appropriate (-dependence of GPDs fulfilling the polinomiality property. Such a construction is not an easy task. Up to our knowledge, the most promising approach to include the effects of the 2-graph is the dispersion formulation of the CQ model 20. Such a formulation allows a covariant evaluation of the Feynman triangle diagram (including the 2-graph), providing therefore hadron form factors which are exactly frame independent. As expected, the dispersion result coincides with the LF one at E = 0. The dispersion CQ model has been also applied 21 to time-like 4-momentum transfers (A2 > O), where the usual LF formalism (see ”) is plagued by the neglect of the 2-graph. The dispersion formulation of the CQ model does already the requested job of including the effects of the 2-graph in case of form factors. Its extension to off-forward matrix elements and the inclusion of the CQ compositeness represent in our opinion the most promising way to achieve a covariant CQ calculation of hadron GPDs.
5. Conclusions
The nucleon generalized parton distributions have been analyzed within the relativistic constituent quark model formulated on the light-front. We have shown that the matrix elements of the plus component of the one-body vector current are plagued by spurious effects related to the dependence on the hyperplane where the nucleon wave function is defined in terms of its constituents. The physical GPDs can be extracted only from the matrix elements of a transverse component of the one-body current. The loss of the polinomiality property is related to the neglect of the pair creation process for non-vanishing values of the skewness. The need of implementing effective many-body currents corresponding to the 2-graph is stressed, and in this respect the use of the dispersion formulation of the constituent quark model 2o is expected to be the most promising way to achieve covariant CQ estimates of the nucleon GPDs fulfilling the polinomiality property.
270 References
1. For a recent review on GPDs see: M. Diehl, Phys. Rept. 388,41 (2003). 2. HERMES coll., A. Airapetian et al., Phys. Rev. Lett. 87,182001 (2001).
CLAS coll., S. Stepanyan et al., Phys. Rev. Lett. 87,182002 (2001). H1 coll., C. Adloff et al., Phys. Lett. B517,47 (2001). 3. X. Ji, W. Melnitchouk and X. Song, Phys. Rev. D56,5511 (1997). 4. V.Yu. Petrov et al., Phys. Rev. D57, 4325 (1998). M. Penttinen, M.V. Polyakov and K. Goeke, Phys. Rev. D62, 014024 (2000). K. Goeke, M.V. Polyakov and M. Vanderhaegen, Prog. Part. Nucl. Phys. 47,401 (2001). 5. S. Scopetta and V. Vento: Eur. Phys. J. A16, 527 (2003); Phys. Rev. D69, 094004 (2004). 6. S. Boffi, B. Pasquini and M. Traini, Nucl. Phys. B649,243 (2003); Nucl. Phys. B680, 147 (2004). 7. L. Frankfurt et al., Phys. Lett. B418,345 (1998). A. Radyushkin, Phys. Lett. B449, 81 (1999). A. Freund and V. Guzey, Phys. Lett. B462, 178 (1999). I.V. Musatov and A. Radyushkin, Phys. Rev. D61,074027 (2000). 8. F. Cardarelli and S. Simula, Phys. Rev. C62,065201 (2000). 9. S. Simula, Phys. Rev. C66,035201 (2002). 10. L.L. Frankfurt and M.I. Strikman, Nucl. Phys. B148,107 (1979). G.P. Lepage and S.J. Brodsky, Phys. Rev. D22, 2157 (1980). M. Sawicki, Phys. Rev. D46,474 (1992). T. F’rederico and G.A. Miller, Phys. Rev. D45,4207 (1992). V.V. Anisovich et al., Nucl. Phys. A563, 549 (1993). N.B. Demchuk et al., Phys. of Atom. Nuclei 59,2152 (1996). 11. X. Ji, Phys. Rev. Lett. 78,610 (1997); J. Phys. G24, 1181 (1998). 12. M. Diehl et al., Nucl. Phys. B596, 33 (2001). S. Brodsky, M. Diehl and D.S. Huang, Nucl. Phys. b596,99 (2001). 13. R. Petronzio, S. Simula and G. Ricco, Phys. Rev. D67,094004 (2003); nuclth/0310015. S. Simula, Phys. Lett. B574,189 (2003). 14. B.D. Keister and W.N. Polyzou, Advances in Nuclear Physics 20,225 (1991). F. Coester, Progress in Part. and Nucl. Phys. 29,1 (1992). 15. V.A. Karmanov and A.V. Smirnov, Nucl. Phys. A546,691 (1992); ib. A575, 520 (1994). For a recent review see: J. Carbonell, B. Desplanques, V.A. Karmanov and J.-F. Mathiot, Phys. Rept. 300,215 (1998). 16. D. Melikhov and S. Simula, Phys. Rev. D65, 094043 (2002); Phys. Lett. B556,135 (2003). 17. V.A. Karmanov and J.-F. Mathiot, Nucl. Phys. A602,388 (1996). 18. S.J. Brodsky and F. Schlumpf, Phys. Lett. B329,111 (1994). 19. B. Desplanques, nucl-th/0405060 and nucl-th/0405059. 20. For a recent review see D. Melikhov, Eur. Phys. J. direct C4,2 (2002) [hepph/0110087] and references therein. 21. D. Melikhov, N. Nikitin and S. Simula, Phys. Lett. B410,290 (1997); Phys. Rev. D57, 6814 (1998); Phys. Lett. B428,171 (1998); Phys. Lett. B430,332 (1998); Phys. Lett. B442,381 (1998). 22. I.L. Grach, I.M. Narodetskii and S. Simula, Phys. Lett. B385,317 (1996).
Baryon Resonances from J / $ Decays B.S.ZOU, representing BES Collaboration Institute of High Energy Physics, CAS, P.O.Box 918 (4), Beijing 100039, China E-mail:
[email protected] Main problems in both theoretical and experimental baryon spectroscopy are briefly discussed. Recent results from baryon program at BES are presented. Many N*, A’ and C’ peaks have been observed from various channels of J / $ decays. Especially, in .I/+ + p7r-n C.C.processes, besides two well-known N’ peaks at 1500 MeV and 1670 MeV, there are two new N * peaks clearly shown up in the p n invariant mass spectra around 1360 MeV and 2030 MeV, respectively. They are the first direct observation of the N*(1440) peak and a long-sought “missing” N * peak above 2 GeV in the 7rN invariant m a s spectrum. In $ + K : p K - A + c .c. decays, no pentaquark state is observed.
+
1. Problems in Baryon Spectroscopy Spectroscopy is a powerful tool for exploring internal structures and basic interactions of microscopic world. Detailed studies of atomic spectroscopy resulted in t h e great discovery of atomic quantum theory, and then detailed studies of nuclear spectroscopy resulted in two Nobel Prize winning discoveries of nuclear shell model a n d collective motion model. Now we are facing baryon spectroscopy in exploring a deeper level of microscopic structure of matter. Comparing with t h e atomic and nuclear spectroscopy, our present baryon spectroscopy is still in its infancy4. Many fundamental issues in baryon spectroscopy are still not well understood’.
Figure 1. Various pictures for internal quark-gluon structure of baryons: (a) 3q, (b) 3qg hybrid, (c) diquark and (d) pentaquark state.
On theoretical side, a n unsolved fundamental problem is: what are effective degrees of freedom for describing t h e internal structure of baryon? Several pictures based on various effective degrees of freedom are shown in Fig.1. T h e more number of effective degrees of freedom, t h e more predicted number of excited
271
272 states. The most successful one in explaining the observed baryon states and their properties is the conventional 3q constituent quark model. Even with this relatively successful model, people met many difficulties. One outstanding problem is that, in many of its forms, the quark model predicts a substantial number of ‘missing N* states’ around 2 GeVfc’, which have not so far been observed’. Another problem is that it cannot make reliable quantitatively reliable predictions for the properties of baryons. The ‘missing N’ states’ problem is argued in favor of the diquark model which has limited success in some aspects and predicts less N* states due to less effective degrees of freedom. Another unsolved fundamental problem is: even if we know the effective degrees of freedom in the baryon, how to deal with the interaction between them? In most fields of physics, in general, two-body force dominates and three-body force is regarded as a residual interaction. In QCD, however, the three-body force among three quarks is expected to be a “primary” force reflecting the SU(3)c gauge symmetry and this is strongly supported by a recent lattice calculation4. An earlier constituent quark model calculation5 also suggested that the three quark potential is directly responsible for the structure and properties of baryons. It’s much more complicated to deal with the three-body force than the usual two body force. Furthermore, the center of the Y-shape gluon field could act as an additional degree of freedom to vibrate. Fortunately, the gluonic excitation energy is found to be about 1 GeV in the typical hadronic scale, which is relatively large compared with the excitation energy of the quark origin ‘. This large gluonic excitation energy justifies the great success of the simple 3q quark model. On the other hand, the three-body Y-shape gluon field interaction is obtained in quenched approximation4; some people believe that the effective interaction field between the constituent quarks should be meson field instead of the gluon field To make things more complicated, mesons may exist in baryons not only in the form of virtual field but also in the form of real particle *; furthermore there may exist genuine pentaquark states So for a baryon state around 2 GeV, it could be a mixture of all four configurations shown in Fig.1. On experimental side, our present knowledge of baryon spectroscopy came almost entirely from partial-wave analyses of T N total, elastic, and charge-exchange scattering data of more than twenty years ago4. Only recently, a new generation of experiments on N* physics with electromagnetic probes has been started at new facilities such as CEBAF at JLAB, ELSA at Bonn, GRAAL at Grenoble and SPRING8 at JASRI. Some nice results have been produced 9310,13,14.However, a problem for these experiments is that above 1.8 GeV there are too many broad resonances with various possible quantum numbers overlapping with each other and it is very difficult to disentangle them. Another problem is that resonances with weak couplings to 7rN and y N will not show up in these experiments. 2. Baryon resonance production from J / + decays at BES
Joining the new effort on studying the excited nucleons, N * baryons, we also started a baryon resonance program at BES15, at Beijing Electron-Positron Collider (BEPC). The J / $ and experiments at BES provide an excellent place
273 for studying excited nucleons and hyperons - N * , A*, C* and =* resonances16. The corresponding Feynman graph for the production of these excited nucleons and hyperons is shown in Fig. 1 where II, represents either J / $ or
Figure 2.
p N ’ , &A*, EX* and ?E* production from e+e- collision through $ meson.
Comparing with other facilities, our baryon program has advantages in at least three obvious aspects: (1) We have pure isospin 1/2 .irN and mrN systems from J / $ -+ N N T and N N T T processes due to isospin conservation, while .irN and T T N systems from rrN and yN experiments are mixture of isospin 1/2 and 3/2, and suffer difficulty on the isospin decomposition; (2) $ mesons decay to baryon-antibaryon pairs through three or more gluons. It is a favorable place for producing hybrid (qqqg) baryons, and for looking for some “missing” N* resonances which have weak coupling to both TN and yN, but stronger coupling to g 3 N ; (3) Not only N * , A*, C* baryons, but also E*baryons with two strange quarks can be studied. Many QCD-inspired models’717 are expected to be more reliable for baryons with two strange quarks due to their heavier quark mass. More than thirty E* resonances are predicted where only two such states are well established by experiments. The theory is totally not challenged due to lack of data. BES started data-taking in 1989 and was upgraded in 1998. The upgraded BES is named BESII while the previous one is called BESI. BESI collected 7.8 million J / $ events and 3.7 million $‘ events. BESII has collected 58 million J / $ events and 14 million events. Based on 7.8 million J / $ events collected at BESI before 1996, the events for J/$ + p p r 0 and p p q have been selected and reconstructed with 7ro and q detected in their yy decay model‘. The invariant mass of yy is shown in Fig. P(1eft) with two clear peaks corresponding to 7ro and q. The p q invariant mass spectrum is shown in Fig. 2 (right) with two peaks at 1540 and 1650 MeV. Partial wave analysis has been performed for the J / $ + ppq channel” using the effective Lagrangian approach1s31gwith Rarita-Schwinger formalism20i21>22>23 and the extended automatic Feynman Diagram Calculation (FDC) package24. There component at M = 1530 =t10 MeV is a definite requirement for a J p =
4-
274
Mpq InasqGeVfd
Figure 3. left: yy invariant mass for J / $ + @y7; right: p v invariant mass spectrum for J / $ + p p v . BESI data with r = 95 f 25 MeV near the 7 N threshold. In addition, there is an obvious resonance around 1650 MeV with J p = preferred, M = 1647 f 20 MeV MeV. These two N* resonances are believed to be the two well and r = 145;: established states, 5'11 (1535) and S11(1650), respectively. In the higher p q ( m ) mass region, there is an evidence for a structure around 1800 MeV; with BESI statistics we cannot determine its quantum numbers. The p r o invariant mass spectrum from J / + -+ p p r o is shown in Fig. 3 with two clear peaks around 1500 and 1670 MeV. and some weak structure around 2 GeV.
a-
%E I
urn-
900
-
2m-
100
'
7 2
1.4
1.5
1.1)
2
-
0 -
~ p mass(GeV/c+) n
Figure 4. p r o invariant mass spectrum for J / $ nary BESII data (right)
+ @pao
from BESI (left) and prelimi-
With 58 million new J / + events collected by BESII of improved detecting efficiency, we have one order of magnitude more reconstructed events for each channel. We show in Figs.3,5,4,7 preliminary results for J / $ t o p p r o , p f i r - +c.c., p K - A c.c., and A%+c.c. channels, respectively. These are typical channels for studying N * , A* and C* resonances.
+
275 For J / $ + pp7ro channel, the N7r invariant mass spectrum looks similar t o the BESI data as shown in Fig.3, but with much higher statistics. L
1.5
-
1.25
-
1 0.75
-
0.5 0.25
-
0 -
Figure 5. The p n - and p d invariant mass spectra for J / + -+ p r - A (left) and pr+n (middle), compared with phase space distribution; And data divided by Monte Carlo phase space vs p r invariant mass for J / + + p s - f i (solid circle) and J / + + pr+n (open square).
For J / $ + pfi7r- channel, proton and 7r- are detected. With some cuts of backgrounds, the missing mass spectrum shows a very clean peak for the missing antineutron. In thepn- invariant mass spectrum as shown in Fig.5 (left), besides two well known N* peaks at 1500 and 1670 MeV, there are two new clear N* peaks around 1360 and 2030 MeV. Its charge conjugate channel p7r'n gives very similar results as shown in Fig.5 (middle). To investigate the behavior of the amplitude squared as a function of invariant mass, we remove the phase space factor and efficiency factor from the invariant mass distribution by dividing the data by Monte Carlo phase space times the detection efficiency. The results are shown in Fig. 5 (right). At low p7r invariant mass, the tail from nucleon pole term, expected from theoretical considerations 25i26, is clearly seen. There are clearly four peaks around 1360 MeV, 1500 MeV, 1670 MeV and 2065 MeV. Note that the well known first resonance peak (A(1232)) in 7rN and yN scattering data does not show up here due t o the isospin filter effect of our J / $ decay. While the two peaks around 1500 MeV and 1670 MeV correspond to the well known second and third resonance peaks observed in 7rN and y N scattering data, the two peaks around 1360 MeV and 2065 MeV have never been observed in 7rN invariant mass spectra before. The one around 1360 MeV should be from N*(1440) MeV which has a pole around 1360 MeV 4327728 and which is usually buried by the strong A peak in 7rN and yN experiments; the other one around 2065 MeV may be due to the long sought "missing" N* resonance(s). For the decay J / $ + "*(2065), the orbital angular momentum of L = 0 is much preferred due to the suppression of the centrifugal barrier factor for L 2 1. For L = 0, the spin-parity of N*(2065) is limited to be 1/2+ and 3/2+. This may be the reason that the N*(2065) shows up as a peak in J / $ decays while no peak shows up for 7rN invariant mass spectra in 7rN and yN production processes which allow all 1 / 2 f , 3 / 2 f , 5 / 2 f and 7 / 2 f N* resonances around 2.05 GeV to overlap and interfere with each other there.
276 A simple Breit-Wigner fit 29 gives the mass and width for the N*(1440) peak as 1358f6 f16 MeV and 179 f26 f50 MeV, and for the new N* peak above 2 GeV as 2068 f;:3: MeV and 165 f 14 f 40 MeV, respectively. Ignoring the isospin breaking effect, a preliminary partial wave analysis indicates that the N*(2065) has spin-parity 3/2+.
5
Figure 6. p K (left) and K A (middle) invariant mass spectra for J/qj + pK-A+c.c., compared with phase space distribution; right: Dalitz plot for J/qj + pK-A+c.c.
For J / $ + p K - A and pK+A channels 30, there are clear A* peaks at 1.52 GeV, 1.69 GeV and 1.8 GeV in pK invariant mass spectrum, and N* peaks near K A threshold, 1.9 GeV and 2.05 GeV for K A invariant mass spectrum. The SAPHIR experiment at ELSA13 also observed a N* peak around 1.9 GeV for K A invariant mass spectrum from photo-production. The N* peak near K A threshold is most probably due to N*(1535) which was found to have large coupling to K R *. The N* peak at 2.05 GeV is compatible with that observed in NN.rr channels. The spin-parity 3/2+ is found preferred for this N*(2050) to reproduce the Dalitz plot. For J / $ + ACT channels, it seems also A* peaks at 1.52 GeV, 1.69 GeV and 1.8 GeV in C n invariant mass spectra, similar to those in the p K A channel, although less clear. In R.rr invariant mass spectra, there is a very clear peak around 1.385 GeV corresponding to the well-established C( 1385) resonance and there is also another C* peak around 1.72 GeV. Inspired by recent reports on evidence of the 0 pentaquark 9i11, we also looked for it from $J -+ KgpK-ii C.C. decays. No evidence of the pentaquark is observed 3 1 . Since its production from decays is expected to be small, nonobservation here does not mean it does not exist. We are also reconstructing J/$J + jip,pKC, p p ~ + ~ ZAK - , and other channels. In order to get more useful information about properties of the baryon resonances involved, such as their J p c quantum numbers, mass, width, production and decay rates, etc., partial wave analysis (PWA) is necessary. The basic procedure for our partial wave analysis is the standard maximum likelihood method: (1) construct amplitudes Ai for each i-th possible partial waves;
+
$J
277
Figure 7. %r (left) and AT (right) invariant mass spectrum for J / $ + A ~ + T -(up) and J / $ -+ AR:-a+ (down), respectively. Very preliminary BESII data
(2) from linear combination of these partial wave amplitudes, get the total ciAiJ2with ci as free parameters transition probability for each event as w = I to be determined by fitting data; ( 3 ) maximize the following likelihood function L to get ci parameters as well as mass and width parameters for the resonances.
xi
N
n=l
sWMC '
where N is the number of reconstructed data events and w d a t a , W M C are evaluated for data and Monte Car10 events, respectively. For the construction of partial wave amplitudes, we assume the effective Lagrangian approach1s31g with Rarita-Schwinger formalism20i21~22. In this approach, there are three basic elements for constructing amplitudes: particle spin wave functions, propagators and effective vertex couplings; the amplitude can be written out by Feynman rules for tree diagrams. ) , ampliFor example, for J / $ -+ N N * ( 3 / 2 + ) + N ( l c l , s l ) N ( l c z , s z ) ~ ( l c sthe tude can be constructed as
+
= G ( h , s Z ) l c Z p P [ ~ ( c l g v X-k C Z ~ l v Y X CShv~lX)Y5~(kl, Sl)$"
(2)
278 where u(k2, sq) and v(k1, s1) are 1/2-spinor wave functions for N and N,respectively; the spin-1 wave function, i e . , polarization vector, for J / $ . The c1, c2 and c3 terms correspond to three possible couplings for the J / $ + ”*(3/2+) vertex. The c1, c2 and c3 can be taken as constant parameters or with some smooth vertex form factors in them if necessary. The spin 3/2 propagator P’” 3/2
for N*(3/2+) is
+
with p = k2 k3. Other partial wave amplitudes can be constructed similarly20923.Partial wave analyses of various channels are in progress. In summary, we have observed several interesting N * peaks in pii..x- & pP.rro & pAK channels, several A* peaks in pAK & ACT channels, and two C* peaks in ACT channels. Very preliminary PWA of pfir-+c.c. and pK-A+c.c. indicates that the new N*(2050) peak has spin-parity of 3/2+. A major upgrade of the collider to BEPCII is going to be finished in about 3 years. A further two order of magnitude more statistics is expected to be achieved. Such statistics will enable us to perform partial wave analyses of plenty important channels for both meson spectroscopy and baryon spectroscopy from the J / $ and decays. We expect BEPCII to play a very important role in many aspects of light hadron spectroscopy, such as hunting for the glueballs and hybrids, extracting uL’U. d d and SS components of mesons, and studying excited nucleons and hyperons, i.e., N*, A*, C* and 5*resonances.
+
Acknowledgements: We would like to thank the organizers for the kind invitation and hospitality for the conference. This work is partly supported by the CAS Knowledge Innovation Project (KJCX2-SW-NO2) and National Science Foundation of China. References
1. Particle Data Group, Phys. Rev. D66, 010001 (2002). 2. %Capstick and W.Robert, Prog. Part. Nucl. Phys. 45, S241 (2000). 3. K.F.Liu and C.W.Wong, Phys. Rev. D28 (1983), 170; A.Cieply, M.P.Locher and B.S.Zou, Z.Phys. A345, 41 (1993). 4. T.T.Takahashi et al., Phys. Rev. Lett. 86, 18 (2001); Phys. Rev. D65, 114509 (2002). 5. S.Capstick and N.Isgur, Phys. Rev. D34, 2809 (1986). 6. T.T.Takahashi et al., Nucl. Phys. A721, 926 (2003). 7. A.Manohar and H.Georgi, Nucl. Phys. B234, 189 (1984); L.Ya.Glozman and D.O.Riska, Phys. Rep. 268, l(1996). 8. E.Oset et al., Int. J. Mod. Phys. A18, 387 (2003); N.Kaiser, T.Waas and W.Weise, Nucl. Phys. A612, 297 (1997).
279 9. T. Nakano et. al., Phys. Rev. Lett. 91,012002 (2003); V.V.Barmin et. al., Phys. Atom. Nucl. 66,1715 (2003); S. Stepanyan et. al., Phys. Rev. Lett. 91, 252001 (2003); J. Barth et. al., Phys. Lett. B572, 127 (2003); A.Airapetian et al., Phys. Lett. B585,213 (2004). 10. H.J.Lipkin, Phys. Lett. B195, 484 (1987); D.Diakonov, V. Petnov and M. Polyakov, 2. Phys. A359,305 (1997); S.L.Zhu, Phys. Rev. Lett. 91,232002 (2003). 11. For a recent review see e.g. E.Klempt, hep-ph/0404270. 12. M. Ripani et al., Phys. Rev. Lett. 91,022002 (2003). 13. M.Q.Tran et al., Phys. Lett. B445,20(1998); T.Mart and C.Bennhold, Phys. Rev. C61,012201 (2000). 14. Y. Assafiri et al., Phys. Rev. Lett. 90,222001 (2003). 15. BES Collaboration, J.Z.Bai et al., Phys. Lett. B510, 75 (2001); BES Collaboration, H.B.Li et al., Nucl. Phys. A675, 189c (2000); BES Collaboration, B.S.Zou et al., Excited Nucleons and Hadronic Structure, Proc. of NSTAR2000 Conf. at JLab, Feb 2000. Eds. V.Burkert et al., World Scientific (2001) p.155. 16. B S Z o u , Nucl. Phys. A684,330 (2001); Nucl. Phys. A675, 167 (2000). 17. L.Glozman, W.Plessas, K.Varga and R.Wagenbrunn, Phys. Rev. D58, 094030 (1998). 18. M.Benmerrouche, N.C.Mukhopadhyay and J.F.Zhang, Phys. Rev. Lett. 77, 4716 (1996); Phys. Rev. D51, 3237 (1995). 19. M.G.Olsson and E.T.Osypowski, Nucl. Phys. B87, 399 (1975); Phys. Rev. D17, 174 (1978); M.G.Olsson et al., ibid. 17, 2938 (1978). 20. W.Rarita and JSchwinger, Phys. Rev. 60,61 (1941). 21. C.F'ronsda1, Nuovo Cimento Suppl. 9, 416 (1958); R.E.Behrends and C.Fronsda1, Phys. Rev. 106,345 (1957). 22. S.U.Chung, Spin Formalisms, CERN Yellow Report 71-8 (1971); Phys. Rev. D48,1225 (1993); J.J.Zhu and T.N.Ruan, Communi. Theor. Phys. 32, 293, 435 (1999). 23. W.H.Liang, P.N.Shen, J.X.Wang and B.S.Zou, J. Phys. G28 (2002) 333. 24. J.X.Wang, Comput. Phys. Commun. 77,263 (1993). 25. R. Sinha and S. Okubo, Phys. Rev. D30 (1984) 2333. 26. W.H.Liang, P.N.Shen, B.S.Zou and A.Faessler, nucl-th/0404024, Euro. Phys. J. A. (2004) in press. 27. R.A. Arndt et al., Phys.Rev.C69, 035213 (2004); M.Manley, talk at NSTAR2004, Grenoble, March 2004. 28. T.P.Vrana, S.A.Dytman and T.S.H.Lee, Phys. Rep. 328 (2000) 181. 29. BES Collaboration, hep-ex/0405030. 30. BES Collaboration, hep-ex/0405050. 31. BES Collaboration, hep-ex/0402012, Phys. Rev. D (in press).
New Trends in Hadron Spectroscopy
v. V E N T O ~ Departamento de Fisica Teo'rica and IFIC Universidad de Valencia- CSIC E-46100 Burjassot (Valencia) SPAIN E-mail: Vicente.
[email protected]
To make a summary of a whole week of detailed presentations and lively discussions is an almost impossible task. These proceedings contain detailed account of the presentations. Let me therefore reflect, as I did in my oral presentation, only my own impressions on the topics covered and the intense discussions.
1. The environment The NSTAR04 meeting took place in Grenoble, a beautiful city surrounded at the time by snowy mountain ranges. There was excitement in the talks and the discussions, motivated in great measure by the recent discoveries of exotic baryons. The scientific program was intense and well balanced between theory and experiment and adequately distributed over the days of the meeting. There was plenty of discussion during the coffee breaks and certainly during lunch time while enjoying delicious French wine. As you can see by glancing at the previous pages, besides the interesting plenary sessions there were many well chosen and well presented talks in the parallel sessions. It would be unwise to repeat here in a superficial manner what has been presented, so carefully and precisely, in the preceding pages. Thus I will simply recall those aspects of the presentations and discussions which had a greater impact on me, in a colloquial way, avoiding citations and referencing. Moreover I will not cite any of the speakers, as I did in the oral presentation, solely their subjects and the laboratories at which experiments took place. In this way any misconception I might write down will be exclusively my own responsibility. 2. The underlying physical scenario
The believe that Quantum Chromodynamics (QCD) is the theory of the strong interactions is firm among most physicists of hadrons. But QCD, described in a relatively simple mathematical way in terms of quark and gluon fields interacting via their color degrees of freedom, has proven impossible to solve exactly, and even more, difficult to approximate in the low energy regime. However, despite "Supported by grants MCyT-FIS2004-05616-C02-01 and GV-GRUPOSOS/O94.
280
281
these difficulties, much have we learned about it since it was initially formulated over thirty years ago. We know its fundamental properties, namely 0
Asymptotic freedom
0
Confinement Spontaneously broken chiral symmetry
Moreover, explicit breaking of chiral symmetry is not governed by the theory and is formulated by introducing parameters, i.e., the quark masses. The main problem that arises in our field is that, in general, it is very difficult to connect the experimental data with QCD itself, except in the deep inelastic regime, since our experiments are carried out with hadrons, not with free quarks and gluons. Therefore, in the low energy the regime, where confinement is operative, we have to rely on effective theories] models and approximations, under the guidance of QCD, by imposing some of its properties by fiat. In this meeting we have attended to presentations of many of these simplified schemes: 0
Constituent Quark Models (CQM) Chiral Soliton Models (CSM) Unitarized Chiral Perturbation Theories (UCPT) Large Nc QCD (NcQCD) Lattice QCD (LQCD)
These approaches can be used to interpret and predict the properties of hadrons and their reactions (see Fig.1). The data are presently obtained in a large number of experimental facilities: BNL, ELSA, ESFR, HERA, JLAB, LNS, MAMI, SPRING8,... with high precision detectors CLAS, Crystal Ball, GRAAL, LEPS, LEGS, NKS, SAPHIR, etc.. From these data one proceeds by means of Dynamical Models and Partial Wave Analysis to extract the properties of hadrons, which one should compare with the theoretical predictions. 3. Hadronic properties
In 1960 the experimental discovery of the R- confirming the flavor SU(3) scheme of Gell-Mann opened the way to the classification of the hadronic spectrum. The history since then leading to the proposal of QCD is well known. However during all these years there has been an experimental feature which did not arise simply from the theory, namely that mesons only appeared as quark-antiquark pairs and baryons as triplets of quarks. The only limitation stemming from QCD is that hadrons are color singlets, and color singlets can be built in many more combinations. Many physicists have studied theoretically the possibility of these, so called exotic, states and they produced a plethora of predictions, non of them
282
LQCD
NcQCD
UCPT
CQM
CSM
Hadronic Properties
I
Dynamical Models Partial Wave Analysys
DATA Figure 1. The relation between the experimental data and the theory has t o be carried out at the level of the hadronic properties due to the confinement of the basic constituents of the theory.
found in experiments. But last year, in a series of brilliant experiments strongly motivated by Chiral Soliton Model calculations, a pentaquark was seen and later confirmed. The O+, as has been named this new exotic state, was by its own merit a distinguished guest of the meeting, and the people that predicted it and those that discovered it gave exiting talks. This excitement did not harm in any way the presentations of more conventional hadronic physics, which as can be seen by simply glancing through these proceedings, were represented by the top theoretical groups and the best experiments.
3.1. Pentaquarks The observation of the Of(1540), its mass determination and its small width have been a matter of several presentations. From the theoretical point of view Chiral Model and Constituent Quark approaches have been reviewed. It was pointed out that the small mass and width of the pentaquark arises naturally in the Chiral Soliton Model as a consequence of the strong correlation built in to produce a light
283 qq pair. In the Constituent Quark Models the dynamics seems more complex since multiquark correlations have to be built in explicitly in order to lower the mass of the more conventional shell model type approaches. Lattice QCD calculations are faced with how to deal with a large number of operators with the appropriate quantum numbers. At present, preliminary calculation obtain a negative parity ground state, opposite to what is expected in all the other approaches. Large Nc QCD leads to an SU(4), symmetry describing a large degeneracy of states. If one uses the exotic decuplet to fix the parameters it predicts a large number of new exotic multiplets. The experimental presentations brought excitement into the audience, by confirming the @+, eliminating recently discussed alternatives, like the kinematical reflection scenario, and bringing to our attention possible new candidates for exotics, the C(l860) at NA49, the excited @+(1573) and O"(1581) at CLAS, a preliminary sighting of the N(1671) by GRAAL, searches by BES of 0 - 0 and rumors of a charmed exotic at 3099 by H1. The first, conservative conclusion, reached by most of the audience, is that the existence of the @+(1540) with quantum numbers S = I = 0 and P = looks like a safe bet. But the excitement made many physicists feel that a "Renaissance of Hadron Spectroscopy" is taking place and that we are beginning to enter a new era of hadron physics. A caveat at last. No signal of the @+ seems necessary in K - N scattering phase shift analysis. This might just a consequence of poor data or maybe a result of a not foreseen complex dynamical mechanism. Therefore a careful study of the phase shifts both experimentally and theoretically was recommended. The plans for pentaquark studies in the near future call for the confirmation of the experimental results, the experimental determination of its quantum numbers in polarization and hadronic production experiments, the search for the remaining elements of the decuplet, and for higher multiplets, a 27 and a 35. Present theoretical explanations of the @+(1540) differ notably in the excited spectrum.
i,
+
3.2. Dynamical Models, Phase shift analysis and Missing Resonances
The studies are being supported by a large number of experimental facilities: BNL, DAPHNE, ELSA, ESFR, HERA, IHEP, JLAB, LNS, MAMI, SPRING8,... with high precision detectors BES, CLAS, Crystal Ball, GRAAL, LEPS, LEGS, NKS, SAPHIR, TAPS/GDH ..., which producing a large amount of high quality data polarized and unpolarized data. The physics beyond the delta region requires coupled channel approaches with large channel space: .rrN,yN, rlN. w N , K h , .rrnN, pN, TA,...Both T and K matrix models have been used, as well as dynamical models. There is still large disagreement between the different approaches. However the importance of the pion cloud has been firmly established. Dynamical models should be guided by QCD in order to establish a systematics which avoids the large variety of approaches. w production is very sensitive to pomeron and no exchanges in the t-channel.
284 More experiments are needed to disentangle the resonance structure. The study of strangeness is supported by a large amount of high quality data. There are dubious resonance structures in various channels and some which seem to be firmly established do not appear in the Constituent Quark Model scheme. Multipion states have been extensively studied both experimentally and theoretically. A complete partial wave analysis has been carried out and dynamical models have been generated. Extensive work in the search of missing resonances by means of partial wave analysis in coupled channels has taken place. Polarization experiments have achieved good agreement with the sum rules. The much discussed E2/M1 ratio for the N - A transitions stand now at -2.74. Polarized data helps comparison between MAID and SAID, the two existing model calculations. The future looks promising with the new Crystal Ball at MAMI in October and the new MAMI by 2005, while LEGS will be able to perform double polarization experiments with the new HD targets. One understands by missing resonances those resonances which appear in the Quark Model Calculations but do not appear in the data. One possible reason why they are not found is because they couple weakly to ~ T N and y N . In order to find them one should look into more difficult channels: p N , w N , .rrN and K Y . Moreover one should treat the photocouplings in a relativistic way and coupled channel unitarity should be implemented. It is clear that hadron beams would help tremendously in the search for resonances also. The J / 9 decays have also been used at IHEP to study and search for resonances. From the theoretical point it was shown that Feynman diagrammatic techniques require too many parameters and can be used mostly as a tool to guide experiments. One should go back to basics, i.e., QCD and inspired models, which require less parameters and are closer to our final aim namely understanding the fundamental theory. In this respect very nice fits with the Quark Model and fewer parameters were shown. Another theoretical scheme which seems to be extremely useful for the description of resonances is non perturbative Unitarized Chiral Perturbation Theory, in particular it was shown how to use it in order t o generate resonances dynamically. The role played by relativity in Nuclear and Hadron physics was discussed. QCD in a fully relativistic theory, thus its reduction to non relativistic approaches seemed always a miracle of the confining phase transitions. Relativistic approaches seem more natural, though not always necessary. Many objectives can be fulfilled and easily understood within non-relativistic schemes. 4. Final Comments
The meeting was intense and exciting. Much experimental information was provided, but luckily there are new experiments and much data to come. This new and more powerful experimental results will become a challenge to theorists. The confirmation of the pentaquark and the experimental determinations of its quantum numbers will bring a renaissance of hadron spectroscopy. The partners in the decuplet and the excited exotics should be searched.
285 In the conventional hadronic studies, model dependence in the analysis should be eliminated. One should keep as close as possible to the fundamental theory, QCD, from which guiding principles should be extracted to avoid the large number of parameters that crowd conventional studies. The missing resonances problem should be dealt with, by clarifying the model dependence of the resonance spectrum, and looking into difficult unconventional channels. Implementing relativity and channel unitarity might help. Polarization experiments are very important because they unveil dynamical mechanisms which otherwise remain hidden. But this meeting was not only one of hard work and intense discussions. We had a beautiful excursion into the Chartreuse range of mountains and a marvellous dinner overlooking the city of Grenoble. Acknowledgments The meeting was a great success because of the hard work of the organizers and, in particular, Jean-Paul Bocqet and Dominique Rebreyend were extremely helpful in making the presentations and the discussions very agile. I would like to thank Jocelyne Riffault and Anne L’Azou for being so helpful in making our work profitable and our stay enjoyable.
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PARALLEL TALKS
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q and n’Photoproduction on the Deuteron: Beam
Asymmetries
A. FANTINIl.’, 0.BARTALIN11i334,V. BELLIN1596,J.P BOCQUET7, M. CASTOLD18, A.D’ANGEL0172,J.P. DIDELEZ’, D. FRANCO1>’, R. DI SALVO^, G. G E R V I N O ~ F. ~ , G H I O ~ ~ B. J ~G, I R O L A M I ~ ~ J ~ , M. GUIDAL’, E. HOURANY’, R. KUNNE’, V. KUZNETSOV576,13, A. LAPIK13, P. LEV1 SANDR14, A. LLERES7, D. MORICCIAN12, V. NEDOREZOV13, D. REBREYEND7, F. RENARD7, N.V. RUDVEN14, C. SCHAERF1>2,M.L. SPERDUT0596,M.C. SUTERA1515, A.TUR1GE1‘, A.ZUCCHIATTI~. Universitd di Roma ”Tor Vergata”,I-00133 Roma, Italy INFN, Sezione Roma II, I-00133 Roma, Italy Uniuersith di Dento, I-38100 Dento, Italy INFN, Laboratori Nazionali d i Frascati, PO Box 13, 1-00044 Frascati, Italy Universitd d i Catania, I-95123 Catania, Italy INFN, Laboratori Nazionali del Sud, I-95123 Catania, Italy Institut des Sciences Nucle‘aires d e Grenoble, 38026 Grenoble, France INFN, Sezione di Genova, I-16146 Genova, Italy Institut de Physique Nuclkaire, 91406 Orsay Cedex, France l o INFN, Sezione d i Torino and Universith di Torino, I-10125 Torino, Italy l1 Istituto Superiore di Sanith, I-00161 Roma, Italy l2 INFN, Sezione Romal, I-00185 Roma, Italy l 3 Institute for Nuclear Research, 117312 Moscow, Russia l4 Institute of Theoretical and Experimental Physics, 117259 Moscow, Russia l5 INFN, Sezione d i Catania, 1-95123 Catania, Italy l6 Kurchatov Institute of Atomic Energy, 123182 MOSCOW, Russia Preliminary results on the beam asymmetry for the and x0 photoproduction off the quasi-free proton and the quasi-free neutron in the deuteron were obtained in the energy range 0.65-1.5 GeV of the incoming photon.
1. Introduction
The GRAAL facility at the ESRF in Grenoble combines a polarized and tagged observables in photon-induced reactions. In separate experimental runs we used both H2 and D2 liquid targets: in this way we are able to extract asymmetries and cross sections on free and bound proton and on the bound neutron. Detailed description of the beam and 4~ detector characteristics can be found in Ref. 1. We made two independent sets of experimental runs using green and UV lines. The energy ranges covered in the two sets of data are 500t1100 MeV and
7 ray beam with a 4~ detector allowing measurements of polarization
289
290 650+1500 MeV respectively. 2. q and
KO
photoproduction on the proton and the neutron
The q and the 7ro photoproduction can be the result of the interaction of the incident photon on the nucleus as a whole object (coherent photoproduction) or on the single nucleon (called “participant”) while the other one can be considered as ”spectator”. The kinematics of the incoherent photoproduction is approximately the same as in the reaction on a free nucleon, except for the smearing due to the Fermi motion. The comparison between the results obtained on the free and the bound proton in the deuteron allows to estimate the contribution of the nuclear effects on the meson photoproduction off the nucleon. We have analysed 9 photoproduction off quasi-free protons and quasi-free neutrons in deuteron for the 17 -+ 27 decay channel, where the two y’s are detected in the BGO calorimeter. The only other particle which we require to detect is the “participant” nucleon in the forward or in the central direction. A two-body kinematics was required in the qN final state: we imposed a two-dimensional cut on A0 vs. A 4
A8 is the difference between the polar angle of the particle missing from q in a two-body kinematics and the “participant” polar angle;
A+ is the coplanarity between the q and the “participant”. In order to well separate the reaction from other background channels (whose main contribution is due to the 27r0 photoproduction when two photons are lost or partially mixed to the others), another two-dimensional cut was applied on the correlation between the missing masses from the two particles detected in the final state.
0
50
100
150
0
+c’m-?l
50
1 00
150
*C*m.v
Figure 1. Preliminary results of the beam asymmetry C in 71 photoproduction on the bound proton in the deuteron (open circles for green data and full triangles for UV data). The solid and dashed lines represent the predictions from MAID isobar model and SAID Partial-Wave Analysis rispectively.
29 1 The procedure to derive the C beam asymmetry from experimental data is described in many articles. In Figure 1 we show the preliminary results of the asymmetry of 7 photoproduction on the bound proton in the deuteron in a quasi free kinematics for two bins of the incident y energy. The asymmetry values are plotted as a function of 7 polar angle in the center of mass system. Full circles rapresent a set of data obtained using the green laser line while the triangles corrispond to data with UV laser line. Only statical errors are plotted in the figure, while the systematic errors have been estimated around 3%, essentially coming from the empty target cell. Together with the data, we have also reported, as solid and dashed lines, the theoretical curves from MAID unitary isobar m 0 d e 1 ~ -and ~ from the SAID Partial-Wave Analysis‘ for the 7 photoproduction on the proton. The behaviour of the asymmetry is approximately the same (within the error bars) for the quasi-free proton and the free proton(see Ref. 1).
0.6
-.................
................... ;
;....................
...........
r:
..............
;.................... ;...........
...................
;....................
:...........
i
;;
...........
-.................
L
...........
_
;................... 4......... ......... ...........
I
50
100
150
*c’m*v
I
,
0
,
,
@
t
.................... :..................
........... -................
0
;
g--- $
i
I$
.i...........
2 ,
,
50
,
,
I
I
1 00
,
,
,
I
,
150
gcYl
Figure 2. The preliminary results of the beam asymmetry C on the bound neutron in the deuteron (triangles for data obtained with UV laser line, circles for green laser line).
In Figure 2 we show the preliminary results of the beam asymmetry C on the bound neutron in the deuteron in a quasi-free kinematics for the same energy bins. Circles and triangles represent the results obtained with green and UV laser line respectively. The behaviour of the asymmetry on the neutron is very similar to the proton one. These data are the first results on the beam asymmetry C of the q photoproduction on the bound proton and the bound neutron in the deuteron . Similar analysis was performed in order to determine the beam asymmetry C for the no photoproduction on the bound nucleons in the deuterium. Behaviors of the beam asymmetry C for the quasi-free proton and the free proton (see Ref. 3) are very similar, while for the bound neutron the asymmetry starts to differ for energies above 850 MeV. In Figure 3 we show the comparison between the very preliminary results of the beam asymmetry C on the bound proton (open triangles) and bound neutron (full circles) for two energy bins.
292 1 0.5
Eo -0.5 -1
0
50
100
150
0
50
100
150
Figure 3. Comparison between the preliminary results of the beam asymmetry C for the T O photoproduction on the quasi-free proton (open triangles) and on the quasi-free neutron (full circles) in the deuteron. .
References
1. 2. 3. 4. 5. 6.
J. Ajaka et al. Phys. Rev. Lett. 81,1797 (1998). J. Ajaka et al. Phys. Lett. B475,372-377 (2000).
A. D'angelo et al. Proc. NSTAR2OOl Mainz,7-10 March 2001 347-354. W.T. Chiang et al. Phys. Rev. C68,045202 (2003). http://www.kph.uni-mainz.de/MAID/eta2003/etamaid2003.html http://gwdac.phys.gwu.edu
Photoproduction of T O and r,~Mesons Off Protons at CB-ELSA” OLIVIA BARTHOLOMY for the CB-ELSA Collaboration Helmholtz-Institut fur Strahlen- und Kernphysik, Universitat Bonn Nwallee 14-16, 53115 Bonn, GERMANY E-mail:
[email protected] Photoproduction of single neutral pseudoscalar mesons was investigated at the CBELSA experiment in Bonn. The main field of interest is the photoproduction of baryonic resonances in the intermediate state. The CB-ELSA experiment covers a rather large percentage of the solid angle, rendering it ideally suited for the observation of angular distributions. Data was taken for incident photon energies between 0.3 and 3.0 GeV, thus extending the region already investigated by other experiments as well in angular as in energy range.
1. Introduction
Photoproduction is a sensitive tool to study the properties of baryon resonances. Most of the properties of N and A states have been obtained in TN scattering. In yp, resonant states are excited in electromagnetic interaction, while they decay via strong interaction. Thus, we have access to hadronic and electromagnetic couplings of the resonances. The often discussed problem of missing resonances (e. g. is an important topic at CB-ELSA. The investigation of photoproduction reactions yields a great discovery potential for some of these missing states. We are not limited to the channel T N , but have access to various final states, some of which are selective due to isospin conservation. The photoproduction of 17 mesons, e. g., selects contributions of N* resonances in the intermediate state. 2. Experiment
The data stem from the first experimental phase of the CB-ELSA experiment. An unpolarized photon beam was produced via scattering of a 1.4GeV or a 3.2 GeV electron beam delivered by the electron stretcher accelerator ELSA, having the 1/E7 distribution typical for bremsstrahlung. The photons are then energy tagged by detecting the corresponding electrons in a magnetic dipole spectrometer. These photons hit a liquid hydrogen target in the center of the CB-ELSA detector, an electromagnetic calorimeter consisting of 1380 CsI crystals. If a reaction occurs, photons originating from the decay of produced neutral mesons aThis work is supported by the Deutsche Forschungsgemeinschaft (DFG)
293
294 are detected with high angular and energy resolution. The proton is detected as well and identified by an inner detector consisting of three layers of scintillating fibers. For the flux determination, a total absorption photon detector was placed further downstream.
3. Results Results on yp -+ p r o and yp + pq were obtained by detection of two photons for 7ro + 2y and 17 + 27 and by detection of six photons for 7 + 37r0 + 67. The proton was either detected in the CB-ELSA detector and identified by the inner detector or, for low-energetic protons, taken from the hit in the inner detector alone. A kinematic fit was applied to the measured values, with known event energy from the tagger and known four-vectors for the decay photons, while the proton for the was left unconstrained. Confidence-level cuts were applied on > two-photon, > lop2 for the six-photon case.
1o6
1o5 1o4
- 2.6 million
1o3
no + 2 y
1o2
100
200
300
400
500 600 myy[MeV/c
1
Figure 1. Invariant mass of two photons in three-particle final states, logarithmic scale, (a) 27 mass, (b) 67 mass, linear scale
A spectrum of invariant masses can be seen in Fig. 1. The two-photon invariant m a s is shown on a logarithmic scale. Insets (a) and (b) show the two- and the six-photon invariant mass in the 17 region. The background is of the order of beneath the 7. magnitude of lop3 underneath the 7ro and
295 3.1. 7p
+ p7P
The angular distributions were calculated using the fitted data. In order to correct for efficiencies, a GEANT-based simulation of the detector system was performed. The normalization was done with the help of the SAID analysis3: For photon energies up to 1.3GeV, the angular distributions were fitted to match the SAID prediction by applying a x2 fit, giving one factor for each energy bin. Above that energy, the Bux was obtained by scaling the experimentally obtained photon flux with one constant scaling factor to get an agreement between SAID and our data daldQ [u blsrl
cos em .1 4 . 5 0 0.5 1 0.5 0 0.5 1
Figure 2. Differential cross sections da/dR of yp t p r o (E-, binned), m: CB-ELSA, solid line: PWA result
The distributions4 in Fig. 2 match well with the predicted values from the SAID analysis, reflecting the good understanding of our detector response. The data can be described well in a partial wave analysis5. The result is shown together with the experimental results.
3.2. YP + Prl The photoproduction of 7 mesons was investigated in its two different neutral, most common decay channels, 27 and 33~’. The obtained cross sections match
296
with a branching ratio of l?q--t3Ko/I'q+2y = 0.825 f 0.001 f 0.005, which is in excellent agreement with the values stated by the PDG'. This again reflects the good description of the detector and enables us to add the statistics from both channels. doldQ [pblsr] 2 1.5 1 0.5
0.6 0.4 0.2
-
-
850 " 900
900 950
950 1000
1150-1200
1200-1250
1250-1300
-
1000 1050
. 1300-1350
c
0.6
0.4 0.2 0.6 0.4 0.2 0.6
. . . . . . -1 -0.5 0 0.5 1 -0.5 0 0.5
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
-0.5 0 0.5 1 -0.5 0 0.5 1 -0.5 0 0.5 1 -0.5 0 0.5 1
cos e,,
Figure 3. Differential cross section da/dR for yp + pq ( E , binned), D: CB-ELSA, other symbols: data from TAPS, GRAAL, CLAS, solid line: PWA result
The data7 shown in Fig. 3 is in excellent agreement with previously published data from TAPS8, GRAAL', and CLASl'. It extends the known region as well in photon energies as in angular range. The resulting fit from a partial wave analysis is shown as well. Evidence is found for two new resonances, Dl~(2070)and P13(2200). A symmetry observed in the results of this partial wave analysis is that the resonances s11(1535), P13(1720), and D15(2070) couple strongly to Nq. In a harmonic-oscillator model, one could assign L = 1, 2, 3 and S = 112 to these states, coupling to J = L - S , giving the measured quantum numbers J p = 1/2-, 3/2', 5/2-. References 1. S. Capstick, W. Roberts, Phys. Rev. D 49 (1994) 4570.
297 2. U. Lohring et al., Eur. Phys. J A 10 (2001) 309. 3. R. A. Arndt et al., http://gwdac.phys.gwu.edu/. 4. 0.Bartholomy et al., in preparation. 5. A. Anisovich et al., Proceedings NSTAR 2004. 6. K.Hagiwara et al., Phys. Rev. D 66 (2002) 1. 7. V. CredC et al., in preparation. 8. B. Krusche et al., Phys. Rev. Lett. 74 (1995) 3736. 9. F.Renard et al., Phys. Lett. B 528 (2002) 215. 10. M.Dugger et al., Phys. Rev. Lett. 89 2002 222002.
Target and Double Spin Asymmetries for e‘ p’ + e’ p no A. BISELLI Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213, USA E-mail:
[email protected] An extensive experimental program to measure the spin structure of the nucleons is carried out in Hall B with the CLAS detector at Jefferson Lab using a polarized electron beam incident on a polarized target. Spin degrees of freedom offer the possibility to test, in an independent way, existing models of resonance electroproduction. The present analysis selects the exclusive channel p’(Z,e’,p)sO from data taken in 2000-2001, to extract single and double asymmetries in a Q2 range from 0.2 to 0.75 GeV2 and W range from 1.1 to 1.6 GeV/c2. Results of the asymmetries will be presented as a function of the center of mass decay angles of the so and compared with the unitary isobar model MAID, the dynamic model by Sato and Lee and the dynamic model DMT.
1. Introduction An extensive experimental program to measure inclusive, semi-exclusive, and exclusive reactions using longitudinally polarized electrons scattering off longitudinally polarized protons and deuterons was carried out with the CLAS detector at Jefferson Lab . The experiment running period was split into two parts: the first part was completed in 1998 with a total of about lo9 triggers at two beam energies, 2.5 and 4 GeV, leading to publications for both inclusive132and exclusive channels 3 , 4 . The second part of the run was completed in 2000-2001 with a total 2.3 x lo1’ triggers at beam energies of 1.6, 2.4, 4.2 and 5.7 GeV. The present analysis is focused on the exclusive channel Z$-+e ’ p O from the data at beam energy of 1.6 GeV. The exclusive cross-section for meson electroproduction can be written as
dd a~ =+
${a
dR*
where dR* = sin e*dO*dc#J*is the solid angle of the meson in the hadronic center of mass, k is the momentum of the pion, k;m is the real photon equivalent energy in the c.m. frame, h is the electron helicity and P is the target proton polarization. It is clear that by performing polarized beam and target experiments one can access the contributions to the cross section, dae/dR*, dat/dR*, and da,t/dR*, in
298
299 addition to the well known unpolarized cross section duo /do* adding information to our understanding of resonance production and background. At the intermediate energies used in this analysis pQCD is not valid and effective field theories were developed to describe the cross sections. These models use previous unpolarized photo- and electroproduction data to fix the various free parameters that arise in the calculation. The polarized cross-sections can then be predicted, and by performing experiments with polarized beams and polarized targets it is possible to verify or constrain the models. For this experiment three models were tested against the data: the Mainz unitary isobar model MAID5, the dynamical model DMT' and the dynamical model by T. Sat0 and H. Lee7. Y
d
.
0.8
0.6 0.4
0 2 -0 -0.2 -0.4
-0.6 -0.8
$0.6 0.4 0.2 0 -0.2 -0.4 -0.6
-150 -100 -50
0
50
100
150
$* [desl
-150 -100 -50
0
50
100 150
O*
[degl
Figure 1. Asymmetry A,t (top) and At (bottom) as a function of the center-of-mass angle of the pion 4* for -0.8 < cos8' < -0.6, 0.223 < Q 2 < 0.379 GeV2/c2 and for W 1.20 < W < 1.25 GeV/c2 (left) and 1.3 < W < 1.4 GeV/c2 (right) intervals. The curves represent the predictions from the MAID2003 model (solid), D M T (dotted), and Sato-Lee model (dashed).
2. The experiment
The data for this analysis were taken with the CLAS detector system" in Hall B at Jefferson Laboratory in Newport News, VA. Since the CLAS detector uses a toroidal magnetic field, which is zero along the beam axis, it is possible to insert a polarized target into the detector. The target 1 1 , coilsisting of solid 1 5 N H 3 , was polarized using dynamic nuclear polarization and was immersed in a T = 1 K 4He cooling bath. The holding field of B = 5 T had a very high uniformity of = With this setup target polarizations of Pe = +79% and Pe = -72% were achieved.
300 In addition t o the 15NH3target a solid I2C target and an empty target cell were used for background studies. 3. Analysis
For the present analysis, data at the beam energy of 1.6 GeV were considered. The target and double spin asymmetries as a function of the decay angles in the center of mass frame of the pion were extracted in a W range from 1.1 to 1.6 GeV/c2, where W is the invariant mass of the hadronic system. The 7ro was identified with a missing mass cut. The asymmetries were calculated by combining the counts of events for the four possible combinations of beam-target polarizations Nij according to:
where $&" is the contribution from the scattering off 15N nuclei and the liquid helium coolant, Pe is the beam polarization, Pp and P!, are the magnitudes of positive and negative target polarizations, respectively, and
The contribution of the 15N background was removed by using data from separate were experimentally extracted using runs with a I2C target. The products the well known asymmetry in the elastic region. An example of the results can be seen in Fig 1 and Fig 2. To estimate quantitatively the agreement between data and the model, a simultaneous x2 comparison of all angular distributions for all Q2 intervals was performed and the results are listed in Table 2. Table 1. x 2 per number of degrees of freedom comparison between data and the three theoretical models. Model
At W
Aet
< 1.3GeV/c2 ndf = 1440
MAID03
1.89
1.05
SL
1.02
1.09
DMT
2.27
1.04
At W
Aet
> 1.3GeV/c2 ndf = 1080
1.14
1.46
1.61
1.02
301
0.6
0.4 0.2 -0 -0.2 -0.4
-0.6 -0.8
d"0.6
-0.6
-1 -0.80.&0.40.2 -0 0.2 0.4 0 . 6 0 . 8
1 -0.8O.CO.CO.2-0 0.2 0.4 0.6 0 . 8
case*
co&*
:
Figure 2. Asymmetry A,t (top) and At (bottom) as a function of the center-of-mass angle of the pion cos0" for -144.0 < 4* < -108.0, 0.223 < Q2 < 0.379 GeV2/c2 and for 1.20 < W < 1.25 GeV/c2 (left) and 1.4 < W < 1.5 GeV/c2 (right) intervals. The curves represent the predictions from the MAID2003 model (solid), D M T (dotted), and Sato-Lee model (dashed). 4. Outlook
Target and double spin asymmetries for the channel Z'p' -+ e'px' were extracted in a range in W from 1.1 to 1.6 GeV/c2. In the A(1232) region preliminary results show overall agreement between the data and the model predictions of the double spin asymmetry, which are dominated by the (M1+I2 term. The models, however, differ in their predictions of the target asymmetry, which is sensitive to interference of the A(1232) resonance with background multipoles such as Eo+, So+, and Sl-.A x2 comparison shows a preference for the Sat0 and Lee model in the A(1232) region. These results are consistent with the already published comparison in ref. 3 , but with much improved statistical accuracy. The higher statistical accuracy of the second data sample allowed us also to extend the analysis t o invariant masses above the A(1232) resonance, where uncertainties in the models due to the many overlapping resonances are bigger. Examples for the higher W region results are shown in the right plots of Fig 1 and Fig 2. Preliminary results show discrepancies in both the target and double spin asymmetries, hut further work is needed to understand the sensitivity of the asymmetries to the different contributions. References 1. R. Fatemi et al. [CLAS Collaboration], Phys. Rev. Lett. 91,222002 (2003) 2. J. Yun et al. [CLAS Collaboration], Phys. Rev. C 67,055204 (2003) 3. A. Biselli et al. [CLAS Collaboration], Phys. Rev. C 6 8 , 035202 (2003)
302 4. R. De Vita e t al. [CLAS Collaboration], Phys. Rev. Lett. 8 8 , 082001 (2002) 5. D. Drechsel, 0. Hanstein, S.S. Kamalov and L. Tiator, Nucl. Phys. A645, 145 (1999) 6. S. S. Kamalov and G. Y. Chen and D. Drechsel and L. Tiator, Phys. Lett. B27,522(2001) 7. T. Sato and T.S. Lee, Phys. Rev. C54, 2660 (1996) 8. R.M. Davidson, N.C. Mukhopadhyay and R.S. Wittman, Phys. Rev. D43, 71 (1991) 9. L.W. Mo and Y.S. Tsai, Rev. Mod. Phys., 45,205 (1969). 10. B. A. Mecking e t al. [CLAS Collaboration], Nucl. Instrum. Meth. A 503,513 (2003). 11. C.D. Keith e t al., Nucl. Instrum. Meth. A 501, 327 (2003).
Compton scattering of polarized photons on the proton at GRAAL 0. Bartalinil, V. Bellini2, J. P. Bocquet3, M. Castoldi4, A. D'Angelo', J.-P. Didelez5, R. Di Salvo', A. Fantini', A.Guisa'1, G. Gervino', F. Ghio7, B. Girolami7, M. Guidal', E. Hourany', V. Kouznetsov2, R. Kunne', A. Lapik', P. Levi Sandrig, A. Lleres3, D. Moricciani', V. Nedorezov', D. Rebreyend3, N. V. Rudnev", G. R U S S OC. ~ , Schaerfl, M. L. Sperduto2, C. M. Sutera2, A. Turinge' , A. Zucchiatti4 INFN Sezione d i Roma 11 and Universitri d i Roma "Tor Vergata", Italy INFN Sezione d i Catania and INFN Laboratori Nazionali del Sud and Universitd d i Catania, Italy IN2P3, Institut des Sciences Nucle'aires, Grenoble, France INFN Sezione d i Genova and Universitd d i Genova, Italy IN2P3, Institut d e Phisique Nucle'aire, Orsay, France INFN Sezione d i Ton'no and Universitd d i Torino, Italy INFN Sezione di Roma I and Istituto Superiore di Sanitri, Roma, Italy Institute for Nuclear Research, Moscow, Russia INFN Laboratori Nazionali d i Frascati, Italy lo Institute of Theoretical and Experimental Physics, Moscow, Russia INFN Sezione di Catania and Universitd. d i Catania and CSFNSM, Italy
'
'
'
''
Compton scattering of polarized photons on the proton has been investigated in the energy range 0.8- 1.5 GeV, where the non-resonance double-pion photoproduction and the excitations of high baryon resonances play an important role among the photoabsorption mechanisms. Data have been collected by the GRAAL facility, whose polarized photon beam is obtained by the backward scattering of laser light onto the ultrarelativistic electrons circulating in the Grenoble's ESRF storage ring. The main background contribution is due to the in-flight decay of 7ro where the two photons are emitted with a small opening angle. We present some preliminary results about the method for the separation of Compton scattering events from the aforesaid background.
1. Introduction
Photoreactions by means of polarized tagged photons constitute a powerful tool in the investigation of the dynamics of the nucleon constituents, providing an important source of information about the spectrum of baryon resonances, thus helping in disentangling the mess of theoretical models in the search for LLmissing resonances". The GRAAL facility provides a polarized and tagged y-ray beam, produced by the Compton backscattering of polarized laser photons onto the 6.04 GeV
303
304 electrons circulating in the ESRF storage ring, The polarization of the photon beam can be easily changed by switching the polarization of the laser light, and its energy spectrum is nearly flat, showing a very high degree of polarization (- 98%) near the Compton edge. The GRAAL detection apparatus 1,2,3 covers almost the whole solid angle. It consists mainly of a BGO ball made of 480 crystals, covering a polar angular region between 25' and 155', supported by cilindirical and plane wire chambers, thin plastic scintillators and a shower wall in the forward direction (0 5 25'), plus a sandwich of plastic scinitllators and lead in the backward direction (0 2 155'). Each of the constituting assemblies allows for the discrimination between charged and neutral particles, and for their identification via time of flight and energy loss measurement. With its maximum energy of 1.6 GeV, the GRAAL beam allows for the study of all baryon resonances with masses above the A and up to 1.8 GeV.
-
-
2 . Compton scattering of polarized photons on the p r o t o n
Although differential cross sections and beam asymmetries for the Compton scattering of polarized photons on the nucleon have already been measured in the low-energy range (from 206 to 310 MeV in Ref.4), very few data exist in the literature for the energy region around 1 GeV '. We started our investigation on this phenomenon by focusing on the events detected in the central region of the GRAAL apparatus (. i.e. the assembly BGO plus cylindrical wire chambers), where the Compton cross section predicts a relevant event contribution. The main background contribution is due to the in-flight decay of r o tTwo cases should be taken into account: (i)- The two y's from the ro are emitted with a small opening angle, thus being both highly energetic. The minimum y opening angle A812 = 2cos-' Pn corresponds to the two photons having equal energies in the laboratory frame.
(ii)- A 'soft' photon from the decay is not detected. Whereas the second source of background can be reduced by detecting the soft photon either in the backward direction or in the BGO ball by using special runs with a lower threshold, the disentanglement of the events from the first background source requires in principle a thorough analysis of the distribution of the deposited energy in each BGO cluster. This is currently 'work in progress'. Nevertheless, the study of the detection polar angle as a function of the minimum opening angle of the two photons from the no decay allows for the identification of the region in which this background source should be more relevant. This dependence is shown to be:
E,
8, = c o s - l (
+ mpc2 - (SE, + +) E, cos
sin
+
305
Figure 1. Detection polar angle of 'r7
as a function of the opening angle A012 of the two photons from its decay at an incident y energy of 1 GeV. and it is partially reproduced in fig.1 for an incident y energy E-, = 1 GeV. From this picture one can easily infer that the effect of the background is relevant only at low values of the polar angle, around 25' degrees, 2.e. in the very first crowns of the BGO ball, where the predicted y opening angle is 18'. So, this is the region in which the analysis of the shower topology in the BGO clusters could be of some help.
-
3. Analysis procedure In order to separate the Compton events from the background, we started by selecting those events with a multiplicity of two in the BGO ball, and constituted by one neutral and one charged particle. Compton events are, of course, to bc scarched for among these ones: in fig.2, we report the distribution of the events selected by imposing the total energy conservation. It is easily seen that a huge background is present (a), and some of the selected events are certainly not belonging to a two-body reaction (b). The azimuthal angle is measured with respect to polarization direction of the incident photon. This background is
306
w -
w -
4O(c
-
fM5-
?ma
-
IM
-
f Figure 2. (a) Events with one neutral and one charged particle, both detected in the BGO ball. (b) Difference between the azimuthal angular coordinates of the two members of the pair. Values different from +180" belong to events corresponding to more-than-two-body reactions.
rejected by requiring the following Compton kinematics conditions: (i)- The coplanarity between the directions of the scattered photon and the
recoil proton (fig.3, upper left). (ii)- The energy-angle relation for the scattered photon(fig.3, upper right) (iii)- The energy-angle relation for the recoil proton (fig.3, lower section).
-
-
As a result, among the 2340000 events processed, nearly 8.5% are events with one charged and one neutral particle in the BGO ball, and, among these, 23.5% have been identified by our analysis procedure as Compton events. Thus, the identified Compton events add up to 0.2% of the total event number. In fig.4 we show the azimuthal angular distribution of the scattered Compton photon (selected as above) for a chosen polarization state. It agrees nicely with the cos2 d-, behaviour predicted by the relativistic Klein-Nishina formula for the crosssection of polarized photons onto unpolarized particles in the Born approximation
-
6,7
4. Conclusions
The GRAAL set-up shows to be very suitable for the analysis of the Compton scattering of polarized photons on the proton. Anisotropy effects on the azimuthal distribution are already visible, even with a low statistics. Further improvements
307
I
(upper left) Events selected by the coplanarity condition. (upper right) Events selected after having added the photon kinematics condition. (lower picture) Events selected after having added the proton kinematics condition.
Figure 3.
are expected to be achieved both by the inclusion of the analysis of events detected in the forward detectors and by the analysis of the topology of the shower energy distribution in the forward clusters of the BGO ball.
308
Figure 4. Azimuthal distribution of the scattered Compton photon for a chosen
polarization state, integrated over the polar coordinate.
References
et al., Phys. Lett. B 544, 1729 (2002) P. Levi Sandri et al., Nucl. Instr. and Meth. in Phys. Res. A 370,396 (1996) M. Castoldi et al., Nucl. Instr. and Meth. in Phys. Res. A 403,22 (1998) V. Bellini et al., Phys. Rev. C 68 (2003) D. Moricciani et al., in Mesons and light nuclei: 8th Conference, edited b y J. Adam et al., American Institute of Physics (2001) 6. L. D. Landau, E. M. LifSits, Teoria quantistica relativistica, Editori Riuniti 1. 0. Bartalini
2. 3. 4. 5.
(1991) 7. M. Kaku, Quantum Field Theory, Oxford University Press (1993)
Total Photoabsorption off the Proton and Deuteron at Intermediate Energies” V. Nedorezov and N. Rudnev for the GRAAL collaboration R A S Institute for Nuclear Research, 11 7312, Moscow, E-mail:
[email protected] Total photoabsorption cross section experiments at GRAAL are described. Measurements have been done in the energy range E, = 600-1500 MeV, with liquid hydrogen and deuterium targets, using the laser back scattered gamma beam and the large aperture LAGRANyE detector. Electromagnetic and hadron backgrounds have been analyzed. A subtraction method, using the empty target measurements, has been applied to derive directly utot for the free proton and deuteron. Experimental results for utot are compared to existing literature data. Large difference between the proton and deuteron, normalized by factor 2, in photoabsorption cross section is seen particularly in the D15 nucleon resonance region.
1. Introduction Existing photoabsorption data for the proton and deuteron above 800 MeV 1 , 2 are scarce, therefore new accurate results are required. Existing data were obtained with tagged bremsstrahlung beams which have a large low energy tail raising as l/E-,. This produces a significant Electromagnetic Background (EMB). At GRAAL we use photon beams obtained by the back scattering of laser light on the electrons of the ESRF storage ring, therefore the Electromagnetic Background (EMB) is considerably reduced as will be shown below. A subtraction method, using the empty target measurements, was applied to derive directly q o t . This method was developed elswhere and realized in the photonuclear experiments using almost 47r NaI(T1) detector. In the present work, we used similar procedures in simplified form which turned out to be successful, due to the particular qualities of the GRAAL beam and detector. 2. E x p e r i m e n t
A general description of the GRAAL experimental set-up can be found elsewhere It is important for the total photoabsorption measurements to use the collimated back scattered gamma-beam which has no low energy tail in contrast to the Bremsstrahlung beams (less than 1%).Therefore, the electromagnetic background (EMB) from the target is negligible in the main part of the LAGRANyE detector, namely a large solid angle BGO ball. aThis work is supported by RFBR 04-02-16996
309
310
In the experiment we separate two sources of the EMB that come from outside the target, namely the accelerator and the beam collimation system. Figure 1 (left) shows angular distribution of BGO events from the full and empty target. No kinematics cuts are applied. The signature of the first EMB part is the large BGO cluster size (MCLUS 1 8, where MCLUS is defined as number of simultaneously activated neighbouring crystals). This EMB corresponds to the large electromagnetic shower which is seen in the accelerator plane. The contribution of this EMB part is equal to 20% as compared with the total yield, approximately. Evidently, this EMB can be eliminated by the cut MCLUS 5 8. The rest of the background (also about 20%) which is seen in fig.1 (left) belongs to the hadron events (HB) from the mylar films. The second EMB part (from the collimating system) looks as a halo at backward angles. This contribution is small as seen in fig.1 (left). Figure 1 (right) shows the difference between the full and empty target yields, normalized by the gamma flux (black poits). The result of simulation also is shown (grey points). One can see very good aggreement between the experiment and simulation. So, we can conclude that electromgnetic background comes outside of the target and it can be subtracted to get the total hadron photoabsorption cross section.
F 3 5
,
.
,
.........
30 25
20 15 10
5
0
e
8
Figure 1. Angular distributions for BGO events. Left: black and grey point correspond to the full and empty target, respectively. Right: black points is the difference between the full and empty target yield; grey points is the result of simulation.
3. Results Total photoabsorption cross section atot(E,) was evaluated from the total hadron yield:
WE,) = N n N, '
'
atot(E,)
'
O(E,)
where Nn is the number of nucleons in the target (2.568.1023 cm-2 for hydrogen, 5.136.1023 cm-2 for deuterium), N, is the flux of photons passed through the target, s2(E,) is the measurement efficiency. BGO hadron events are identified by the condition: total energy release in BGO (hard trigger) is greater than 160
31 1 MeV. Then the cut (MCLUS < 8) is applied to decrease the EMB from 40% to 20%, approximately (as compared with the total yield). Then the rest of the background (HB, halo etc) was eliminated by subtraction of the empty target contribution. Total number of the hadron events collected during one day was enough (about 2 . lo7 events) to provide the statistical error bars smaller than 2% in each energy bin of 16 MeV width. The measurement efficiency O(E7) was simulated (see Table 1). This efficiency is closed to the geometrical solid angle (0.9 T) for both proton and deuteron target and it does not depends on the energy of gamma-beam, naturally. These features are favorable for the total photoabsorption measurements. Table 1. Total measurement efficiency (in percents) for the liquid proton (LH) and liquid deuteron (LD) targets for different BGO thresholds (100 and 160 MeV)
E7,MeV
550
650
LH, 100 MeV
87
87
88
LH, 160 MeV
82
82
82
750
850
950
1050
1150
1250
1350
1450
88
88
88
89
89
90
90
83
83
83
84
84
84
84
LD, 100 MeV
88
87
88
88
88
88
89
90
90
90
LD, 160 MeV
81
82
82
83
83
84
84
84
84
84
The flux was measured by the total photoabsorption monitor ("spaghetti") in coincidence with the tagging system. The efficiency of the single hits was between 60% and 70%, depending on the runs the laser line. Random coincidences do not exceed 3%. The correction for overlapping signals was done, finally.
s
t 5311
26P
m 450
lob
60
Figure 2. Total photoabsorption cross section for the proton (left) and deuteron, normalysed by A = 2 (right). Black points are the GRAAL data, open ones correspond to and Mainz data (below 800 MeV) Armstrong data '9'
31 2 The results on the total photoabsorption cross section for the hydrogen and for the deuterium obtained by the subtraction method are shown in Figure 2. The data for the proton obtained with the green and UV laser were analyzed independently, covering the energy range of 600-1100 MeV and 900-1500 MeV, respectively. Statistical errors are within points. Analysis of the data for deuteron at 900-1500 MeV is in progress now. One can see that the absolute values are in agreement with the literature ones, especially below 800 MeV. Above 800 MeV the GRAAL data are slightly but systematically lower in the third resonance region than Armstrong data.
4. Conclusions We demonstrated the low background conditions of the GRAAL facility which is favorable for the total photoabsorption precise measurements. Especially, for investigation of the GDH sum-rule, nuclear media effects in the total and partial meson photoproduction channels. References 1. 2. 3. 4. 5. 6.
T.A.Armstrong e.a. Phys.Rev. D7,5 1640 (1972). T.A.Armstrong e.a. NucLPhys. B41 445 (1972). Collaboration GRAAL NudPhys. A622 110 (1997). M.Anghinolfi e.a. Phys.Rev. C47,3 922 (1993). M.Mirazita e.a. Phys.Lett. B407 225 (1997). M.MacCormick e.a. Phys.Reu. C1,53 41 (1996).
Study of nucleon resonances in (-y,r)N + cpX reactions within a coupled-channel Lagrangian model. V. V. SHKLYAR, G. PENNER, and U. MOSEL” Institut fur Theoretische Physik Heinrich-Buff-Ring16, 0-35392 Giessen E-mail:
[email protected] We study pion- and photo-induced reactions on the nucleon within a coupledchannel effective Lagrangian model to extract baryon resonance properties. All available experimental data on the (y/n)N -+ nN, 2aN, qN, wN reactions in the 6 2GeV are simultaneously analysed to constrain energy region mrr+ m N f baryon resonance parameters. A good description agreement of calculated observables with experiment is achieved and baryon resonance parameters are extracted.
The baryon resonance analysis has attracted much interest in the last few years. Despite great efforts made in the past the properties of baryon resonances are still not very well fixed Since the all information on the nucleon resonance properties is obtained from the analysis of the photo(meson)-nucleon scattering data, the extraction of baryon spectra turns out to be an extremely difficult task. The first difficulty consists in the solving the full scattering problem to describe experimental observables. The lack of our knowledge of non-resonant background contributions makes the task more complicated. The use of a coupled-channel effective Lagrangian approach which maintains unitarity is a possible way to solve the problem. Moreover, a simultaneous analysis of all available experimental data provides necessary constraints on the parameters and therefore can reduce the model dependence to obtained resonance properties. Such a model (Giessen model) for nucleon resonance analysis has been developed in In the previous analysis of the ( y / r ) N -+ mB reactions the contributions from spin-; states were neglected, whereas our last results reveal important contributions from the spin-? resonances to the w N final state. Thus, the aim of the present work is to perform a new combined study of the pion- and photon induced reactions to extract baryon resonance properties. The details of the model can be found in
a Work
partially supported by FZ Juclich
313
314
3,214.
The following experimental scattering data
7rN -+ 7rN 7rN -+ 27rN 7rN -+ 7 N 7rN -+ wN 7rN -+ K A 7rN + KC
+
< fi <
in the energy region mT m N 2 GeV have been simultaneously analysed t o constrain baryon parameters. Except the recent results on the K A and KC photoproduction measured by SAPHIR and CLAS our database includes all available experimental information on the reactions under consideration. A good description of the experimental data in all final states is achieved. In Figure 1 the results for the (yl7r)N -+ q N reactions are shown in comparison with the experimental data (see for the data references). We corroborate our previ-
3
e ^ 2
E
v
13
1
0 &(GeV)
6(GeV)
Figure 1. Calculated total cross sections for the 1)-meson production in comparison with the experimental data.
ous findings for the 7-meson production mechanism: the main contributions to 7r-p + 7n come from the ,911 and 4 1 partial waves. The peaking behaviour in the P11 partial wave cross section at 1.7 GeV (see Figure 1, left) is due to the Pl1(1710)-state excitation which is found to have large decay branching ration to q N . Despite its small coupling t o 7rN this resonance is excited due t o rescattering effects in the 27rN channel and gives a significant contribution to the total cross section. The major contributions t o the 7-meson photoproduction come from the Sll(1535) and Sll(1650) resonances. The P11-states play only a minor role here due to their small electromagnetic couplings. The results for the w-meson photoproduction are shown in Figure 2 in comparison with the recent SAPHIR data
315
1 'k-
'k-= 1.736 GeV
= 1.959 GeV
2 h
IM
B3
v
.
. .
- Giessen model
Figure 2. Calculated differential w-meson photoproduction cross sections in comparison with the SAPHIR data.
.............. -0.4
1.7
- cos ecm= 0.90
-0.4
1.9
1.8
'k-(GeV)
2
1.7
+
Giessen model 1.9
1.8
2
&(GeV)
Figure 3. Calculated spin density matrix element poo for the w-meson photoproduction in comparison with the SAPHIR data.
The peaking behaviour at forward angles (Figure 2,right) is due to the tchannel no-exchange, whereas the resonance production mechanism dominates at lower c o s ( 0 ) . In Figure 3 the calculated spin density matrix element poo is presented as a function of 6 at fixed angles (left). On the right panel of Figure 2 the calculated average value of p00 is shown in comparison with the SAPHIR data. A successful description of the spin density matrix measured by SAPHIR provides an additional constraints on the w-meson production mechanism. The results for the .rrN + w N and y N -i wN-reactions are given in Figure 4. It can be observed that the calculated cross sections are in very good agreement with experiment. In summary, we have performed an extended analysis of the pion- and photon-induced reactions in the resonance energy region to extract nucleon resonance properties. The obtained resonance resonance parameters can be found in '.
316
"
1.7
1.8
1.9
6(GeV)
2
4.7
1.8
1.9
2
&-(GeV)
Figure 4. Calculated total w-production cross sections in comparison with the experimental data. References
1. K. Hagiwara et al., Phys. Rev. D66, 010001 (2002), http://pdg.lbl.gov. 2. G. Penner and U. Mose1,Phys. Rev. 66, 055211 (2002); G. Penner and U. Mose1,Phys. Rev. C66, 055212 (2002). 3. V. Shklyar, G. Penner, and U. Mosel, Eur. Phys. J A in print. 4. G. Penner, PhD thesis, Universitat Gieaen, 2002, available via http://theorie.physik.uni-giessen.de. 5. J. Barth et al, Eur. Phys. J. A18, 117 (2003). 6. V. Shklyar, G. Penner, and U. Mosel, in preparation.
Helicity-Dependent Angular Distributions in Double-Charged-Pion Phot oproduct ion” S. STRAUCH for the CLAS Collaboration Department of Physics The George Washington University Washington, D. C. 20052, USA E-mail:
[email protected] Two-pion photoproduction in the reaction T p + p7r+7r- has been studied at Jefferson Lab Hall B using a circularly-polarized tagged photon beam in the energy range between 0.6 GeV and 2.3 GeV. Beam-helicity-dependent angular distributions of the final-state particles were measured. The large cross-section asymmetries that have been found exhibit strong sensitivity to the kinematics of the reaction, and are compared with preliminary model calculations by Mokeev and Roberts.
1. I n t r o d u c t i o n
Many nucleon resonances in the mass region above 1.6 GeV decay predominantly through AT or N p intermediate states into Nmr final states (see the Particle-Data Group review’). This makes electromagnetic exclusive double-pion production an important tool in the investigation of N* structure and reaction dynamics, as well as in the search for “missing” baryon states. Unpolarized cross-section measurements of double-pion electroproduction have been reported recently by the CLAS collaboration.2 Further constraints are to be found in polarization observables. Here, for the first time in the resonance region, a measurement of the T p -+ ~ T + T -reaction is reported, where the photon beam is circularly polarized and no nuclear polarizations (target or recoil) are specified. The cross-section asymmetry is defined by: 1 of-oA=--. (1) Pr o + + o where Pr is the degree of circular polarization of the photon and o* is the cross section for the two photon-helicity states A, = f l . For this kind of study, a final state of at least three particles is necessary, since reactions with two-body final aThis work was supported by the U.S. Department of Energy under grant DE-FGOZ95ER40901. Southeastern Universities Research Association (SURA) operates the Thomas Jefferson National Accelerator Facility under U.S. Department of Energy contract DE-AC05-84ER40150.
31 7
318 states are always coplanar and have identical cross sections for unpolarized or circularly polarized photons, so that A = 0. 2. Experiment
The ;Jp + p7r+n- reaction was studied with the CEBAF Large Acceptance Spectrometer (CLAS)3 at Jefferson Lab. A schematic view of the reaction is shown in Fig. l.b Longitudinally polarized electrons with an energy of 2.4 GeV were inci-
Figure 1. Angle definitions for the circular polarized real-photon reaction T p t p s + ~ in the helicity frame; 8,, is defined in the overall center-of-mass frame, 8 and 4 are defined as the n+ polar and azimuthal angles in the rest frame of the n+n- system. dent on the thin radiator of the Hall-B Photon Tagger' and produced circularlypolarized tagged photons in the energy range between 0.6 GeV and 2.3 GeV. The collimated photon beam irradiated a liquid-hydrogen target. The circular polarization of the photon beam was determined from the electron-beam polarization and the ratio of photon and incident electron energy.7 The reaction channel was identified by the missing-mass technique, which requires the detection of at least two out of three final-state particles ( p ,,'n and T - ) . Owing to the large angular acceptance of the CLAS, complete azimuthal angular distributions of the cross-section asymmetries were observed.
3. Results The T p + p'nreaction has been analyzed for center-of-mass energies W up to 2.3 GeV. Figure 2 shows preliminary 4 angular distributions of the cross-section helicity asymmetry for various selected 25-MeV wide c.m. energy bins between bThe definition of 4 is following the convention of Schilling, Seyboth and Wolf4, and differs by a phase of K from CP' in Ref. '.
319
W = 1.40 GeV and 1.65 GeV. The data are integrated over the full CLAS acceptance. The preliminary analysis shows large asymmetries, with the symmetry A ( 4 ) = -A(2n - 4). This is expected from parity con~ervation.~ A more detailed analysis has revealed a rich structure of these data with rapid changes of the angular distributions with photon energy or with any other kinematical ~ariable.~ 0.2
.................
............................
.....
+?
'-,
-0.2
................................... .
90
180
d (deg)
270
360 0
++ +
'. .'++ *
90
+ +
+++ 180
@ (deg)
270
360 0
90
180
270
360
@ (deg)
Figure 2. Preliminary angular distributions for six different center-of-mass energy bins (AW = 25 MeV) of the cross-section asymmetry for the T p + p n f n - reaction. The dashed curves are calculations by Roberts8 (47r integrated, W 5 1.60 GeV). The solid curves are calculations by Mokeev et aLg (acceptance corrected, W 2 1.45 GeV).
K. Schilling, P. Seyboth and G. Wolf discussed the case of photoproduction of vector mesons by polarized photons on an unpolarized nucleon and their subsequent decay d i s t r i b ~ t i o n Preliminary .~ calculations of cross-section asymmetries in the general case of ;Jp -+p7rf7r- were done by Oed and Roberts using a phenomenological Lagrangian approach.8 It is important to note that the calculations performed to date have been integrated over 47r, whereas the experimental data have been measured only over the coverage of the CLAS. The results of these calculations are shown in Fig. 2 as the dashed curves. Calculations including the CLAS acceptance will be available soon. In general, a very good description of the data has been achieved. Results have also been obtained by Mokeev et al. in a phenomenological calculation using available information on the N and A state^.^ Parameters of this phenomenological code have been fitted to CLAS cross-section data for real- and virtual-photon double-charged-pion production.
320 The results are shown in Fig. 2 as the solid lines. The CLAS acceptance was taken into account in this calculation. Neither model has yet been adjusted to the polarization data, and therefore these results are preliminary. There clearly is room for improvement in the model parameters. In fact, current studies have indicated a strong sensitivity of the helicity a s y m e t r i e s to the relative contributions of various isobaric channels and interference among them These data will therefore prove to be an important tool in baryon spectroscopy. References
1. K. Hagiwara et al., Phys. Rev. D 66,010001 (2002). 2. M. Ripani et al., Phys. Rev. Lett. 91, 022002 (2003); see also M. Ripani, contribution to these proceedings. 3. B. A. Mecking et al., Nucl. Instrum. Methods A503,513 (2003). 4. K. Schilling, P. Seyboth, and G. Wolf, Nucl. Phys. B15,397 (1970). 5. S. Strauch (CLAS Collaboration), Proceedings of 2nd Int. Conf. on Nuclear and Particle Physics with CEBAF at Jefferson Lab, Dubrovnik, 26-31 May 2003, to be published in Fyzika B, nucl-ex/0308030. 6. D. I. Sober et al., Nucl. Instrum. Methods A440,263 (2000). 7. H. Olsen and L. C. Maximon, Phys. Rev. 114,887 (1959). 8. W. Roberts and A. Rakotovao, hep-ph/9708236 for formalism; and T. Oed and W. Roberts, private communication (2003). 9. V. I. Mokeev et al., Phys. Atomic Nucl. 66,1282 (2003); V.I. Mokeev et al., Phys. Atomic Nucl. 64,1292 (ZOOl), and references therein; V. I. Mokeev, private communication (2004).
Baryon states in double charged pion photo- and electroproduction V.I. MOKEEV, V.D. BURKERT and L. ELOUADRHIRI Jefferson Laboratory, 12000 Jefferson Awe, Newport News VA 23606, E-mail:
[email protected]
USA
G.V. FEDOTOV, B.S. ISHKHANOV, E. ISUPOV, and N.S. MARKOV Nuclear Physics Institute a t the Moscow State University
M .RIPAN1 Phenomenological analysis of recent CLAS ZK photo- and electroproduction data is presented. This effort is a part of CLAS Collaboration activity on development of physics analysis methods with a goal to determine N * parameters.
1. Introduction
Recent analysis of the CLAS 27r photo- and electroproduction data 1 , 2 have considerably improved our understanding of non-resonant mechanisms for this exclusive channel. These improvements allowed to observe the manifestation of the P33(1600) and a possible new state at the photon point. 2.
New information on background f r o m CLAS data.
As a starting point in the analysis we used a dynamical model This approach was used in previous studies of the CLAS N7r7r electroproduction data and revealed a signal from a possible new baryon state 3/2+(1720). However, this analysis was limited to 7r+r-,7r+p invariant mass and 7r- angular distributions. In the current analysis 7r-p mass distributions were also included and evaluated within the framework of the m ~ d e l ~The .~~ model . parameters were fixed at the best value achieved in data fit. At energies above the rfD13(1520) production threshold (WL1.66 GeV) the calculated 7r-p mass-distributions underestimated the measured ones in the 7r-p mass range between 1.5-1.55 GeV (dashed lines on Fig 1). We implemented a new channel y p 4 r+Dy3(1520) to overcome this shortcoming. The channel amplitude was described by a minimal set of gauge invariant Reggetized Born terms, outlined in The coupling of the r-Regge trajectory to the pD13(1520) current was fitted to the data. We obtained a reasonable description of all observables in the electroproduction data (solid lines on Fig 1). x2 per data points was improved by almost factor 2, suggesting considerable evidence for contributions from the new isobaric channel in 27r photoproduction. 3112.
'
321
'
322 Table 1. P33(1600) parameters.
Mass, GeV
Our fit
PDG data
1.686 f 0.010
1.55 - 1.70
338 f 100
250 - 450
65 f 6
40 - 70
Total width, MeV BF (TA), % A l l 2 * 103GeV-'/2 A312
* 103GeV-'/2
ii-P
mass. GeV
* 10
-29 iz 20
-17 f 10
-19 h 20
-30
n- P moss. GeV
Figure 1. T - p invariant mass distributions at W=1.78 GeV, Q2 = 0.65GeV2 (left) and Q2 = 0.95GeV2 (rigth). Solid (dashed) lines are the calculations after (before) implementation of y p + T+D:,( 1520) channel
New CLAS 2 i ~data at the photon point allowed for the first time a combined analysis of r + ~ - ,T'P, 7r-p mass and i ~ - angular distributions. Our reaction model, accounting the new isobaric channel and including the contribution from conventional N * with PDG parameters as well as contribution from a possible 3/2+(1720) state with photocouplings fitted t o the CLAS data, revealed the following discrepancies (dashed lines on Fig. 2): a)angular distributions deviate considerably from the ones calculated at backward angles; b)shapes of the measured and calculated T ' T mass distributions were in disagreement at W between 1.6-1.7 GeV; c) measured A' peaks in r - p mass distributions at W>1.7 GeV were underestimated. In order to improve the background description, we substituted naive 3-body phase space treatment of approach l 2 for the part of background beyond tree diagrams by a set of u-channel processes, presented in '. This improvement allowed us to reproduced both r- angular and T ' T mass distributions. Reasonable description of r'p, r - p mass distributions was achieved, implementing an additional t-channel term in T A sub-channels '.
323
$70 D
E
-60
$
50
40 30 20
10 0
0
1 1.2 1.4 theto n-.deg
n+
jr-
Moss.GeV
jr-
P moss. GeV
Figure 2. 2-.rr cross-sections at Q2=O[2]: 7r- angular distribution at W=1.50 GeV (left); P+T- mass distribution at W=1.61 GeV (central); r - p mass distribution at W=1.78 GeV (right). Solid (dashed) lines are calculated cross-sections after (before) model improvements at the photon point.
I w
GeV
Figure 3 . 2-7r cross-section at the photon point [Z]. Thick (thin) solid lines are complete calculations with 3/2+( 1720) state switched-on (off). The contributions from background, N*' s and resonance-background interference are shown by dashed, dotteddashed and dotted lines.
To eliminate remaining shortcomings in the description of the data near 1.6 GeV we added the P33(1600) 3-star PDG state. The parameters of this state were varied together with the parameters of a possible 3/2+(1720) state. The final fit provides reasonable description of all available CLAS real photon data at W11.8 GeV (Fig2, Fig3).
324 3. The parameters of possible new 3/2+(1720) and conventional P33(1600) states
Table 1 contains the extracted photocopuplings and hadronic parameters of P33(1600) state. The hadronic parameters obtained in our analysis are inside uncertainties of data with hadronic probes. The photocouplings are in good agreement with the ones derived from single pion photoproduction. Analysis of CLAS 2.x data suggested considerable photoexcitation of possible 3/2+(1720) state at Q2=0 ( , / ~ = 0 . 1 3 2 & 0 . 0 3 0 GeV-lI’), clearly seen in the resonant part of cross-section (Fig 3). However, the huge background and a destructive resonance-background interference mask the resonance signal of the possible new state in the total cross-section. We performed a combined fit of the real and virtual photon data, testing various spin-parity assignment for the new state. Minimal x2 per data points was obtained for spin-parity 3/2’, confirming the quantum numbers, derived in the previous electroproduction analysis’. References 1. M. Ripani, V. D. Burkert, V. I. Mokeev, et. al. (CLAS Collaboration), Phys. Rev. Lett. 91, 022002 (2003). 2. M.Bellis, AIP Conf. Proc. 698, 535 (2004). 3. M. Ripani, V. Mokeev, et. al., Nucl. Phys. A672, 220 (2000). 4. V. D.Burkert, V. I. Mokeev, et. al., Phys. At. Nucl. 66, 2149 (2003). 5. V. D.Burkert, V. I. Mokeev, http://lpsc.in2p3.fr/congres/nstar2004/.
Double r oPhotoproduction and the Second Resonance Region M. KOTULLA, for the TAPS and A2 Collaborations Department of Physics and Astronomy, University of Basel, Klingenbergstr. 82, CH-4056 Basel (Switzerland), E-mail: Martin.
[email protected] The reaction 7 p + ao7rop has been measured using the TAPS BaF2 calorimeter at the tagged photon facility of the Mainz Microtron accelerator in the beam energy range from threshold up to 820 MeV. The 7r07ro channel is particularly suitable to investigate resonance properties due to the strong suppression of background terms. We present very accurate data and a preliminary partial wave analysis within an isobar model.
1. Introduction
Nucleon resonances are studied in a variety of experiments in an attempt to obtain information on the structure of the nucleon by identifying the effective degrees of freedom from comparison to baryon structure calculations. So far, most information has been gathered through TN scattering and photoproduction into single meson final states. A complementary access is the double meson production where the unique features of the 2 ~ 'channel - the strong suppression of the direct production (A Kroll-Rudermann, Born terms,. . . ) - open new prospects to improve the knowledge. Already for resonances above the A(1232) multiple meson production contribute significantly through decay chains of higher lying resonances into lower lying states. Previously, two measurements of the reaction yp -+ n'~'p were intensively studied in order to extract information on nucleon resonances. The MAMI results' were interpreted by the Valencia model2 and gave a strong indication for a dominance for the D13(1520)-+ AT. In a recent paper, the GRAAL collaboration reported on a measurement of the 2 ~ 'channel from 650 MeV up to 1500 MeV3. These data were interpreted by an extention of the Laget-Murphy model3. Despite the poor coverage of the P11(1440) resonance with the incident beam energy, the authors emphasized that the data could be only explained by a dominance of the P11(1440)-+ U N reaction process. We present and discuss new and very precise data with its preliminary interpretation by a partial wave analysis within the isobar model.
325
326 2. Experimental Setup and Data Analysis The reaction ~p + n 0 r o p was measured at the electron accelerator Mainz Microtron (MAMI)415using the Glasgow tagged photon f a ~ i l i t y and ~ ' ~ the photon spectrometer TAPS8>'. The photon energy covered the range 285-820 MeV with an average energy resolution of 2 MeV. The TAPS detector consisted of six blocks each with 62 hexagonally shaped BaF2 crystals arranged in an 8 x 8 matrix and a forward wall with 138 BaF2 crystals arranged in a 11x14 rectangle. The six blocks were located in a horizontal plane around the target at angles of f54', f103' and f153' with respect to the beam axis. Their distance to the target was 55 cm and the distance of the forward wall was 60 cm. This setup covered ~40% of the full solid angle. The liquid hydrogen target was 10 cm long with a diameter of 3 cm. Further details of the experimental setup can be found in ref. 10
The y p + TOTOP reaction channel was identified by measuring the 4-momenta of the two T O mesons, whereas the proton was not detected. The T O mesons were detected via their two photon decay channel and identified in a standard invariant mass analysis from the measured photon momenta. Events were selected, were both of the two photon invariant masses fulfilled simultaneously the following cut: 11OMeV < myy < 150MeV. Furthermore, the mass M X of a missing particle was calculated. In case of the reaction yp -+ r o ~ O pthe missing mass M X equal to the mass of the (undetected) proton m p confirmed the clean identification of this channel. Background originating from random time coincidences between the TAPS detector and the tagging spectrometer was subtracted in the usual way, using events outside the prompt time coincidence window7. The partial wave analysis is done within the acceptance and efficiency of the detector setup and the analysis cuts. A detailed GEANT simulation of the 27r0 channel in pure 3 body phase space kinematics including the whole detector setup and geometry as well as the analysis cuts is used as a reference. So far, the partial wave analysis includes in addition to the s-channel processes describing the production and decay of the resonances also the production of AT by t-channel pexchange. The angular dependence of the amplitudes has been calculated using the operator formalism11712and the resonances are presently introduced as BreitWigner resonances. To fit the amplitudes to the data an event based maximum likelihood fit has been performed. This method has one big advantage compared to fits performed only to total and differential cross sections: It takes all the correlations between the 5 different variables the p.rro.rro final state depends on properly into account. The information on the correlation gets lost if only differential cross sections are considered since they correspond to projections of the multi-dimensional phase space. 3. Preliminary Results The invariant mass distributions and the angular distributions of the TOP and the ToTosystems are shown in Fig. 1 for beam energies between 650 and 730 MeV. The data and the preliminary partial wave fits13 are shown within the acceptance of the detector system and agree very well. The invariant mass of the TOP system
327
Figure 1. Upper row: invariant mass distributions of the a o p and the aonosystems. Lower row: angular distributions of the a o p and the aoaosystems. The partial wave fit is shown by the solid line, the contributions of the D13(1520) and the Pii(1440) resonances by the dotted and dashed lines.
shows a pronounced signal of the A(1232) intermediate state. This is supported by the partial wave analysis and suggest a dominant contribution of the AT intermediate state in the production mechanism. The angular distributions show a large sensitivity to discriminate the Pll(l440) and the D13(1520) resonances and indicate a stronger contribution of the Dl~(1520)resonance. These observations are in contradiction to the claimed oN dominance in the Laget Model3 and in agreement with the Valencia model2. The final partial wave analysis will extract the properties of the contributing resonances. Especially the P11(1440) resonance is interesting, since its nature and properties are still not established. Acknowledgments
The presented data are part of the results of the experimental program of the TAPS and A2 collaborations. We thank the accelerator group of MAMI as well as many other scientists and technicians of the Institut fuer Kernphysik at the University of Mainz for the outstanding support. This work was supported by Schweizerischer Nationalfond, DFG Schwerpunktprogramm: "Untersuchung der hadronischen Struktur von Nukleonen und Kernen mit elektromagnetischen Sonden", SFB221, SFB443 and the UK Engineering and Physical Sciences Research
328 Council. References
Wolf, M., et al., Eur. Phys. J. A 9 (2000) 5-8 (2000). Tejedor, J. G., and Oset, E., Nucl. Phys. A, 600,413 (1996). Assafiri, Y., et al., Phys. Rev. Lett., 90,222001 (2003). Walcher, T., Prog. Part. Nucl. Phys., 24,189-203 (1990). Ahrens, J., et al., Nucl. Phys. News, 4, 5-15 (1994). Anthony, I., et al., Nucl. Instr. Meth., A 301,230-240 (1991). 7. Hall, S., et al., Nucl. Instr. Meth., A 368,698 (1996). 8. Novotny, R., IEEE Trans. Nucl. Sci., 38,379-385 (1991). 9. Gabler, A., et al., Nucl. Instr. Meth., A 346, 168-176 (1994). 10. Kotulla, M., Prog. Part. Nucl. Phys., 50/2,295-303 (2003). 11. Anisovich, A., et al., J. Phys. GI 28 (2002). 12. Anisovich, A., et al., in preparation (2004). 13. Thoma, U., priv. communication (2004).
1. 2. 3. 4. 5. 6.
N* Photoproduction from Nuclei S. SCHADMAND
II. Physikalisches Institut Justus-Liebig-Universitat Gieuen Heinrich-Bug-Ring 16 0-35392 Gieu en E-mail:
[email protected] Differences in the photoproduction of mesons on the free proton and on nuclei are expected to reveal changes in the properties of hadrons. Inclusive studies of nuclear photoabsorption and photofission have provided clear evidence of medium modifications. However, the results have not been explained in a model independent way. A deeper understanding of the situation is anticipated from a detailed experimental study of meson photoproduction from nuclei in exclusive reactions.
1. Introduction Photoabsorption on the free nucleon experiments demonstrate the complex structure of the nucleon and its excitation spectrum. For the first and second resonance regions, the observed resonance structures have been studied using their decay via light mesons, showing that the photoabsorption spectrum can be explained Fig. 1 shows the nuclear by the sum of T , T T and 7 production cross sections photoabsorption cross section per nucleon as an average over the nuclear systematics The A resonance is broadened and slightly shifted while the second and higher resonance regions seem to have disappeared. This evidence for modifications of hadron properties in the nuclear medium and has not yet been explained in a model independent way. An in-medium broadening of the D13(1520) resonance could arise from a coupling to the N p final state since the p-meson itself is expected to broaden in the nuclear medium lo. In another approach 11, the disappearance of the peak is modelled via a cooperative effect of the interference in double pion production processes, Fermi motion, collision broadening of the A and N * resonances, and pion distortion in the nuclear medium. A deeper understanding of the situation is anticipated from the experimental study of meson photoproduction from nucleons embedded in nuclei which can be related to the excitation of certain resonances or production mechanisms. Fig. 1 shows the status of the decomposition of nuclear photoabsorption into meson production channels. On the free proton, the photoproduction of 7-mesons in the second resonance region proceeds almost entirely through the excitation of the Sll(l535) resonance. An observation of the reaction over a series of nuclei 6,7 did not show a depletion of the in-medium strength. This result is in line with theoretical findings that
329
330
10
10
0.2
0.4
0.6
0.8
1
Figure 1. Status of the decomposition of nuclear photoabsorption into meson production channels (scaled with A a , a = 2 / 3 ) . Solid circles are the average nuclear photoabsorption cross section per nucleon (a=l) '. For reference, the elementary cross section The solid line is the is shown (dashed curve). Meson production data are from sum of the available meson cross sections between 400 and 800 MeV. 4,5,6377s.
the change of the S11 self energy in the medium is small. The data are in excellent agreement with model calculations that take the trivial in-medium effects and final state interactions into account l 4 , I 5 . A recent study l6 shows that the data could be described over the full energy range by applying a momentum dependent S11 potential. An attempt to study the in-medium properties of the D13 resonance was undertaken with a measurement of quasifree single 7ro photoproduction which, on the free nucleon, is almost exclusively sensitive to the D13 resonance. In contrast to total photoabsorption the second resonance bump remains visible. However , exclusive reaction channels are dominated by the nuclear surface region where in-medium effects are smaller. Furthermore, as discussed in 17, resonance broadening effects are even more diluted for reactions which do not contribute to the broadening, due to the averaging over the nuclear volume. 2. Double Pion Production
Fig. 2 shows preliminary cross sections for 7r07ro and 7r07r* photoproduction on calcium and lead from a recent TAPS analysis. The nuclear cross sections are divided by A2f3 and compared to results from the free proton and from nucleons bound in deuterons. With the scaling with A2f3, the nuclear data agree almost exactly with the cross sections on the nucleons. Thus, the total nuclear i v r cross sections do not seem to show any modification beyond absorption effects. It may be speculated that the strong 27r decay branch via A intermediate states (N" + AT -+ Nw7r), together with the fact that the A resonance itself does not dramatically change in medium, dominate this behavior. Also, in the reaction TOT*, the two pions can stem from the decay of the p meson while the decay p -+ 7r07ro is forbidden. Accordingly, detailed studies of differential cross sections might
331 h
-2
60
'
40
(y,lPx+'-)
.
""Pb
20
0.3
0.4
0.5
0.6
0.7
0.8
E,(GeV)
0
0.3
0.4
0.5
0.6
0.7
0.8
E,(GeV)
Figure 2. Preliminary total cross sections for AT photoproduction from lead along with results from the deuteron 1 8 , 1 9 . The nuclear cross sections are divided by A2I3, the T O T O deuteron cross section by 2. reveal different modifications of the m r correlations. This work is underway 20. A first result came from the investigation of m r invariant mass distributions in the incident photon energy range of 400-460 MeV 21 providing indication of an effect consistent with a significant in-medium modification in the A(y, n o r o )(I=J=O) channel. Conclusions
The systematic study of the total production cross sections for single T O , q, and m r cross sections over a series of nuclei has not provided an obvious hint for a depletion of resonance yield. The observed reduction and change of shape in the second resonance region are mostly as expected from absorption effects, Fermi smearing and Pauli blocking, and collisional broadening. The solid line in Fig. 1 is the sum of the available meson cross sections between 400 and 800 MeV demonstrating the persistence of the second resonance bump when at least one neutral meson is observed. Here, it would be desirable to complete the picture by investigating single charged pion as well as 7r+.rr- production from nuclei. It has to be concluded that the medium modifications leading to the depletion of cross section in nuclear photoabsorption are a subtle interplay of effects. Their investigation and the rigorous comparison to theoretical models requires a detailed study of differential cross sections and a deeper understanding of meson production in the nuclear medium. Acknowledgments
This work was supported by Deutsche Forschungsgemeinschaft, the U.K. Engineering and Physical Sciences Research Council, and Schweizerischer Nationalfond. References
1. S. Schadmand, proceedings NSTARO2.
332 2. V. Muccifora, et al., Phys. Rev. C60 (1999) 064616. 3. D. E. Groom, et al., Review of particle physics, Eur. Phys. J. C15 (2000) 1-878. 4. J. Arends, et al., Z. Phys. A305 (1982) 205. 5. B. Krusche, et al., Phys. Rev. Lett. 86 (2001) 4764-4767. 6. M. Roebig-Landau, et al., Phys. Lett. B373 (1996) 45-50. 7. H. Yamazaki, et al., Nucl. Phys. A670 (2000) 202-205. 8. S. Janssen, PhD thesis, University of Giessen (2002) and to be published. 9. U. Mosel, Prog. Part. Nucl. Phys. 42 (1999) 163-176. 10. F. Klingl, N. Kaiser, W. Weise, Nucl. Phys. A624 (1997) 527-563. 11. M. Hirata, N. Katagiri, K. Ochi, T. Takaki, Phys. Rev. C66 (2002) 014612. 12. M. Post, S. Leupold, U. Mosel, nucl-th/0309085. 13. T. Inoue, E. Oset, Nucl. Phys. A710 (2002) 354-370. 14. M. Effenberger, A. Hombach, S. Teis, U. Mosel, Nucl. Phys. A614 (1997) 501-520. 15. R. C. Carrasco, Phys. Rev. C48 (1993) 2333-2339. 16. J. Lehr, M. Post, U. Mosel, Phys. Rev. C68 (2003) 044601. 17. J. Lehr, U. Mosel, Phys. Rev. C64 (2001) 042202. 18. V. Kleber, et al., Eur. Phys. J. A9 (2000) 1-4. 19. A. Zabrodin, et al., Phys. Rev. C55 (1997) 1617-1620. 20. S. Schadmand, Letter of Intent to the PAC ELSA/5-2003. 21. J. G. Messchendorp, et al., Phys. Rev. Lett. 89 (2002) 222302.
Multi Resonance Contribution to the Eta Production in Proton-Proton Scattering S. CECI, A. SVARC and B. ZAUNER
RuV e r Boikovic'
Institute, Bijenitka c. 54, 10 000 Zagreb, Croatia E-mail:
[email protected]
Two body scattering amplitudes, obtained in the unitary, coupled channel model, have been used in the few-body analysis. The simplest two-body process that can be completely determined using the two-body amplitudes is p p + p p 9 . It has been shown that the experimental data far from threshold are well described using S-waves only. The choice of final state interaction model is vital, especially for the pp subsystem. We apply the factorization approximation for the three body final state interaction and use the two body Jost functions in the low energy effective range approximation. Contrary to recent models which demand a strong contribution from rho meson exchange, it has been shown that the destructive interference between pi and eta depicts the data quite well.
1. Introduction T h e 71 production in proton-proton scattering is a process which can b e described in a meson-exchange formalism via N* resonance excitation. W i t h t h e completion
Pl
Pt
P2
Figure 1. The ingredients of the model. IS1 and FSI represent the initial and final state interactions. V , is the Bonn vertex, while the E,, is the 11 production amplitude.
of new m e a ~ ~ r e m e n t ~t h e~ experimental ~ ~ , ~ ~ ~situation , ~ ~ ~is~improving. ~ ~ * Most
333
334 of the recent theoretical models9'10,11,12113,14,15 consider excitation of only one, the first SllN(1535) resonance, and one model constructs amplitudes using the additional single-resonance partial-waves16. In ref.17 we have calculated two body partial-wave amplitudes for T N and gN channels which include more then one resonance in the g production vertex, and have used them to calculate the p p -+ p p q processlg. The transition from the multi-resonance amplitude to the singleresonance model, what we need in order to compare our approach with previous models, is not a straightforward procedure, and can be simulated by setting the proper model parameters to zero. I
10
Irn
Ima
Figure 2. The total cross section. In addition to the S-wave, P and D waves are as well used in xN + qN amplitudes.
The ingredients of the model are depicted in Figure 1. The model is in full details explained in our recent publication". Let us just give a general outlay: we have used the Bonn-potential parameters in proton-proton-meson vertex, our two-body amplitudes17 in g-emission vertex and have estimated the final state interaction by using the s-wave Jost function in the multiplicative approximation21. We had to extrapolate our amplitudes in energy in order to reach the last three data points in Fig 2. and Fig 3. in order to bridge the existing gap in experimental data. 2. Results
We present the results of our calculation in Fig 2. We show model D where the full final state interaction18721is included (proton-proton, as well as eta-proton FSI). As shown in Fig 2. our model describes data fairly well. The inclusion of higher partial-waves in two-body amplitudes improves the cross section at higher energies. The contribution of the S11 N(1535) resonance is up to now reported to be dominant. We estimate its importance within the framework of our model by simulating the exclusion of all other S-wave resonances in the aforementioned way, and then adding other S-wave resonances one by one. Results are shown in Fig.
335 I
d
IM
10
1 0
. A
lhlb
I
lax,
CW(NMu(A[II
s m 3 121 P l N M 131
ia
IM
iaa
Q [MeV
Figure 3. The total p p t p p q cross section when individual Sll wave resonances are consecutively added to form the q-production amplitude. The resonance nomenclature is taken over from PDG.
3. As can easily be seen, the single resonance contribution fails to reproduce the shape of the total cross section. Only upon the addition of higher S11 resonances] N(1650) and N(2090), the agreement in shape between the model and experiment is obtained. Let us mention that the N(2090) resonance improves the result not by causing the change of shape, but only by the shift of overall normalization scale. 3. Conclusions
Partial-waves higher then S11 are not needed to describe the p p -+ p p q process at lower energies. However, the S11 resonances heavier then 1535 MeV must be included into the model in order to obtain the shape and size of the low-energy experimental cross section. The final state interaction effects play important role in the model. Additional experimental data for excess energies in the range from 30 MeV to 300 MeV would be greatly appreciated. References 1. E. Flamino et al., CERN-HERA Report 84-01. 2. A. M. Bergdolt et al, Phys. Rev. D 48 (1993) R2969; F. Hibou et al., Phys. Lett. B 438 (1998) 41. 3. E. Chivassa et al., Phys. Lett. B 232 (1994) 270. 4. H. C a l h et al., Phys. Lett. B 365 (1996) 39; H. CalCn et all Uppsala University preprint TSL/ISV-95-0124 . 5. H. Calen et al., Phys. Rev. C 58 (1998) 2667. 6. H. Calen et al., Phys. Lett. B 458 (1999) 190. 7. J. Smyrski et al., Phys. Lett. B 474 (2000) 182. 8. P. Moskal, et al., nucl-ex/0307005. 9. J. F. Germond and C. Wilkin, Nucl. Phys. A 518 (1990) 308. 10. J. M. Laget and F. Wellers, Phys. Lett. B 257 (1991) 254.
336 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
T. Vetter et al, Phys. Lett. B 263 (1991) 153. C. Wilkin, Phys.Rev. C 47 (1993) R938. G. Faeldt et al., Nucl. Phys. A 604 (1996) 441. A. B. Santra and B. K. Jain, Nucl. Phys. A 634 (1998) 309. E. Gedalin, A. Moalem and L. Razdolskaja, Nucl. Phys. A 634 (1998) 368. K. Nakayama et al., Phys. Rev. C 68 (2003) 045201. M. BatiniC, et al., Phys. Rev. C 51 (1995) 2310; M. BatiniC, e t al., Physica Scripta 58 (1998) 15. S. Ceci, A. Svarc, and B. Zauner, nucl-th/0402040. M. BatiniC, A. Svarc and T.-S. H. Lee, Physica Scripta 56 (1997) 321. R. Machleidt, Adu. Nucl. Phys. 19,(1989) 189. M. L. Goldberger and K. M. Watson: Collision Theory, John Wiley & Sons, Inc. (1964).
Nucleon Resonances and Processes Involving Strange Particles S. CECI, A. SVARC and B. ZAUNER Rudjer BoSkoviC Institute, BzjeniEka c. 54, 10 000 Zagreb, Croatia E-mail:
[email protected] An existing single resonance model with S l l , P11 and P13 Breit-Wiegner resonances in the s-channel has been re-applied to the old .rrN 4 KA data. It has been shown that the standard set of resonant parameters fails to reproduce the shape of the differential cross section. The resonance parameter determination has been repeated retaining the most recent knowledge about the nucleon resonances. The extracted set of parameters has confirmed the need for the strong contribution of a Pll(1710) resonance. The need for any significant contribution of the P13 resonance has been eliminated. Assuming that the Baker. et a1 data set' is a most reliable one, the P11 resonance can not but be quite narrow. It emerges as a good candidate for the non-strange counter partner of the established pentaquark anti-decuplet .
In spite of t h e fact that t h e experimental d a t a for t h e process TN -+ KA, which show a distinct peeking around t h e energy range of 1700 MeV, are available for quite some timeli2 the existence of a P11(1710) resonance in t h a t energy range is not generally accepted, but even questioned However, all coupled channel models5 do accept the P l l ( l 7 1 0 ) state as a legal and needed state, and t h e general agreement is t h a t it is strongly inelastic. The confirmation and the additional proof for t h e existence of t h e Pll(1710) resonance turned out t o b e critically needed quite recently in light of reported observations of exotic pentaquark O(1539) and E(1862) states6, as the mentioned state turns out t o belong quite naturally into t h e pentaquark anti-decuplet configuration predicted by recent chiral soliton7 and q44 strong color-spin correlated' models. Keeping in mind t h e accumulated knowledge about nucleon resonances5 we have applied t h e existing, single resonance model of .rrN -+ KA processg t o t h e existing d a t a set2, and allowed for t h e explicit presence of a narrow P11 resonance. The single resonance model calculation has been repeated using t h e standard set of parameters for t h e S11(1650), Pll(1710) and P13(1720) resonances of ref.4, and they are given in Table 1 denoted as "PDG". As it is shown in Figs.1 and 2. (thin solid line) that choice of parameters reproduces only t h e absolute value of t h e total cross section quite well, and manages t o reproduce the shape of t h e angular distribution only at w=1683 MeV. It fails miserably in reproducing t h e
337
338 shape of the differential cross section at other energies. To eliminate the problem we have fitted the KA branching ratios in the Breit-Wigner parameterization of the afore discussed resonances to the available experimental data set, enforcing a good description of the absolute value of the total cross section simultaneously keeping the shape of the differential cross sections of the r N -+KA process linear in cos(8) (indicated by experimental data of ref.'). The following resonance parameter extraction method has been applied: we have started with the belief that when a set of resonance parameters (masses, widths and branching fractions) is once established in any analysis using channels other then K A channel, the only parameter which we are allowed to vary is a branching fraction to K A channel, while everything else (masses, widths, branching fractions to other channels) can not be changed. Hence, as starting values we have used the resonant parameters for the ,911, P11 and Pi3 resonances obtained in the coupled channel analysis of r-nucleon scattering based on the r-elastic and r N -+ 77 N channels2. The only parameter which was allowed to vary was the branching fraction to the K A channel. Table 1.
Resonance parameters for the single resonance model.
M s11
PDG
r[MeV]
4 1
p13
1650 1710 1720
sll
pl1 p 1 3
150 100 150
XTN s11
[%I
4 1
p13
XKA[%o] sll p l 1 p 1 3
70 15 15
7 15 6.5
Sol 1
1652 1713 1720
202 180 244
79 22 18
2.4 23 0.16
Sol 2
1652 1713 1720
202 180 244
79 22 18
2.4 35 0.16
Sol 3
1652 1700 1720
202 60 244
79 22 18
4 30 0.16
~~
~
The three solutions for the choice of resonant parameters are obtained, nd axe together with the "standard" (PDG) solution given in Table 1. The agreement with the experimental data is given in Figs. 1. and 2. In extracting new resonance parameters we have kept in mind that the overall data set',' is mutually inconsistent. In addition, as the latest measured set of data' shows a surprisingly narrow width when compared to the overall trend, we have treated it separately with special care. We fit the "lower" and "upper" band of the total cross section imposing the correct angular dependence at the same time, and obtain Sol 1 (dotted line) and Sol 2 (dashed line). To obtain the Sol 3 (thick solid line) we fit only Baker et a1 data'. "Standard" (PDG) solution introduces "too much curvature" in the differential cross section throughout the whole energy range indicating too big P-waves contribution relative to the S-wave. If the shape of the angular dependence is to be reproduced, contrary to the standard belief6>4,the contribution of Pi3 partial wave is negligible for all obtained solutions. The branching ratio of Sll resonance to K A channel is somewhat smaller then previously believed. The branching ratio of P11 resonance to K A channel is significantly bigger. If the latest Baker et a1 data' are t o be taken very seriously the best agreement with the experi-
339 Total crosssection 1000
T
750 B
x
u
b
500
250
1600
1650
1700
1750
1800
1850
1900
wo,WV) Figure 1. The agreement of the available experimenta1 data for the total cross section (ref.’ (full boxes); ref.2-open boxes) with the single resonance model predictions using different inputs for the resonance parameters: ”standard” (PDG) set (thin solid line); Sol 1 (dotted line); Sol 2 (dashed line) and Sol 3 (thick solid line).
ment is obtained for very narrow P11 resonance, not observed in other processes and strongly inelastic - Sol 3; hence a candidate for a non-strange pentaquark counter-partner. The re-measuring of the differential cross section for the TN + K h process in the energy range 1600 MeV < w < 1800 MeV is badly needed. The decisive conclusion about the existence of the 4 1 non-strange pentaquark counter-partner will be possible only when the improved set of data is fully incorporated in one of the existing coupled channel partial wave analyses5. References
R.D. Baker et. al., Nucl. Phys. B141, 29 (1978). Landolt-Bornstein, New Series, ed. H. Schopper, 8 (1973). R.A. Arndt, J.M. Ford and L.D. Roper, Phys. Rev. D32, 1085 (1985). R. A. Arndt et. al., Phys. Rev. C69, 035213 (2004). R.E. Cutkosky, C.P. Forsyth, R.E. Hendrick and R.L. Kelly, Phys. Rev. D20, 2839 (1979); M. BatiniC, I. Slaus, A. Svarc and B.M.K. Nefkens, Phys. Rev C51, 2310 (1995); T.P. Vrana, S.A. Dytman and T.S.-H- Lee, Phys. Rep. 328, 181 (2000). 6. T. Nakano et al., Phys. Rev. Lett. 91, 012002 (2003); : NA49 Collaboration, Phys.Rev.Lett. 92, 042003 (2004). 7. D. Diakonov, V. Petrov and M. Polyakov, 2. Physik A359, 305 (1997). 8. R. Jaf€e and F. Wilczek, Phys. Rev. Lett. 91, 232003 (2003).
1. 2. 3. 4. 5.
340 2oo,
~ 4 6 9 MeV 4
200,
I
,
2001
,
100,
100,
,
w=1721MeV
I
/I
cowl
to$@
w=1792MeV
w46pMeV
,
- 4 8 2 5 MeV
Figure 2. The agreement of the available experimental data for the differential cross section' (full boxes) with the single resonance model predictions using different inputs for the resonance parameters: "standard" (PDG) set (thin solid line); Sol 1 (dotted line); Sol 2 (dashed line) and Sol 3 (thick solid line).
9. K. Tsushima, A. Sibirtsev a n d A.W. Thomas, Phys.Rev. C 6 2 , 064904 (2000). 10. K. Hagiwara et.al., Phys. Rev. D66, 010001 (2002.) 11. M. BatiniC, I. Dadie, I. Slaus, A. Svarc, B.M.K. Nefkens and T.S.-H. Lee, Physzca Scrzpta 58, 15 (1998)
Multichannel X N Scattering and Hyperon Resonances D. M. MANLEY and J. TULPAN K e n t State University, Department of Physics and Center for Nuclear Research, K e n t , OH 44242, USA E-mail:
[email protected] The resonance parameters of the established A and C hyperons were determined almost entirely from energy-dependent partial-wave analyses of EN scattering data. Some of these analyses attempted to obtain a consistent set of parameters for reactions involving different final states ( K N , r A , rC),but unitarity was not enforced and various features (e.g., backgrounds) were not treated consistently. This work presents some preliminary results from a new unitary, multichannel description of several I ( N reactions.
1. Introduction
Our current knowledge of the properties of strangeness -1 hyperon resonances is derived almost entirely from energy-dependent partial-wave analyses of K N scattering data. In a typical such analysis (for example, see that of Gopal et al.'), the pure isospin partial-wave T-matrix amplitudes were parametrized as T = TB TR, where TB is a background term and TR is a sum of Breit-Wigner resonance terms. Such a parametrization is inconsistent with the requirement that the corresponding S-matrix be unitary. Now that precise K - p + neutrals data are beginning to be published by the Crystal Ball C o l l a b ~ r a t i o n it , ~is~ timely to take a fresh look at the strangeness -1 hyperons. One of the authors (DMM) has developed a new, unitary, multichannel parametrization. This parametrization was initially developed to extract resonance parameters from 7rN amplitudes, but has now been modified t o describe K N scattering. The general form of the partial-wave S-matrix is
+
S = BTRB = I
+ 2iT,
(1)
where T is the corresponding partial-wave T-matrix. Here R is a generalized Breit-Wigner matrix. The matrix R is constructed t o be both unitary and symmetric (in order to satisfy time-reveral invariance). Deviations from the Breit-Wigner form are ascribed t o background terms, which are parametrized through the unitary matrix B and its transpose BT. A major feature of the new parametrization concerns how R is constructed. This is accomplished by defining a resonant K-matrix such that
R = K ( I - iK1-l .
341
(2)
342 The K-matrix has elements of the form N ff=l
where the index a denotes a particular resonance and N is the number of resonances in the energy range of the fit. The energy dependence of the phases Sa is determined in a nontrivial and novel way to facilitate the determination of the pole positions in the S-matrix. The immediate goal of the present work is to obtain a consistent set of “unitarized amplitudes” and to determine the corresponding resonance parameters. The longer-term goal is to perform a new partial-wave analysis of the world data set for ZN reactions] including the precise new data measured by the Crystal Ball Collaboration at Brookhaven National Laboratory’s Alternating Gradient Synchrotron. 2. Results and Summary
A multichannel fit has been performed using the published partial-wave amplitudes for several different reactions (see Table 1). Our fits also include the channels qA and qC for the Sol and S11 waves, respectively. To absorb flux as mandated by the unitarity requirement, we also sometimes include quasi-twor body channels] a A and axl where here a denotes the broad isoscalar, S-wave m interaction. In the following, we show two examples of the observables that can be calculated with the unitarized partial-wave amplitudes. Figures 1 and 2 are differential cross sections for the reactions K - p + K - p and K - p + r0A, respectively, at approximately the same beam momentum. The curves are the predictions based on our unitarized partial-wave amplitudes. In both cases, the agreement with the data is quite good. In the case of K - p + T’A, it should be noticed that the uncertainties in the experimental data are relatively large compared to those for elastic scattering. Since much of the older data base come from bubble-chamber experiments] which are best suited for charged-particle final states, one typically finds somewhat large uncertainties in old measurements of reactions such Table 1. Reactions and amplitudes included in the present analysis. Reaction -
KN KN KN
Document ID
CM Energy Range (MeV)
--f
EN
GOPAL 77
Ref. [l]
1480-2170
--f
nA
GOPAL 77
Ref. [l]
1480-2170
GOPAL 77 CAMERON 78
1770-2170
+ .irC --f
nA(1520)
CAMERON 77
Ref. [l] Ref. [6] Ref. [7]
--f
KIN
CAMERON 78B
Ref. [8]
1830-2170
K N -+ FA
LITCHFIELD 74
Ref. [9]
1930-2150
-
K N -+ sC(1385)
-
KN KN -
1480-2170 1710-2 170
343 4
as K - p + K n and K - p -+ .rr°Co, which have final states involving neutral particles. Reactions with all-neutral final states are exactly those which were measured with high statistics using the Crystal Ball multiphoton spectrometer, albeit over a rather narrow momentum range that extended up to -750 MeV/c. We have found that our unitarized amplitudes agree well with most of the older existing data; however, our predictions disagree significantly with the precise new differential cross-section and polarization measurements made by the Crystal Ball Collaboration. Since A* and C* resonance parameters can be determined from the partial-wave amplitudes, it is important that they be redetermined by a new partial-wave analysis which incorporates the Crystal Ball data. We plan to perform such an analysis. Our unitarized amplitudes can be used to predict observables not only for two-body reactions but also for several reactions of the type FN -+ 7rFN; however, we have no plan to include reactions with three-body
. h
ti
0.0' " -1.0
"
I '
-0.5
' ' "
0.0
cos e
"
"
I '
0.5
"
"
1.0
Figure 1. Differential cross section for K - p --f K - p at lab momentum 935 MeV/c. The curve is from the unitarized partial-wave amplitudes discussed in the text, and the d at a are from Albrow et aZ.'O
0.0 " " ~ " " ~ ' " ' ~ " " -1.0 -0.5 0.0 0.5 cos 0
1.0
Figure 2. Differential cross section for K - p + n O A at lab momentum 936 MeV/c. The curve is from the unitarized partial-wave amplitudes discussed in the text, and the data are from Jones et al."
Acknowledgments
This work is supported in part by the U.S. Department of Energy under Contract DE-FG02-01ER41194. The data shown in the figures are from a compilation
344
prepared by Hongyu Zhang. References
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
G. P. Gopal et al., Nucl. Phys. B119, 362 (1977). A. Starostin et al., Phys. Rev. C 64, 055205 (2001). M. Borgh et al., Phys. Rev. C 68,015206 (2003). J. Olmsted et al., Phys. Lett. B588, 29 (2004). S. Prakhov et al., Phys. Rev. C 69 042202 (2004). W. Cameron et al., Nucl. Phys. B143, 189 (1978). W. Cameron et al., Nucl. Phys. B131, 399 (1977). W. Cameron et al., Nucl. Phys. B146, 327 (1978). P. J. Litchfield et al., Nucl. Phys. B74, 39 (1974). M. G. Albrow et al., Nucl. Phys. B21, 413 (1971). M. Jones et al., Nucl. Phys. B90, 349 (1975).
New Evidence for the Breathing Mode of the Nucleon
from High Energy Proton-Proton Scattering HANS-PETER MORSCH Institut fur Kernphysik, Forschungszentrum Julich, 0-52425 Julich, Germany E-mail;
[email protected] PAWEL ZUPRANSKI Soltan Institute for Nuclear Studies, P1-00681 Warsaw, Poland E-mail:
[email protected] A reanalysis of inelastic proton spectra at beam energies between 6 and 30 GeV/c confirms the evidence for a strong monopole excitation at a m a s of -1400 MeV (Saturne resonance) covering a large fraction of the scalar energy weighted sum rule. Data on p + p t p p n+x- support the prediction of a large 27rN decay branch of this P11 resonance.
1. Introduction The lowest N*, a P11 resonance at about 1400 MeV (called Roper resonance in 7r-N) is both experimentally and theoretically not well understood. In the present talk the following aspects are discussed: - Theoretical studies of the lowest P11 resonance. - Saturne experiment on a - p scattering. - What is the structure of the Roper resonance? - New analysis of p-p scattering at beam momenta 5-30 GeV/c. 2 . Theoretical studies of the lowest Pi1 resonance
The spectrum of baryon resonances shows directly the dynamical structure of quantum chromodynamics, however, the origin of these resonances is so far not well understood. In particular, the lowest N* resonance, P11 at a mass of about 1400 MeV, has been discussed controversially in many different models. In the non-relativistic constituent quark model' glum exchange yields a mass of the lowest P11 , which is much larger than found experimentally. The assumption of pion exchange' gives rise to a lowering of the P11, in much better agreement with experiment. In the relativistic constituent quark model3 the lowest P11 is quite well described. A monopole mode has been described in the bag model by an oscillation of the bag4. In the Skyrmion model5 the P11 is naturally the lowest N* excitation, similar t o algebraic models describing N* resonances by flat top'.
345
346 The lowest P11 has also been discussed in terms of a hybrid structure' or being generated dynamically by a strong u-N coupling'. Finally this resonance has been studied in recent lattice QCD calculationsg, which are not yet conclusive. 3. Saturne experiment on a - p scattering
In the study of N* production in a - p scattering" a strong monopole excitation has been found in the region of the P11(1440) resonance (Fig. 1). Detailed studies of the differential cross sections show", that this excitation exhausts a
30000
,
25000
20000
9
$
15000
J
10000
5000
n
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
w (GeV)
Figure 1. Energy transfer spectrum of a-p scattering from ref.lO. The lower solid line indicates the estimated collimator background, the dashed line the contribution due to projectile excitation, and the dot-dashed line a P11 excitation at a mass of about 1400 MeV.
large fraction of the energy weighted monopole sum rule, which allows to extract information on the nucleon compressibility12. 4. What is the structure of the Roper resonance?
-
- -
In a comparison of a - p and x-N scattering the shape of the P11 observed in ap (m, 1400MeV,I' 200MeV) was quite different from that of the Roper 1440MeV,r 300 - 350MeV). In a T-matrix resonance seen in n-N ( m , description the different results could be understood con~istently'~ by assuming two structures in the Roper resonance, a radial or breathing mode observed in a-p (Saturne resonance), and a second structure, which was interpreted by a second
-
347 order excitation of the A(1232). With real photons the radial mode should not be excited. Indeed, in photo-induced reactions only the second structure is observed, see Fig. 2.
14
1.1
1.2
1.3
1.4
1.5
1.6
7
moss (GeV)
Figure 2. Cross sections of the reaction y + p -+ 27r0 p in comparison with our calculations of the two P11 components. Whereas the data are consistent with excitation of the 2. resonance, the first resonance (breathing mode) is not observed.
5. Analysis of p-p scattering at beam momenta 5-30 GeV/c
To study further N* excitations we analysed old p-p scattering d a t a l 4 ~ l 5In . these data several structures have been observed, the A(1232) and resonances at about 1400 MeV, 1520 MeV, 1680 MeV and 2190 MeV. It is important to mention, that in these data taken at many different momentum transfers evidence just for these few resonances was found (in contrast to low energy n-N, in which many more resonances show up). This indicates a high selectivity in the excitation of N* resonances, which can be explained by the fact, that Pomeron-exchange (of scalar character) is the dominant part of the interaction. Spectra at different p-momenta together with our resonance fits are shown in Fig. 3. For the strongest resonance a centroid mass and width of mo = 1400 flOMeV and r = 200 f20MeV has been extracted. This is in excellent agreement with the results from a - p scattering. The t-dependence of the differential cross section of this resonance shows a much larger slope than for the other resonances. DWBA calculations show, that this indicates clearly L=O excitation of a scalar P11 resonance. The absolute cross
348 I
5 o k
p+p 9.9GeV/c
a 35
30 25
10
2
0
$
15 10
5
s o 0
1
2
1.1
1.2
1.3
11
1.5
1.6
1.7
1.8
1.9
2
1
45sc
30
......................
25
m 15
.................
10
5 0 1
1.1
1.2
1.3
1.4
l.5
1.6
1.7
1.8
1.9
2
missing moss (GeV)
Figure 3. Missing mass spectra of p S p + p 2 at different beam momenta in comparison with our resonance fits. The resonance at 1400 MeV is the strongest N* observed.
sections are consistent with the full energy weighted sum rule", again supporting the results from a-p. Information on the decay of the strong P11 resonance can be deduced also from high energy experiments. A study of 4 prong events of the reaction p p -+ ppn+nhas been made16 at a beam momentum of 6.6 GeV/c. In the invariant 7r+nmass spectrum, see Fig. 4, a strong rise of the yield has been observed above the 2nN threshold. We calculated the 7r+n- mass spectrum corresponding to the resonances observed in Fig. 3. We found, that the resonance at 1400 MeV gives rise t o a strong peak in the 7r'irspectrum, whereas the resonances at higher mass are smeared out. By taking into account correctly the multi-pion background, we obtain a good description of the spectrum with a 27r-N decay branch Bzrr of the scalar P11 at 1400 MeV of 753~20%.
349 9w
p+p + p p n* n-
am 700
6.6 GeV/c
-
n*n-invariant mass (GeV)
Figure 4. Invariant a+r- mass spectrum from ref.16 in comparison with a resonance fit consistent with Fig.3. The multi-pion background is given by the dotted line.
6. Summary
jFrom experiments on a - p scattering evidence for the breathing mode of the nucleon has been obtained, which is confirmed by the analysis of high energy p-p scattering data. This P11 resonance at 1400 MeV (Saturne resonance) has most remarkable properties: it is the strongest N*, which covers a large fraction of the scalar energy weighted sum rule. Further, it decays preferentially into the 2xN channel. At this workshop new data on the lowest P11 have been presented also from electromagnetic probes. New results on helicity amplitudes from Maim presented by H.J. Arends are consistent with our picture of two structures in the Roper resonance. Further, new data on the P11 excitation in (e,e’n) were presented from the CLAS collaboration by C. Smith. Detailed calculations have t o be performed to see, whether these data are consistent with our picture of the breathing mode.
350 References
1. N. Isgur and G. Karl, Phys. Rev. D 18, 4187 (1978); S. Capstick and N. Isgur, Phys. Rev. D 34, 2809 (1986) 2. L.Y. Glozman and D.O. Riska, Phys. Rep. 268, 263 (1996) 3. B. Metsch et al., Eur. Phys. J. A 10, 395 (2001) 4. P.J. Mulders et al., Phys. Rev. D 27, 2708 (1983); P.A.M. Guichon, Phys. Lett. 164 B, 361 (1985) 5. C. Hajduk and B. Schwesinger, Phys. Lett. 140 B, 172 (1984); B. Schwesinger, Nucl. Phys. A 537, 253 (1992) 6. F. Iachello, Phys. Rev. Lett. 62,2440 (1989) 7. T. Barnes and F.E. Close, Phys. Lett. 125 B, 89 (1983); Z.P. Li, V. Burkert and Z. Li, Phys. Rev. D 46, 70 (1992) 8. 0. Krehl, et al., Phys. Rev. C 62, 025207 (2000) 9. W. Melnitchouk, et al., hep-lat/0202022 (2003); S.J. Dong, et al., hep-ph/0306199 (2003); and refs. therein 10. H.P. Morsch, et al., Phys. Rev. Lett. 69, 1336 (1992) 11. H.P. Morsch, W. Spang and P. Decowski, Z. Phys. A 348, 45 (1994); and Phys. Rev. C 67, 064001 (2003) 12. H.P. Morsch, Z. Phys. A 350, 61 (1994) 13. H.P. Morsch and P. Zupranski, Phys. Rev. C 61 (1999) 024002 14. E.W. Anderson, et al., Phys. Rev. Lett. 16, 855 (1966) 15. R.M. Edelstein, et al., Phys. Rev. D 5, 1073 (1972); 16. E. Colton, P.E. Schlein, E. Gellert, and G.A. Smith, Phys. Rev. D 3, 1063 (1971)
Generalized Sum Rules of the Nucleon in the Constituent Quark Model Universiti d i Genova and Sezione INFN d i Genova 16146 Genova, Italy E-mail: gorshtey @ge.infn.it Universitat Mainz, Institut fur Kernphysik 0-55099 Mainz, Germany We study the generalized sum rules and polarizabilities.ofthe nucleon in the framework of the hypercentral constituent quark model. We include in the calculation all the well known 3' and 4' resonances. The CQM calculations provide a good description of most of the presented generalized sum rules in the intermediate Q2 region (above 0.2 GeV2) while they encounter difficulties in describing these observables at low Q 2 , where the effects of the pion cloud, not included in the present calculation, are expected to be important.
-
1. Introduction The sum rules for real and virtual Compton scattering are constructed as energyweighted integrals over the various contributions to the inclusive cross section. For instance, the GDH sum rule relates the value of the anomalous magnetic moment of the nucleon IENt o an integral over the helicity difference cross section N N - u1/2 ( v ) l
+
with the pion photoproduction threshold vthr = m, m;/(Z&i"). This and the other sum rules serve as a powerful tool to study the nucleon structure by providing a bridge between the static properties of the nucleon (such as charge, mass, and magnetic moment) and the dynamical properties (eg., the transition amplitudes t o excited states) in a wide range of energy and momentum transfer Q 2 . For a general and complete consideration of the nucleon sum rules in the photoinduced reactions and their generalization to the case of the virtual photon probe, we readress the reader to the review '. Recently, precise measurements of the generalized sum rules and related observables have become available in a series of experiments 3 - 8 . Furthermore, the MAID model 1 4 , l5 yields a detailed analysis of the (mainly) single pion photo- and electroproduction channels in a wide energy and Q2 range. We study the generalized sum rules for the nucleon within a hyper central constituent quark model (HCQM) previously reported in ', ll. The model is
' ' ,
351
352
+
based on the lattice QCD inspired potential of the form V(z) = -$ px plus the standard hyperfine form part Vhyp, and allows for a consistent description of the baryonic spectrum with a minimal number of parameters. The electromagnetic transition helicity amplitudes are defined as A1/2,3/2 = -(el&) <
R; 1/2,3/21J+IN, ~ 1 / > 2 and Sl/2 = -(el&) < R, 1/21plN, 112 >, where 112, 3/2 stands for the spin projection of the initial (nucleon) and final (resonance) hadronic state, and the definition was used, J+ = -(Jz i J y ) / f i . For the relations of the generalized sum rules integrals to the helicity amplitudes within zero-width approximation we adress the reader to Ref.12.
+
2. Results
In this section we present some of our results for the generalized nucleon sum rules obtained with the following 14 resonances (3* and 4* in the PDG classification): &(1232), Pii(1440), Sii(1535), 013(1520)1 &i(1620), Sii(1650), 015(1675), F1:,(1680), pi1 (1710), 0 3 3 (17OO), Pi3(1720), 0 1 3 (17OO), &(1905), F37(1950). To test the dependence on the particular quark model, we also consider the harmonic oscillator type of the CQM 13. In Fig.1, we show our predictions for the purely transverse generalized GDH integral I T T ( Q ~on ) the neutron. The data
-1.2 -1.4 0
0.2
0.4
0.6
0.8
1
1.2
1.4
Q2 (GeV')
Figure 1. The CQM predictions for the GDH integral on the neutron, Z F T . The curves represent the results of HCQM (thick solid), HO (dashed-dotted), MAID (dashed). The shadowed areas correspond to the evaluation of the ZTT integral using the data on DIS structure functions with corresponding error bars. See text for further details.
points are from Refs. (solid squares) and with the nuclear corrections included (solid circles) l6 and without these corrections (open circles). The phenomenological parametrization (thin solid) was chosen so as to reproduce the sum rule value at the real photon point (solid star) (see, e.g., 2). As one evidences from Fig.1, the two quark models underestimate the strength in the low Q2 region. Since the effect of the negative parity resonances is nearly zero in the neutron case, the only significant deviation from the pure A( 1232) contribution comes from the Roper. Due to characteristic Gaussian form factors, the HO model is
353 able to reproduce the data only up to Q2 = 1 GeV2, but falls short of the data beyond this region. On the contrary, the HCQM prediction decreases significantly slower with increasing Q2, as compared to the HO model. However, for Q2 > 0.4 GeV2 it follows the phenomenological fit and is in very good agreement with the evaluation of the I& integral with the DIS data and the data point from Ref. gl(s, Q2)dz, Another generalization of the GDH sum rule integral is 1 1 = which contains also contribution from longitudinal photons. We next study the isovector combination of 11. For Q2 + co it is fixed by the Bjorken sum rule, r p - rn 1 - ( 9 ~ / 6 ) with , rl = gl(z, Q 2 ) d z ,while at Q2 = 0, it recovers the
sto
si
K:
-2
GDH sum rule, I r ( 0 ) - I,”(O) = p . In Fig.2, we compare our CQM results to the experimental data. The solid and open triangles from Ref. 4 , the solid and open circles represent the combined proton data from and neutron data from *, with only statistical errors shown. Unlike the MAID model with the one-pion contribution only, which in this case gives the wrong sign of the sum rule, the two CQM models predict the right sign of this sum rule but overestimate its value which however favors HCQM model. Clearly, the isovector integral is only sensitive to the N* resonances and not to the A resonances, which contribute equally for proton and neutron. At 0.5 GeV2 < Q2 < 1.2 GeV2, the HCQM model reproduces the “resonant” SLAC and JLab data nicely. (I: - I ; ) . Q’ / 2M2 0.25 0.2 0.15 0.1 0.05
0 0
0.5
1
1.5
Qz (GeVz)
0
1
2
3
Q2 (GeV’)
Figure 2. The isovector integral Zf - 1,. as calculated in the HCQM and HO models in comparison with the MAID results and the Bjorken sum rule. The sum rule value is given by the star at Q2 = 0. Further notation as in Fig. 1.
References 1. S. Gerasimov, Yad. Fiz. 2 (1965) 598 [Sov.J.Nucl.Phys.2 (1966) 4301, S.D. Drell and A.C. Hearn, Phys.Rev.Lett.16 (1966) 908.
354 2. D. Drechsel, B. Pasquini, M. Vanderhaeghen Phys. Rept. 378 99-205 (2003), and references therein. 3. J. Ahrens et al. (GDH and A2 Collaboration), Phys. Rev. Lett. 84 (2000) 5950. 4. K. Abe et al. (El43 Collaboration), Phys. Rev. D 58 (1998) 112003. 5. A. Airapetian et al. (HERMES Collaboration), Eur.Phys.J.C26 (2003) 527. 6. R. Fatemi et al. (CLAS collaboration), Phys.Rev.Lett.91 (2003) 222002. 7. M. Amarian et al. (JLab E94010 collaboration), Phys. Rev. Lett. 89 (2002) 242301. 8. M. Amarian et al. (JLab E94010 collaboration), Phys. Rev. Lett. 9 2 (2004) 022301. 9. M. Ferraris, M.M. Giannini, M. Pizzo, E. Santopinto, L. Tiator Phys.Lett. B364 231-238 (1995). 10. M. Aiello, M. Ferraris, M.M. Giannini, M. Pizzo, E. Santopinto Phys.Lett. B387 215-221 (1996). 11. M. Aiello, M.M. Giannini, E. Santopinto, J.Phys.G: Nucl.Part.Phys.24 753762 (1998). 12. M. Gorchtein, D. Drechsel, M.M. Giannini, E.Santopinto, L. Tiator hepph/0404053 (submitted to Phys.Rev.C). 13. N. Isgur and G. Karl, Phys. Rev. D 18 4187. 14. D. Drechsel, 0. Hanstein, S. Kamalov, L. Tiator, Nucl.Phys.A645 (1999) 145. 15. D. Drechsel, S.S. Kamalov, L. Tiator, Phys.Rev.D63 (2001) 114010. 16. C. Ciofi degli Atti and S. Scopetta, Phys.Lett.B404 (1997) 223.
Strong Decays of N and A Resonances in the Point-Form Formalism T. MELDE, W. PLESSAS, and R.F. WAGENBRUNN Institut fiir Physik, Theoretische Physik Universitat Graz, Universatatsplatz 5, A-8010 Graz, Austria E-mail: thomas.melde@una-graz We present covariant predictions of relativistic constituent quark models for 7r and 7 ) decay widths of N and A resonances. The results are calculated for a model decay operator within the point-form spectator approximation. It is found that most theoretical values underestimate the experimental data considerably.
1. I n t r o d u c t i o n It has long been of interest to describe strong decays of baryon resonances with realistic constituent quark models (CQM). Most of the modern calculations have investigated the effects of the dynamics of the underlying CQM, the nature of the decay operator (e.g., elementary emission vs. quark pair creation) or relativistic corrections ',213i4. In addition one has faced considerable uncertainties regarding the phase-space factor, since the transition amplitudes have not been derived in a relativistically invariant manner. Recently, we obtained direct predictions of a relativistic CQM from a PoincarB invariant calculation of baryon resonance decays in the pion channel '. The decay operator was based on the point-form spectator approximation (PFSA), itn approach that already proved successful in the description of the electroweak structure of the nucleons '. 2. Theory
Here, we study the 7r and 77 decays of N and A resonances in a relativistic approach. Specifically, the theory is formulated along PoincarB-invariant quantum mechanics 7 1 8 . We adhere to its point-form version, since it allows to calculate the observables in a manifestly covariant manner '. This approach, being distinct from a field-theoretic treatment, relies on a relativistically invariant mass operator with the interactions included according to the Bakamjian-Thomas conThereby it fulfils all symmetries required by special relativity. At struction this instance, we use a rather simplified model for the decay operator, because our first goal is to set up a fully relativistic CQM formulation of strong decays of baryon resonances. Baryons are simultaneous eigenstates of the mass operator 2 and the fourvelocity operator V (or equivalently of the four-momentum operator p p ) ,the
'.
355
356 total-angular-momentum operator j , and its z-component 2.We denote these states by the corresponding eigenvalues 121, M , J , C). The transition amplitude for the decays is defined in a Poincar6-invariant fashion, under overall momentum conservation (Mvin - M‘vout = QT), by
F (in -+out) = (vOutIM ’ , J‘, C’[ Da1qn,M , J , C)
I
( P i ,Pi!, $4;0; ,oh ,0; f i a
IPl 7 P 2 , P 3 ; ‘ T 1 1 0 2 > 0 3 ),
(1)
where the baryon wave functions !If*, and ,,, ~ P, M, J C enter as representations of the rest-frame baryon states ( M ’ , J’, C‘l and IM, J, C), respectively. In a first attempt, we assume a decay operator in the PFSA with a pseudovector coupling. In particular, the decay operator is given in the form
(Pi,Ph! Pi;U:,
[
0410; B a
IPl , P 2 , P 3 ; 0 1 , T 2 , 0 3 )
where gqT is the pion-quark coupling constant, X a the flavour operator for the particular decay channel, m the quark mass, and M as well as M’ are the masses of the decaying resonance and the final nucleon, respectively. It should be noted that in PFSA the impulse delivered to the quark that emits the pion is not equal to the impulse delivered to the baryon as a whole. Thus, the momentum transferred to the single quark is a fraction of the momentum QT transferred to the residual nucleon; it is determined uniquely by the overall momentum conservation and the two spectator conditions. 3. Results In table 1 we show the direct predictions for the decay widths in the pion channel for the Goldstone-Boson-Exchange (GBE) l 1 and the One-Gluon Exchange (OGE) CQMs calculated in PFSA. We also include corresponding results for the Instanton-Induced CQM (11) obtained in a Bethe-Salpeter approach 1 2 . It is clearly seen that all but one (the N;535)decay widths are considerably underestimated for all of these relativistic models. Furthermore there is a general trend in the results, namely, the larger the branching ratio into AT, the bigger the deviation of the theoretical results from the experimental data. This becomes apparent from the comparison in the last four columns of table 1, where we have quoted the AT branching ratios and expressed the theoretical predictions as percentage values relative to the experimental widths given by the PDG 1 3 .
357 In table 2 we show analogous predictions for the 7 decay channel. All but two decay widths are quite small, what is congruent with the experimental data. However, for the N:535 and N,*50 decays the relative magnitudes are opposite to the ones observed in experiments. In these cases there are also appreciable difference between the relativistic and nonrelativistic results. In summary the theoretical description of baryon resonance decays is by no means complete. In addition to the possible improvements expected from a more refined decay operator , it appears necessary to include explicit couplings between different channels. Furthermore, a more realistic description of the resonance wave functions beyond pure three-quark bound states seems to be required. This work was supported by the Austrian Science Fund (Project P16945). References
S. Capstick and W. Roberts, Phys. Rev. D 47,1994 (1993). P. Geiger and E. S. Swanson, Phys. Rev. D 50,6855 (1994). F. Stancu and P. Stassart, Phys. Rev. D 39, 343 (1989). L. Theussl, R. F. Wagenbrunn, B. Desplanques, and W. Plessas, Eur. Phys. J. A12,91 (2001). 5. T. Melde, W. Plessas, and R. F. Wagenbrunn, Few-Body Syst. Suppl. 14,37
1. 2. 3. 4.
(2003). 6. R. F. Wagenbrunn, S. Boffi, W. Klink, W. Plessas, and M. Radici, Phys. Lett. B511, 33 (2001); L. Y. Glozman, M. Radici, R. F. Wagenbrunn, S. Boffi, Table 1. Theoretical predictions for comparison to experimental data Decays
Experiment'
N?520
decay widths of various relativistic CQMs in
Rel. CQM
-+ ~ N 9 3 9 N;440
T
AT
GBE
OGE
I1
(227 f 18)fgi
30
37
38
(6656):
17
16
% of Exp. Width GBE
OGE
I1
20 - 30%
13
16
17
38
15 - 25%
26
25
58 49
w535
(67 f 15)+;8,
93
123
33
< 1%
130
180
N?650
(109 f 26)f36,
29
38
3
1 - 7%
26
35
3
N?675
(68 zt 8)'';
6
6
4
50 - 60%
9
9
6
N?700
(10f5)'
1
1
0.1
> 50%
9
12
1
4
2
nfa
15 - 40%
27
15
nfa
N;710
;
(15 f 5)z3;
;
A1232
(119zt 1)'
34
32
62
nla
28
27
52
A1600
(61 f 26):;
0.1
0.5
nla
40 - 70%
0
1
nla
A1620
(38418)'
10
15
4
30 - 60%
27
38
11
A 1700
(45 f 15)z::
3
3
2
30 - 60%
6
7
4
358 Table 2. Theoretical predictions for q decay widths of the GBE and OGE CQMs in comparison to experimental data and a nonrelativistic calculation in the elementary emission model (EEM). Decays
Experiment13
+ qN939 N;,,, T535
7. 8. 9. 10. 11. 12. 13.
(0.28 f 0.05)+:::: (64f19)f
N;650
(10f5)f
N;675
(0 f 1.5)+
N;700
(0 f l ) +
N;710
( 6 f 1)'
288 :!
'i
Rel. CQM Models
EEM GBE
GBE
OGE
dir
rec
0.04
0.03
0.03
0.05
36
46
0.06
155
72
95
0.9
288
0.8
0.8
0.8
1.6
0.4
0.4
0.2
0.4
1.0
1.4
0.1
2.2
W. Klink, and W. Plessas, Phys. Lett. B516, 183 (2001); S. Boffi, L. Y. Glozman, W. Klink, W. Plessas, M. Radici, and R. F. Wagenbrunn, Eur. Phys. J . A14, 17 (2001). P.A.M. Dirac, Rev. Mod. Phys. 21, 392 (1949). B. D. Keister and W. N. Polyzou, Adv. Nucl. Phys. 20, 225 (1991). W. H. Klink, Phys. Rev. C58, 3587 (1998). B. Bakamjian and L.H. Thomas, Phys. Rev. 92, 1300 (1953). L. Y. Glozman, W. Plessas, K. Varga, and R. F. Wagenbrunn, Phys. Rev. D 58,094030 (1998). B. Metsch, hep-ph/0403118 (2004). K. Hagiwara et al, Phys. Rev. D66, 010001 (2002).
Chiral Dynamics of the Two A(1405) States D. JIDO', J.A. OLLER2, E. OSET3, A. RAMOS4 AND U.-G. MEISSNER5 ECT" , Villa Tambosi, Strada delle Tabarelle 286, I-38050 Villazzano, Italy Departamento de Fisica, Universidad de Murcia, 30071 Murcia, Spain Departamento de Fisica Teo'rica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Aptd. 22085, 46071 Valencia, Spain Departament d'Estructura i Constituents de la Matkria, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain HISKP, University of Bonn, N w a l l e 14-16, 0-53115 Bonn, Germany
'
The A( 1405) resonance is studied by a chiral unitary approach, in which the resonance is dynamically generated in coupled-channel meson-baryon scattering. Investigating the analytic structure of the scattering amplitudes obtained by the chiral unitary approach, we find two poles around the energies of the A(1405) coupling differently to the meson-baryon states. We reach the conclusion that the A(1405) resonance seen in experiments is not just one single resonance, but a superposition of these two states.
The A(1405) resonance has been a long-standing example of a dynamically generated resonance appearing naturally in scattering theory with coupled mesonbaryon channels'. Modern chiral formulations of the meson-baryon interaction ~'~. within unitary frameworks all lead to the generation of this r e ~ o n a n c e ~ 'Yet, it was shown that in some models one could obtain two poles close to the nominal A(1405) resonance, as it was the case within the cloudy bag model5. Also, in the investigation of the poles of the scattering matrix within the context of chiral dynamics3, it was found that there were two poles close to the nominal A(1405) resonance both contributing to the TC invariant mass distribution. This was also the case in other works [6].In this paper, we summarize this important theoretical finding of the two pole structure of A(1405) based on Ref. 7. The A(1405) resonance here is described as a dynamically generated object in coupled-channel meson-baryon scattering with S = -1 and I = 0 within the chiral unitary approach'. Respecting the flavor SU(3) symmetry, we consider the octet mesons ( T , K , q) and the octet baryons ( N , A, C, E) in the scattering channels. The unitary condition is imposed by summing up a series of relevant diagrams non-perturbatively in a way guided by the well-established procedures in the 60's, such as the N/D method, which are generally expressed in complicated integral equations. The good advantage of our approach is to obtain an analytic solution of the scattering equation under a low energy approximation in which one takes only the s-channel unitarity and limits the model space of the unitary integral to one meson and one baryon states3. This is essential to study the
359
360 resonance structure in detail, since the resonance is expressed as a pole of the scattering amplitude in the second Riemann sheet. The details of the model are given in Refs. 3, 4. Table 1. Pole positions and couplings to Z = 0 physical states from Ref. 4. 1390 - 662
=R
Igil
9i TC
-2.5
1426 - 162
+ 1.52
2.9
Si 0 . 4 2 + 1.42
1680 - 202 Igil
Si
Igil
1.5
-0.003 +0.272
0.27
KN
1.2 - 1.72
2.1
-2.5-0.942
2.7
0.30 - 0 . 7 1 i
0.77
qh
0.01 -0.772
0.77
-1.4 -0.212
1.4
-1.1+0.12i
1.1
KZ
-0.45+0.412
0.61
0.11 +0.332
0.35
3.4 - 0.142
3.5
Shown in Table 1 are the positions of the poles in the second Riemann sheet of the scattering amplitude with S = -1 and I = 0 obtained by the chiral unitary approach4. The coupling strengths of the resonances to the meson-baryon states are also obtained as the residues of the amplitude at the pole position. We see that there are two poles around the energies of the R(1405) showing a different nature of the coupling strength: the lower resonance strongly couples to the T E state, while the higher pole dominantly couples to the E N state.
-
Rl+R2
i
6
4
\\.-.
2 1340
1360
1380
,E
1400
1420
[MeV1
1440
1460
1340
1360
1380
E,
1400
1420
1440
1460
[MeV]
Figure 1. The aC mass distributions calculated from the toy model in Eq. (1) for aC -+ aC (left panel) and Eq. (2) for K N + aC (right panel). The dashed, dotted and solid lines denote the contributions from the first term, the second term and the coherent sum of the two terms, respectively. The histogram in the left panel shows experimental datag. Units are arbitrary.
Let us see how these two poles appear in the physical observable using a toy model in which amplitudes are described by the sum of two Breit-Wigner formulae corresponding to two resonances, R1 and R2,such that:
361 where the resonance parameters have been taken from Table 1. The former amplitude corresponds to the process 7rC -+ .rrC and the later does to EN -+ 7rC. Shown in Fig. 1 is the modulus square of these two amplitudes multiplied by the 7rC momentum as a function of the energy. We also show the contribution of each resonance by itself (dotted and dashed lines). In both cases only one resonant x ~ in the left panel shape (solid line) is seen, but the simulated T n ~ + amplitude of Fig. 1 produces a resonance at a lower energy and with a larger width. This case reproduces very well the nominal experimental h(1405). However, if the invariant mass distribution of the 7rC states were dominated by the EN -+ 7rC amplitude, then the second resonance R2 would be weighted more, since it has a stronger coupling to the E N state, resulting into an apparent narrower resonance peaking at higher energies as shown in the right panel of Fig. 1. The existence of the two pole is strongly related to the flavor symmetry. The underlying SU(3) structure of the chiral Lagrangians implies that a singlet and two octets of dynamically generated resonances should appear, to which the h(1670) and the C(1620) would belong4, and that the two octets get degenerate in the case of exact SU(3) symmetry. In the physical limit, the SU(3) breaking resolves the degeneracy 1340 1360 1380 1400 1420 1440 1460 E,, [MeV1 of the octets, and, as a consequence, one of them appears quite close to the singlet pole Figure 2. The .rrC mass distributions around energies of the h(1405) resonance. with Z = 0 constructed from the .rrC + The double pole structure of h(1405) K C (dotted lile) and K N + .rrC (solid found here should be confirmed by new ex- line) amplitudes obtained by the chiperiments. Clearly a reaction which forces ral unitary approach. The histogram the initial channel to be K N produces a shows experimental datag. Units are different distribution with a narrower peak arbitrary. at higher energy than the original distribution observed in the 7rC -+ 7rC channel, since the former reaction gives more weight to the second resonance as shown in Fig. 2, where we show the .rrC mass distributions with I = 0 initiated by the 7rC (dotted line) and K N (solid line) states in the chiral unitary approach4. One problem here is that one cannot access the second resonance directly from the K N scattering, since the resonance lies below the threshold of the K N state. Therefore one has to lose energy of the K N state before the creation of the resonance. One possibility is to have the I? lose some energy by emitting a photon, as done in Ref. 10 in the study of the K - p -+ yA(1405) reaction. Another possibility is provided in Ref. 11, where the photo-induced K* production on proton has been discussed, and this process has been found suitable to isolate the second resonance. In conclusion, the chiral unitary approach suggests that two resonances are dynamically generated around energies of the nominal A(1405). Since they are located very close to each other, what one sees in experiments is a superposition
362 of these two states. The existence of the two poles can be found out by performing different experiments of the creation of the A(1405) initiated by the K N state. If one could confirm the double pole structure, it would be one of the strong indications that the structure of the h(1405) is largely dominated by a quasibound meson-baryon component. References
1. M. Jones, R.H. Dalitz and R.R. Horgan, Nucl. Phys. B129,45 (1977). 2. N. Kaiser, T. Waas and W. Weise, Nucl. Phys. A612, 297 (1997); U.-G. Meiuner, J.A. Oller, Phys. Rev. D 64, 014006 (2001); E. Oset and A. Ramos, Nucl. Phys. A 635,99 (1998). 3. J.A. Oller and U.-G. Meiuner, Phys. Lett. B 500,263 (2001). 4. E. Oset, A. Ramos and C. Bennhold, Phys. Lett. B 527, 99 (2002); B530, 260 (2002) (E). 5. P.J. Fink, G. He, R.H. Landau and J.W. Schnick, Phys. Rev. C41,2720 (1990). 6. D. Jido, A. Hosaka, J.C. Nacher, E. Oset and A. Ramos, Phys. Rev. C 66, 025203 (2002); C. Garcia-Recio, J. Nieves, E. Ruiz Arriola and M.J. Vicente Vacas, Phys. Rev. D67,076009 (2003). 7. D. Jido, J.A. Oller, E. Oset, A. Ramos and U.-G. Meiuner, Nucl. Phys. A 725,181 (2003). 8. A review of the chiral unitary approach for the baryon resonance is given in this proceedings by A. Ramos et al. 9. R.J. Hemingway, Nucl. Phys. B253,742 (1985). 10. J.C. Nacher, E. Oset, H. Toki and A. Ramos, Phys. Lett. B461, 299 (1999). 11. T. Hyodo, A. Hosaka, M.J. Vicente Vacas and E. Oset, nucl-th/0401051.
Baryon Form Factors in the Three Forms of Relativistic Kinematics” B. JuliA-Diaz, D. 0. Riska Helsinki Institute of Physics and Department of Physical Sciences POB 64, University of Helsinki, F I N 00014, Finland E-mail:
[email protected]
F. Coester Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA E-mail:
[email protected] The electromagnetic and axial form factors of the nucleon and its lowest positive parity excitations, the A(1232) and the N ( 1440), are calculated with constituentquark models that are specified by simple algebraic representations of the massoperator eigenstates. Instant and front form kinematics demand a spatially extended wave function, whereas in point form kinematics the form factors may be described with a quite compact wave function.
A calculation of baryon form factors requires consistent representations of the current-density operators and the baryon states. While kinematic current density operators are represented by functions of quark velocities and spinor indices, the baryon states are represented by, eigenfunctions of the m a s operator, which are functions of internal momenta, k i , and spin variables. The relation between the two representations depends on the “form of kinematics”, which specifies a There are mainly three forms of kinematic subgroup of the Poincar6 group kinematics that have been used in the literature: instant form, point form and front form. In order to explore the phenomenological applicability of the forms of kinematics with single quark kinematic currents we employ a simple spectral representation of the mass operator which is independent of quark masses, and consider the nucleon, the A(1232) and the N(1440). Generalization to other states is straightforward. A two-parameter family of algebraic functions is employed for the representation of the ground state, 4~ = (1 P2/4b2)-a, which allows variation of the range and the shape of the function. Using hyperspherical coordinates, the spatial wave function of the N(1440) baryon is constructed to be ‘12.
+
aThis work is partially supported by European Euridice network (HPRN-CT-200200311), the Academy of Finland through grant 54038 and by the U.S. Department of Energy, Nuclear Physics Division, contract W-31-109-ENG-38.
363
364
Figure 1. Magnetic form factor of the proton, left, and quotient ppGE,/GMp compared to the recent experimental data measured in TJNAF, Ref. 3. Solid, dotted and dashed lines correspond to the instant, point and front forms respectively.
-
orthogonal to the ground state with a single node. For a satisfactory description of the electric form factor of the neutron a small admixture of 1-2 % of a mixed symmetry S-state is included in the ground state wave function. These models have been described in detail in Ref. 2. The quark mass, mq, appears as a scale parameter in the kinematic quark currents. The parameters, a, b and mq are fixed for each form of kinematics so that the magnetic moment of the proton and also the high Q2 behavior of the magnetic form factor of the proton are reproduced. The values of the parameters are (mq[MeV],b[MeV],a): (350,640,9/4), (250,500,4) and (140,600,6) for point, front and instant form respectively. In Fig. 1 we show the result for the magnetic form factor of the proton (the corresponding value for the magnetic moment is listed in Table 1). It should be noted that the rms radius T O of the wave function is always smaller than the charge radius with the largest value for instant kinematics and the smallest for Lorentz kinematics. The results reveal that it is possible to reach agreement with the empirical data for the elastic electric and magnetic form factors of the proton and neutron '. The quotient ppGEp/Gn/lp,Fig. 1, is found to be sensitive to the form of Table 1. Values of the form factors at Q2 together with the proton charge radius.
GMp(0) G1l.ln(0) G A (0) . C P W
Instant
Point
Front
2.7
2.5
2.8
-1.8 1.1 0.89
-1.6
1.1 0.84
-1.7
+0
EXP 2.793 -1.913
1.2
1.2670
0.85
0.87
365
-loo 0 0.5 1
1.5 2 Q'(G~v')
2.5 3
Figure 2. Magnetic A -+ N transition form factor, left, and helicity amplitude for "(1440) electroexcitation. Solid, dotted and dashed lines correspond to the instant, point and front forms respectively. Experimental data are from Refs. 8 and Refs. 9 for the A and N(1440) respectively. The solid triangles corresponds to a preliminary analysis from CLAS lo. kinematics. Front form kinematics produces a cancellation in Ge := F1 - qF2 at about 6 Gel''. Such behavior is in fact suggested by the recent experimental data for the quotient p p G ~ p / G'.~ Our p results emphasize the differences between the three forms of kinematics as well as the discrepancies in the form factors of the proton at medium energies. The main qualitative difference is between canonical-spin representations (instant and Lorentz kinematics) and null-planespin representations (fi-ont-form kinematics) of the kinematic quark currents. With instant form kinematics reasonable agreement with the empirical values of the nucleon magnetic moments requires a very small quark mass of 140 MeV. With larger quark mass values the magnitude of the calculated magnetic moments is too small, feature also present in Ref. 7. In Fig. 2 we show results for the magnetic N + A(1232) form factor together with helicity amplitudes for the N + N(1440) transition. The wave functions are explicitly given in Ref. 2. Concerning the A(1232) transition we see that in the case of instant form kinematics the impulse approximation describes the empirical form factor and the transition magnetic moment well. This is a notable improvement compared to non-relativistic quark models. The magnetic moment is too small by about 30 % in both point and front kinematics. The results obtained for the N + N(1440) helicity amplitude differ qualitatively depending on the form of kinematics. However the extant data of the helicity amplitude for the N + N(1440) transition, shown in Fig. 2'>1°, are manifestly inadequate. Current experimental effort is on the way. Preliminary analysis seems to confirm the presence of a node in the helicity amplitude lo. The interpretation of baryon wave functions of constituent-quark models as a description of a physical structure that is observed by electro-weak processes depends on the choice of a form of kinematics. To assess the effectiveness of
366 a choice of kinematics it is important to consider the full range of elastic and inelastic transitions at low and medium energies. Examination of a broad range of features with a crude model structure revealed no drastic failure that would rule out any of the forms of kinematics considered. For most form factors permutation symmetric S-wave functions were adequate. The electric form factor of the neutron required a small mixed-symmetry admixture. References
1. P. A. M. Dirac, Rev. Mod. Phys., 49,392 (1949). 2. B. Julia-Diaz et al., Phys. Rev. C 69 035212 (2004). 3. Jones et al., Phys. Rev. Lett. 84,1398 (2000); 0.Gayou et al., Phys. Rev. Lett. 88, 092301 (2002); J. Arrington, Phys. Rev. C 69,022201 (2004). 4. K. Hagiwara et al., Phys. Rev. D 66,010001 (2002). 5. S. Boffi, et al., Eur. Phys. J. A 14,17 (2002). 6. F. Coester and D. 0. Riska, Nucl. Phys. A728,439 (2003). 7. K. Dannbom et al., Nucl. Phys. A 616,555 (1997). 8. W.W. Ash et al., Phys. Lett. B 24,165 (1967); W.Bartel et al., Phys. Lett. B 2 8 , 148 (1968); F. Foster and G. Hughes, Rep. Prog. Phys. 46,1445 (1983); S. Stein et al., Phys. Rev. D 12,1884 (1975); V.V. Frolov et al., Phys. Rev. Lett. 82,45 (1999); Galster et al., Phys. Rev. D 5 , 519 (1972). 9. V. Burkert, Research Program at CEBAF 11, edited by V. Burkert et al., (CEBAF, USA, 1986) p. 161; C. Gerhart et al., Z. Phys. C 4,311 (1980). 10. V. D. Burkert, arXiv:hep-ph/0210321; C. Smith, these proceedings.
Electromagnetic Form Factors of Hyperons in a Relativistic Quark Model T. VAN CAUTERENa, T. CORTHALS, S. JANSSEN and J. RYCKEBUSCH Ghent University, B-9000 Gent, Belgium D. MERTEN, B. METSCH AND H.-R. PETRY Helmholtz-Institut fur Strahlen- und Kernphysik Bonn University, 0-53115 Bonn, Germany The relativistically covariant constituent quark model developed by the Bonn group is used to compute the EM form factors of strange baryons. We present form-factor results for the ground-state and some excited hyperons. The computed magnetic moments agree well with the experimental values and the magnetic form factors follow a dipole Q 2 dependence.
1. Motivation
The photo- and electroproduction of mesons from the nucleon is a process in which both electromagnetic and strong interactions occur. One particularly interesting process is the electroproduction of kaons, where a strange quark/antiquark pair is produced from the QCD vacuum. Data from Jefferson Lab have recently been published ', but an appropriate theoretical description using isobar models is still lacking. One of the main uncertainties in these models is the incompleteness or absence of any knowledge about the form factors, strong or electromagnetic, of the nucleon and hyperon resonances. This work focusses on the latter. We have used the constituent quark (CQ) model developed by the Bonn group to calculate the electromagnetic form factors of ground-state hyperons and the helicity amplitudes of hyperon resonances. The Bonn CQ model is Lorentz covariant and is therefore well suited to describe baryon properties up to high Q 2 , which involve large recoil effects '.
2. EM Form Factors in the Bethe-Salpeter Approach 2.1. The Bethe-Salpeter Equation
x-
The Bethe-Salpeter (BS) amplitude is the analogue of the wave function in the Hilbert space of three quarks with Eirac, flavor and color degrees of freedom. Starting from the six-point Green's function, in momentum space, the following ae-mail:Tim.VanCauteren@UGent .be
367
368 integral equation for the BS amplitude can be derived :
This expression incorporates all features of the model. It is Lorentz covariant in its inception, and the integral kernel is the product of the free three-quark propagator
- (2)
Gop and the sum of all three- and two-particle interactions K?) + K P . The free P
three-quark propagator is approximated by the direct product of three free CQ propagators. We use a linear three-quark confinement potential for K?) and the
-
P
(2)
’t Hooft instanton induced interaction for K F . Both interactions are assumed to be instantaneous. Once the BS amplitudes are known, one can calculate any matrix element between two baryon states, provided that the operator is known. When computing electromagnetic form factors, the operator of interest is the electromagnetic current operator. We use the operator j f = which describes the photon coupling to a structureless CQ in first order of the electromagnetic interaction. \k and 5 are the CQ destruction and creation operators and d is the CQ charge operator. The current matrix element (CME) is then computed in the c.0.m. frame of the incoming baryon (p’ = G ) according to :
s@yp@,
where r and F are the amputated BS amplitude and its adjoint, and S& is the i’th CQ propagator 2 .
2.2. Form Factors and Helicity Amplitudes
The electromagnetic properties of particles are usually presented in terms of form factors, which are functions of the independent scalars of the system. The most frequently used expression for the spin-1/2 EM-vertex is :
where we have introduced the Dirac and Pauli (transition) form factors F:IB and F?IB, and the anomalous (transition) magnetic moment K B I B . Often, the elastic form factors of the ground-state hyperons are expressed in terms of the
369 Sachs' electric and magnetic form factors :
The response of hyperon resonances is commonly expressed in terms of helicity amplitudes] which are directly proportional to the spin-flip (A1/2 and A312)and non-spin-flip (C112)CME's, with proportionality constant
JZ
3. Results and Conclusions Table 1. Static electromagnetic properties of the ground-state hyperons. Magnetic moments are given in units of p,rq, square radii in units of fm2.
0.40
-0.613
c+ co c-
2.458
2.47
0.69
0.79
-
0.73
0.69
0.150
-1.160
-0.99
0.81
0.49
ICo + A1
1.61
1.52
1.96
-0.120
20
-1.25
-1.33
0.47
0.140
-_ -
-0.65
-0.57
0.38
0.47
I
-0.61
0.038
A
Table 2. Static electromagnetic properties of the hyperon resonances for which experimental results are available. Photo-amplitudes are given in units of GeV-1/2 and widths in units of MeV.
pi3 (1385)
62.8
108
1.46
0
Sol (1405)
51.5
-
0.912
0.019
Do3( 1520)
5.50
41.2
0.258
0.0876
13.9
~
0.035
~
-
0.166
In Tables 1 and 2, we summarize the obtained results for the static properties of the ground-state hyperons and resonances respectively. The magnetic moments are generally in very good agreement with the experimental values. The electric mean-square radius of the C- is in agreement with the values of 0.91 f 0.32 f
370 0.40 fm2 of Adamovich et al. and 0.60 f0.08 f0.08 fm2 from Eschrich et al. '. The decay widths of the hyperon resonances are poorly known. However, from Table 2 it is clear that the one for the A(1405) is badly reproduced in our model, which may indicate the special nature of this resonance '. The elastic Sachs' electric and magnetic form factors of the ground-state hyperons, as well as the transition Dirac and Pauli form factors of the Co + A transition, are presented in Ref. '. There it is shown that the magnetic form factors have a dipole dependence on Q2 with cutoffs ranging from 0.79 to 1.14 GeV. We also observed that some electric form factors change sign at a finite value of Q 2 . The results for the helicity amplitudes of two P& to A decays are displayed in Fig. 1. For the P01(16OO), the All2 peaks at a finite value of Q2. Accordingly, our results indicate that resonances which are of minor importance in photoproduction reactions can play a major role in the corresponding electroproduction process.
Po,(l600)to h P,,(1810) to A
-10 " '-12 -1 4 -20 0
4
2 Q2
6 lG.+l
Figure 1. Helicity amplitudes A l l 2 and C l / z for the P01(1600) (full line) and the Pol (1810) (dashed line) resonances.
References
1. 2. 3. 4. 5. 6. 7.
R. M. Mohring et al., Phys. Rev. C67,055205 (2003). D. Merten et al., EUT.Phys. J. A 1 4 , 477 (2002). U. Loring et al., EUT.Phys. J. A 1 0 , 309 (2001). T. Van Cauteren et al., EUT.Phys. J . A 2 0 , 283 (2004). M. I. Adamovich et al., EUT.Phys. J . C8, 59 (1999). I. Eschrich et al. (SELEX Collaboration), Phys. Lett. B522 No.3-4, 233 (2001). T. Hyodo et al., a~XaI/:nuc~-th/0404031 (2004).
BARYON RESONANCE ANALYSIS GROUP PREMEETING TALKS
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Presence of Extra
Resonances in Zagreb Analysis Since 1995
PI1
S. CECI, A. SVARC and B. ZAUNER Rudjer BoSIcoviC Institute, BijeniMa c. 54, 10 000 Zagreb, Croatia E-mail:
[email protected] The partial wave T-matrices for the T N , q N and .rr2N channels have been obtained within the framework of the coupled channel model using the n N elastic and n N + q N d a t a base as input. It has been shown that for the 4 1 partial wave and an equally good representation of the experimental data (namely the T=N,=N T T ~ ,T-matrices) D ~ can be obtained using either three, or four poles for the Green function propagator. However, the three Green function pole solution is not acceptable due to the structure of the extracted resonances. The two out of four P11 resonances, those lying in the energy range 1700 MeV < M R < 1800 MeV, are poorly determined, but they seem t o be strongly inelastic. The inclusion of other inelastic channels is needed to determine masses and widths of missing resonances with greater precision.
The partial wave T-matrices for the 7rN, qN and 7r2N channels have been obtained within the framework of the three body coupled channel model (CMULBL) using the 7rN elastic and 7rN + ON data base as input As it has been shown in Fig.1 the number of Green function poles (N), the respective pole positions ( s i ) and the channel-resonance mixing parameters (-yai) are the input parameters of the fitting procedure which are adjusted in such a way that the experimental input (7rN elastic T-matrices and 7rN + qN data base) is well reproduced. In reality, the number of T-matrix poles (the Green function poles s i ) , which are to be interpreted as resonant states, is chosen in advance, and the only criterion is the quality of data reproduction. The schematic representation of the fitting procedure is shown with full lines in Fig.1. Only upon obtaining the full coupled channel T-matrices set which satisfactory reproduces the experimental data, the resonance parameters are extracted from the final set of obtained T-matrices. Let us emphasize that the resonance parameters are extracted a posteriori. We have no influence upon the type of resonance which we are going to obtain during the fitting procedure] we just know their number, namely, the number of Green function poles. As it is shown in Fig.2. the same quality of the fit to the input experimental data base, which is reflected through almost identical form of the T=N,=Nand T=N,~N is ,obtained with three (N=3, thin solid line) and four (N=4, thick solid
373
374
= CMU-LBL
The INPUT
The OUTPUT
L
Figure 1. The schematic representation of resonance extraction in the coupled channel formalism (CMU-LBL). The full lines represent the present situation, the dashed lines are the suggested and needed modifications.
line) poles in the Green function, respectively. However, as it is shown in Fig.3 the prediction for the remaining coupled channel T-matrices T,,N,,,Nand T + N , n ~ N is dramatically different for the three and four pole solution (thick and thin line). The resonance parameters, extracted from both solutions are given in Table 1. We claim that the obtained three body solution is not acceptable because it shows strong coupling of second and third resonance to the qN channel only, and shows no branching ration to the third, effective channel which includes processes like 7rN + 7rrN and 7rN + K A which are experimentally firmly established.
We offer two alternative explanations: either our fitting procedure is technically inadequate to find a better three pole solution, or we indeed need four resonances in the 9 1 partial wave, second and third strongly inelastic, exactly as indicated in Table 1. We conclude that using 7rN elastic and 7rN + qN data base is, at the present moment, insufficient even to determine the qN elastic channel. In order to improve the fitting technique, we propose to include the resonance parameters as the "quasi input" into the fitting procedure (dashed lines in Fig.1). That would enable us to search for a particular type of a three body solution, namely solution which reproduces the experimental data set simultaneously
375 Table 1. Resonance parameters for the three and four pole solution.
12(9)
60(35)
83(5)
06
O?
5 5 $
z
01
05 04
01
5 03
0
- 02
2
01
-0 1 1500
2000
2500
300
0
MMevl
Figure 2. The P11 partial wave T-matrices for three (thin lines) and four (thick lines) T-matrix poles for TN --t TN and TN + q N processes.
with imposing that one of the resonances is inelastic in other then 7N channel. If such a procedure fails in the end, the statement that we need more then three resonances in a 9 1 partial wave is fully justified.
376
1500
% ~0~~~ Z -005 D
-0 1 -015
1500
2000
Wevl
2500
3000
~1
1500
2000 %MeV1
2000 MMevl
2500
2500
3000
3000
Figure 3. The 4 1 partial wave T-matrices for three (thin lines) and four (thick lines) T-matrix poles for qN + q N and x 2 N t a 2 N processes. References
1. R.E. Cutkosky et. al., Phys. Rev. D20, 2804 (1979); R.E. Cutkosky, C.P. Forsyth, R.E. Henrick and R.L. Kelly, Phys. Rev. D20, 2839 (1979); R.L. Kelly and R.E. Cutkosky, Phys. Rev. D20, 2872 (1979). 2. M. BatiniC, I. DadiC, I. Slaus, A. Svarc, B.M.K. Nefkens and T.S.-H. Lee, Physica Scripta 5 8 , 15 (1998)
Electromagnetic Multipoles - Theory Issues M.M. GIANNINI Dipartamento di Fisica and I N F N , Genova, Italy Some predictions of the Hypercentral Constituent Quark Model for the helicity amplitudes are discussed and compared with data and with the recent analysis of the Mainz group; the role of the pion cloud contribution in explaining the major part of the missing strength at low Q2 is emphasized.
1. The h y p e r c e n t r a l C o n s t i t u e n t Quark Model
In the hypercentral Constituent Quark Model (hCQM) one introduces the hyperspherical coordinates, which are obtained from the standard Jacobi coordinates p' and x' substituting the absolute values p and X by
where x is the hyperradius and the hyperangle. The potential for the three quark system, V, is assumed to depend on the hyperradius x only, that is to be hypercentral. It can be considered as a two-body interaction in the hypercentral approximation, which has been shown to be valid specially for the lower energy states '. It can also be viewed as a true three-body potential; actually the fundamental gluon interactions, predicted by QCD, lead to three-quark mechanisms. The situation is similar to the flux tube models, where two-body (A-shaped) and three-body (Y-shaped) interactions are considered. For a hypercentral potential, in the three-quark wave function one can factor out the angular and hyperangular parts, which are given by the known hyperspherical harmonics and the Schrodinger equation is reduced to a single equation for the hypercentral wave function. Such hypercentral equation can be solved analytically at least in two cases, that is for the h.0. potential and the hypercoulomb one. The two-body h.0. potential turns out to be exactly hypercentral, since a<j . 2 k -T:)~ = k z2 . The S U ( 6 ) states in the h.0. model are too degenerate with respect to the observed spectrum. The 'hypercoulomb' potential Vh,,(z) = -$ is not confining, however it leads to a power-law behaviour of the proton form factor and of all the transition form factors and it has a perfect degeneracy between the first O+ excitated state and the first 1- states. The former can be identified with the Roper resonance and the latter with the negative parity resonances. This degeneracy seems to be in agreement with phenomenology but such feature cannot be reproduced in models with only two-body forces, since the excited L = 0 state, having one more node, lies above the L = 1 state.
c.
(c
'13
377
378 the confining hypercentral potential is assumed to be of the
In the hCQM form
7-
V ( x )= -2
+ ax,
(2)
A standard hyperfine interaction 6 , treated as a perturbation, is added in order to describe the splittings within the SU(6) multiplets. The non strange spectrum is described with r = 4.59 and a = 1.61 fm-' and the standard strength of the hyperfine interaction needed for the N - A mass difference '. The model, keeping fixed these three parameters, has been applied in order t o calculate, that is predict, various quantities of interest, namely the photocouplings 7, the transition helicity amplitudes *, the elastic nucleon form factors and the ratio between the electric and magnetic form factors l o . In the following the results of this model for the transition helicity amplitudes will be discussed. The model has been modified in two respects in order to improve the description of the spectrum. First, isospin dependent terms have been added to the spin-spin ones l l ; the second modification is that to use the correct relativistic kinetic energy 12. The resulting spectrum is considerably improved, in particular the correct ordering of the Roper resonance and the negative parity states is achieved. 2. The helicity amplitudes
The electromagnetic transition amplitudes, All2 and A312, are defined as the matrix elements of the transverse electromagnetic interaction, H:,m., between the nucleon, N,and the resonance, B,states:
The baryon states are obtained using the
with the parameters fixed in the previous section. The transverse transition operator is assumed to be
c [$ 3
Hem t =
-
( p l ' Aj
i=l
+ Aj .pi) + 2pj ;s
'
1
(fj x Aj) ,
(5)
where spin-orbit and higher order corrections are neglected 13)14. In Eq. 5 m j , = e j , sl , p7 and pj denote the mass, the electric charge, the spin, the momentum and the magnetic moment of the j-th quark, respectively, and Xj = A j ( r - )is the photon field. The proton photocouplings of the hCQM have the same overall behaviour of other CQM, probably because all models have the same SU(6) structure in
379 common. In many cases the strength is underestimated and this is a problem for all CQMs. Taking into account the Q2-behaviour of the transition matrix elements, one can calculate the hCQM helicity amplitudes in the Breit frame '. The hCQM results for the Sll(1535) resonance are given in Fig. 1. The agreement is remarkable, the more so since the hCQM curve has been published three years in advance with respect to the recent TJNAF data 1 5 . In general the Q2 behaviour of the helicity amplitudes is reproduced, except for discrepancies at small Q 2 , especially in the A312 amplitudes. These discrepancies could be ascribed either to the non-relativistic character of the model or to the lack of explicit quarkantiquark configurations, which may be important at low Q2 . However, the kinematical relativistic corrections at the level of boosting the nucleon and the resonances states to a common frame are not responsible for these discrepancies, as it has been demonstrated in Ref.".
'
~~~
-Capstick and Keister (Rel)
160
k-f+
Old data
+++Amstrong et. al.
140
CLAS published NewCLASdata
- .- .- .-
120
Aiello, Giannini. Santopinto
: 100 l 2 (3
-
Tz
80
N
4-
60 40
20
0
J
I
I
I
I
I
I
0
0.5
1
1.5
2
2.5
3
3.5
4
0 ' (GeV')
Figure 1. Comparison between the experimental d a t a I 7 , l 5 for the helicity amplitude AT,2 of the 511(1535) resonance and the calculations with the hCQM, lower curve also compared with the Capstick and Keister result, upper curve 18.
Keeping fixed the parameters, the hCQM has also been applied to the calculation of the longitudinal helicity amplitudes 19. An interesting feature is that many amplitudes vanish in the S U ( 6 ) limit, therefore a detailed study of the longitudinal strength may be a good test of the S U ( 6 ) breaking mechanisms.
380 It should be mentioned that the r.m.s. radius of the proton corresponding to the parameters of Eq.4 is 0.48 f m , which is just the value fitted in l 3 to the 0 1 3 photocoupling. Therefore the missing strength at low Q2 can be ascribed to the outer region of the nucleon, where the lack of quark-antiquark effects are probably important. This view is enforced by a recent analysis 20721, which compares the results of the hCQM for the helicity amplitudes and the calculation of the pion cloud contributions performed with the dynamical model of the Mainz Group. As an example, the A312 for the N - A transition is shown in Fig. 2. The pion cloud turns out to be important at low Q2 and diminishes strongly up to 3 f GeV2;it accounts for the major part of the discrepancy between the data and the hCQM results. Particularly important is the longitudinal A transition, where the very small hCQM values are compensated by the dominant pion contribution (see 2 0 ) .
0.0 0.5 1.0 1.5 2.0 2.5 3.0 Q2
(GeV/c)2
Figure 2. The Q2 dependence of the N + A A3,2 helicity amplitude. The solid curve is the result of the superglobal fit with MAID 2 2 , the data points at finite Q2 are obtained with single-Q2 fits 2 1 . The dashed and dotted curves are, respectively, the predictions of the hyperspherical constituent quark model and the pion cloud contributions calculated with DMT by the Mainz group 23. At Q 2 = 0 the photon coupling from PDG is shown 1
References 1. M. Fabre de la Ripelle and J. Navarro, Ann. Phys. (N.Y.) 123, 185 (1979). 2. J. Ballot and M. Fabre de la Ripelle, Ann. of Phys. (N.Y.) 127,62 (1980). 3. E. Santopinto, M.M. Giannini and F. Iachello, in ”Symmetries in Science VII”, ed. B. Gruber, Plenum Press, New York, 445 (1995); F. Iachello, in ”Symmetries in Science VII”, ed. B. Gruber, Plenum Press, New York, 213 (1995). 4. E. Santopinto, F. Iachello and M.M. Giannini, Nucl. Phys. A623, lOOc (1997). 5. M. Ferraris, M.M. Giannini, M. Pizzo, E. Santopinto and L. Tiator, Phys. Lett. B364, 231 (1995). 6. N. Isgur and G. Karl, Phys. Rev. D18, 4187 (1978); Phys. Rev. D19, 2653 (1979).
381 7. M. Aiello, M. Ferraris, M.M. Giannini, M. Pizzo and E. Santopinto, Phys. Lett. B387,215 (1996). 8. M. Aiello, M. M. Giannini, E. Santopinto, J. Phys. G: Nucl. Part. Phys. 24, 753 (1998) 9. M. De Sanctis, E. Santopinto, M.M. Giannini, Eur. Phys. J. Al,187 (1998). 10. M. De Sanctis et al., Phys. Rev. C62,025208(2000). 11. M.M. Giannini, E. Santopinto, A. Vassallo, Eur. Phys. J . A12,447 (2001). 12. M.M. Giannini, E. Santopinto, A. Vassallo, to be published. 13. L. A. Copley, G. Karl and E. Obryk, Phys. Lett. 29,117 (1969). 14. R. Koniuk and N. Isgur, Phys. Rev. D21,1868 (1980). 15. R.A. Thompson et al., Phys. Rev. Lett. 86,1702 (2001). 16. M. De Sanctis, E. Santopinto, M.M. Giannini, Eur. Phys. J. A2,403 (1998). 17. V. D. Burkert,arXiv:hep-ph/0207149. 18. S. Capstick and B.D. Keister, Phys. Rev.D 51,3598 (1995). 19. M.M. Giannini and E. Santopinto, to be published. 20. L. Tiator, Contribution to the Brag Meeting, these Proceedings. 21. L. Tiator et al., Eur. Phys. 3. A19 (Suppl. l),55 (2004). 22. D. Drechsel et al., Nucl. Phys. A645 (1999) 145; http://www.kph.unimainz. de/M AID.
23. S. Kamalov et al., Phys. Rev. C 64 (2001) 032201;http://www.kph.unimainz.de/MAID/dmt/. e t al. (Particle Data Group), Phys. Rev. D 66 (2002)010001.
24. K. Hagiwara
Pll and SI1Resonances in Multichannel
7rrN
Scattering
D. M. MANLEY K e n t State University, Department of Physics and Center for Nuclear Research, Kent, OH44.242, USA E-mail:
[email protected] Recently several independent experiments have found evidence for the extremely narrow 0+(1540) pentaquark state. Several models suggest that this state has spin-parity although neither of these quantum numbers have yet been measured experimentally. The 0+(1540) is expected to have an N' pentaquark partner with the same quantum numbers. For that reason, we have taken a fresh look at the P11 and S11 T N scattering amplitudes to see if there are any suggestions of narrow states, or extra states beyond those expected as q3 configurations.
;*,
The author has performed unitary multichannel fits that include amplitudes for xN + x N ,xN + x x N , and y N -+ xN.Results for the S11 partial waves are well described by including only three resonances. The lowest two resonances are the well-known N(1535);- and N(1650)$-. I find the mass and width of the N(1535);-
to be 1528f1 MeV and l l l f 9 MeV, respectively. I find the mass and
width of the N(1650):t o be 1649 f1 MeV and 108 f14 MeV, respectively. In addition, I find some evidence for a third resonance with mass 2000 f 1 MeV and width 132 f16 MeV. All three of these states are easily understood as traditional q3 baryons and all three produce peaks in a speed plot, where the speed is defined as speed = IdT/dWI. Here T is the elastic T-matrix amplitude at c.m. energy
W. For the P11 waves, I achieved good fits in the c.m. energy range 1080 t o 2100 MeV with three resonances. The lowest resonance is well known as the Roper resonance, or N(1440) The second resonance is traditionally denoted
i'.
by N(1710);'.
Its properties are extremely uncertain. Here I present two alter-
native fits, one with a broad N(1710)$+ (the preferred fit) and one with a narrow
N(1710)++. These two fits were obtained by varying the input parameters and both fits had the same number of free parameters. The overall x2 was similar for the two fits. Table 1 summarizes some of the resonance parameters for the lowest two resonances in the 4 1 partial wave from these two fits. Figure 1 shows the speed plot for the elastic nN amplitude corresponding to the preferred fit. (The speed plot for the other fit looks similar.) What is evident is a large peak associated with the Roper resonance. No other peaks appear in the speed plot, even though
382
383 two additional resonances were included in the fit. In summary, the properties of the Roper resonance appear surprisingly robust. By contrast, almost nothing is known with any certainty about the N(1710);’ (assuming that it exists) other than its mass is about 1700 MeV and it is highly inelastic. More precise data measured with pion beams are probably needed to improve our knowledge of the resonances in the 9 1 partial wave.
Acknowledgments
This work is supported in part by the U.S. Department of Energy under Contract DE-FG02-01ER41194.
Table 1. Parameters for the lowest two 4 1 resonances, based on two multichannel fits. The quantities “mass” and “width” are conventional Breit-Wigner parameters, whereas “pole mass” and “pole width” are the real part of the pole position and -twice the imaginary part of the pole position, respectively. The elasticity is the T N branching fraction.
Fit 2
Fit 1
mass (MeV)
1418 f 3
1419 & 6
width (MeV)
276
* 13
264 f 16
pole mass (MeV)
1355
1362
pole width (MeV)
194
202
elasticity
0.61 f 0.03
0.63
mass (MeV)
1718 f 4
1691 & 83
width (MeV)
368 f 85
50
pole mass (MeV)
1644
1688
pole width (MeV)
293
50
elasticity
0.08
* 0.03
* 0.03
* 44
< 0.04
384
LO
P11 8
6
4
2
0 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1
W (GeV)
Figure 1. Speed plot for the P11 amplitude in a N elastic scattering fitted with a broad P11(1710) resonance. The peak corresponds to the well-known Roper resonance.
Model Dependence of Nucleon Resonance Parameters” L. TIATOR’ and S. KAMALOV172 Institut fur Kernphysik, Universitat Mainz, 0-55099 Mainz, Germany J I N R Dubna, 141980 Moscow Region, Russia E-mail:
[email protected],
[email protected] Nucleon resonance parameters as mass, width, branching ratios and electromagnetic helicity amplitudes cannot be determined in a model independent way. The best way to obtain such elementary quantities is in terms of a partial wave analysis and a separation of resonance and background. In this work we have concentrated on the extraction of the e.m. helicity amplitudes A l p and A312 from electric and magnetic multipole analyses that were obtained from different groups with different techniques. We make a comparison of our results for the resonances P11(1440), 013(1520) and s11(1535). The variation that we find can be considered as a measure of the model uncertainty in these quantities.
1. Introduction Our knowledge of nucleon resonances is mostly given by elastic pion nucleon scattering. All nonstrange baryon resonances that are listed in the Particle Data Tables have been identified in partial wave analyses of .rrN scattering both with Breit-Wigner analyses and with speed-plot techniques. From these analyses we know reasonably well the masses, widths and the branching ratios for the .rrN and .rr.rrN channels. These are reliable parameters for all resonances in the 3 and 4 star categories. The branching ratios for electromagnetic decays, however, are not so well known. They are usually given in terms of helicity amplitudes All2 and A312 that carry in addition to the branching ratios also the information of a relative sign. For the A(1232) these numbers are very well known to a precision of less than 10% but for many other resonances the uncertainty is much larger. In particle data tables helicity amplitudes are usually given with statistical errors of a few percent only. Probably the most difficult case among the prominent 4 star resonances is the Sll(1535). In Fig. 1 we give the helicity amplitudes for this resonance which can be found in the literature over the last 25 years, many of them are found in the particle data tables. It becomes obvious, that with the beginning of new and precise measurements with high duty cycle electron accelerators in the 9Os, the situation for his amplitude has even become worse. Of course it is clear that this is not due to statistical or systematical errors in the experimental data aThis work is supported by Deutsche Forschungsgemeinschaft (SFB443).
385
386
........................ 1975
1980
1985
1990 year
, , , , . . , I
1995 2000 2005
Figure 1. Photon decay helicity amplitudes for the Sll(153.5) resonance reported in the literature over the last 25 years for the proton target. The x analysis is from A z n a ~ r y a n ( 1 9 7 7 ) ~Crawford( 1980,1983)', Arndt(1990,1996,2002)3~5,Drechsel( 1999)6 and Chen(2003)7. The 1) analysis is from Krus~he(1995,1997)~ and the coupled channels analysis from KSU, Pitt-ANL and GW-Gie~sen(2001)~. PDG averages are reported since 1995.
base, but entirely due to the model uncertainty. But it also reflects that a lot of new activities have started in the last decade and it seems to be time to clarify this situation. The figure includes numbers from partial wave analyses, from model calculations for T and eta photoproduction and from coupled channels calculations. The PDG averages have been introduced around 1995 and give in recent issues a value of 90 zt 30 to accommodate with this unsatisfactory situation.
Table 1. Nucleon resonance parameters from Particle Data Group'. In the eta channel only the s11(1535) has a sizeable branching ratio of & = 0.51 z t 0.05.
In our analysis we have to face the following problems: 0
0
We need very precise partial wave amplitudes which are derived from approaches that fit very well the experimental cross sections and polarization observables. We need a separation of background and resonant contributions that is as far model independent as possible. This will require an extensive study and exchange among different groups.
387 0
We need to know very precisely the hadronic parameters, mass, widths and branching ratios, which are in principle already known from pion scattering. However, a closer look in details, especially in the widths, reveals a large uncertainty for many states.
2. Separation of Resonance and Background
The starting point of our resonance analysis is a set of multipoles Ee+, Me* which are complex numbers and are obtained from a partial wave analysis or a model calculation. In order to separate background and resonance parts, we are guided by the concepts of dynamical models, unitary isobar models and phenomenological analyses of the GW/SAID group. In each case the background contains Born and vector meson exchange terms plus an additional phenomenological contribution. The resonance contribution will always be parameterized with a Breit-Wigner ansatz using dressed hadronic parameters as mass M R , width r R and branching ratios Pn = r,/rR, PV = r,,/I?R and ,&, = r 2 , / r R . Finally, the whole amplitude should be unitarized, which is especially important for energies below the 27r threshold where the Watson theorem is strictly valid. For our analysis in the second resonance region this is not so critical and the unitarization phases can be treated as free parameters. In the following we propose 3 forms,
b) A = [ ( l + i t , ~ ) ( B o r n + A ) + R t : F ] e ~ ~ ,
+
c ) A = (1 i t,N)(Born
+ A) + R t,NBW eiqJ .
(2)
(3)
Form a) has recently been used by the GW/SAID group in the SM02 analysis 5 , form b) gives the previously used SAID parametrization l o and form c) is an ansatz used in the unitary isobar model MAID. The forms b) and c) are very similar and also in the numerical fitting procedures they give almost the same results. In all cases the K-matrix part of the background will be calculated from pseudoscalar Born terms and p , w vector meson exchange contributions. In addition an energy dependent real contribution A = (a1 a2 z ) is added to account for pion loop effects. The unitarization phase 4 = ( b l b2 z)(Im t , N - ItnN12 appearing in forms b) and c) are also energy dependent and vanish for energies below the 27r threshold. The energy dependence will be taken proportional to the photon energy in the c.m. frame, z = wcm/m,. In the recent SM02 analysis of pion photoproduction data, the SAID group found an improved description of new and precise measurements with form a), where an additional complex term (c+io ) ( I m t,N- lt,NI2) is added with constant parameters = c l , D = d l . It vanishes for energies below the 27r threshold, but gives additional freedom in the energy region which is not constraint by the Watson theorem. However, it has been found that the energy dependence in this term has so much flexibility that
+
+
388 it can take away some strength from the resonance part, i.e. it can mix resonance and background. The 7rN t-matrix appears twice in all 3 forms, first as the full t-matrix from pion nucleon phase-shift analysis, which is as usually expressed in terms of the phase-shifts 6 and the inelasticities 71, txN = (qe2ib - 1)/22 and consequently Im t,N - ItrN12 = (1 - q2)/4, which will be zero below the 27r threshold, where QE1. Second, in the resonance part, the t-matrix is expressed as an ideal BreitWigner resonance
with t:r(W = M R ) = i . For the e.m. vertex we use a rather simple parametrization, which gives basically a correct threshold behavior. No additional form factor as in model calculations will be used,
with r,(W) = k 2 . The only free parameter rl is a real number and can be directly related to the reduced multipoles and to the helicity amplitudes, k is the photon momentum in the c.m. frame and takes a value of k~ at resonance. As the result of hadronic dressing, the width of the resonance is an energy dependent function. The parametrization of the energy dependence will be taken as in Ref.376. Following Ref.3, and the Particle Data Group4, the photon decay helicity amplitudes are obtained from the photoproduction multipoles. The reduced mulare evaluated at the resonance position W = M R , where tipoles A, z El*, the resonant part of the multipole should be purely imaginary (definition of a Breit-Wigner resonance)
with an isospin factor C,N = -l/& for I = 112 and for I = 312 and f x N = [(lcRmrx)/((2j 1)7rqx,RhfRri)]1'2. It is important to note that only in such a Breit-Wigner definition the helicity amplitudes are given as real numbers. Only in this case they can be compared to the definition of helicity amplitudes as electromagnetic matrix elements between nucleon and resonance states as calculated in quark models.
+
3. Results In the following we will discuss only the N* resonances 5'11 (1535), P11(1440) and &3(1520). First, for all 3 forms, Eqs. (1,2,3) the resonant amplitude is given by
389 In particular, the phases 4, that appear in forms b) and c) do not belong to the resonant part itself but are artifacts of the background. From Eq. (6) we get the reduced multipoles for isospin 1/2
For our numerical analysis we have used 5 energy-dependent global solutions and 2 single-energy solutions: SM02 : GW/SAID partial wave analysis, solution SM02 MD03 : MAID unitary isobar model, solution MAID03 AZUIM : Yerevan/JLab unitary isobar model l 1 AZDR : Yerevan/JLab dispersion theoretical analysis GWCC : GW/Giessen coupled channels analysis l 2 SEGW : GW/SAID single-energy analysis SEMZ : MAID single-energy analysis An overview over these different approaches can be found in Ref. 1 3 . Due to the limited space a comparison of the multipoles cannot be shown but a few observations are worth mentioning: The global solutions are mostly close together, but for the S11 amplitude a large discrepancy around the 7 cusp, below the resonance position is visible in the real part and in the imaginary part the MAID solution has a narrower shape than all other solutions. The real part of the electric 0 1 3 amplitude SM02 and the AZUIM model are considerably larger than MAID which is very close to the dispersion theoretical solution AZDR. The imaginary part of the magnetic 0 1 3 amplitude of the GW/Giessen coupled channels analysis is about 20% lower than all other solutions which will have direct consequences on the numerical results of the helicity amplitudes. We have fitted our forms a) and c) from Eqs. (1,3) to each solution and each partial wave separately. Both forms have 5 parameters, (form a): a1 ,a2, c1, dl , and form c): a l , a 2 , b l ,b ~ ~ 7 - 1In ) . addition we also vary the mass and the width of the resonance, MR, r R , while we keep the branching ratios fixed at the PDG values, see Table 1. This results in a total of 7 free real parameters for the ,911 and 9 1 fits and 12 parameters for the 0 1 3 , where we have to fit 2 multipoles simultaneously, where only the mass and width of the resonance are the same for electric and magnetic multipoles. In our fits we find large differences in the resonance widths. Therefore it does not make sense to evaluate the helicity amplitudes, Eq. (8) with the fitted parameters. This would suggest an enormous uncertainty that does not really arise from the electromagnetic coupling. Therefore, we will evaluate the helicity amplitudes A,,,, A3,2 with the current standard values of PDG as listed in Table 1 and call them 'normalized' helicity amplitudes. Comparing the different forms, we found very similar results with forms b) and c) but often quite large differences with form a) and will therefore only discuss the results with forms a) and c ) . For the S11 we find mostly lower values with form a) and a bigger spread among the solutions. This is also visualized in Fig. 2. The x2 values are very
390
C.UWab
C.UdY.11
Figure 2. A,/z helicity amplitudes for 511(1535) obtained with forms a) and c). The analyses 1-7 are GW/SAID SM02, Maid03, Yerevan UIM, Yerevan DR, GW coupled channels, GW/SAID single energy and Mainz single energy solutions, respectively (see also text). The asterisk (8) is the PDG’ value and the triangle (9) is from Ref.5. The amplitudes are evaluated from the reduced multipoles by Al/z = -&+. The average values of our fits are 80 13 with form a) and 93 & 10 with form c). similar for both forms, only the SAID SM02 solution is better fitted with form a). The problem with form a), however, is a strong dependence on the fitted energy range. For our fits in this study we have always used an energy range of ? V ~R rR/2 < < M R r R / 2 , which is a somewhat natural choice. By changing this we found very different helicity amplitudes for the solution SM02, as low as 36, which comes very close to the published value, that is also shown in Fig. 2 as the last point (analysis 9). The figure shows also 2 error bands, the lower (green) band gives the standard deviation of our fitted values and the upper (red) band gives the estimate of different analyses from eta photoproduction by Krusche et al.14. As a main result we find a more stable and robust fit with form c) leading in a smaller spread among the different solutions and getting in overlap with the analysis of eta photoproduction, where the background resonance separation does not play such a role as in pion photoproduction. This could be a solution of the so-called ‘eta puzzle’ that the helicity amplitudes from pion and eta analyses were almost a factor of 2 apart. For the P11 partial wave we found only small differences between forms a) and c) with the average values of -65 f 11 with form a) and -73 f 10 with form c). Finally, in Fig. 3 we show our results for the 0 1 3 resonance, a resonance which is the second best known resonance after the A ( 1 2 3 2 ) . Also here the spread in the width gives a factor of two, if we consider form a). However, by comparing the amplitudes in Fig. 3, a clear preference of form c) becomes obvious with a good agreement with the PDG values.
w
+
4. Summary and Conclusions
In summary, we have performed a resonance analysis for 3 prominent nucleon resonances, &1(1535), p11(1440) and D13(1520). We have studied the model dependence of resonance and background separation of partial waves and have compared 7 different solutions from 4 different groups. We have discussed 3 different forms that allow a separation of background terms from the pure resonance contribution. With forms a) and c) we have made extensive studies and found a clear preference to use form c).
391 form c )
I ,
,
,
,
,
?
,
,
1
2
3
4 5 8 analysl"
7
8
8
,
1 1
2
3
4 5 8 analy,iS
7
8
8
Figure 3. Al,2 (lower set of points) and A3,2 (upper set) helicity amplitudes for 013(1520) obtained with forms a) and c). Notation as in Fig. 2. The amplitudes are evaluated from the reduced multipoles by A l l 2 = ( 3 M z - - &-)/2, A3/2 = + M z - ) / Z . T h e average values of our fits are -22 f 27, 203 55 with form a) and 93 10, 157 5 with form c ) .
-a(&-
*
*
*
As a conclusion we want to stress that such kind of analyses should be performed with other resonances as well and that in the future, an additional model error should be given, when helicity amplitudes are reported in the literature. Acknowledgments We would like to thank Dick Arndt, Inna Aznauryan, Cornelius Bennhold, Igor Strakovsky, Agung Waluyo and Ron Workman for providing us with their numerical multipoles that we have used in our comparison, and for stimulating discussions on the subject of resonance and background separation. References
1. 2. 3. 4. 5.
K. Hagiwara et al. (Particle Data Group), Phys. Rev. D 66 (2002) 010001. Reported by Particle Data Group, Rev. Mod. Phys. 56 I1 (1984) S220. R.A. Arndt et al., Phys. Rev. C 42 (1990) 1864. Particle Data Group, Phys. Rev. D 45 I1 (1992) 1.1. R.A. Arndt, W.J. Briscoe, 1.1. Strakovsky and R.L. Workman, Phys. Rev. C 66 (2002) 055213; http://gwdac.phys.gwu.edu/. 6. D. Drechsel, 0. Hanstein, S.S. Kamalov and L. Tiator, Nucl. Phys. A 645 (1999) 145; http://www.kph.uni-mainz.de/MAID. 7. G.-Y. Chen, S. Kamalov, S.N. Yang, D. Drechsel, L. Tiator, Nucl. Phys. A 723 (2003) 447. 8. B. Krusche et al., Phys. Lett. B 358 (1995) 40;Phys. Lett. B 397 (1997) 171. 9. C. Bennhold et al. Proc. of NSTAR2001 workshop, Mainz 2001, eds. D. Drechsel and L. Tiator, (World Scientific, 2001) p. 109. 10. R.A. Arndt, 1.1. Strakovsky and R.L. Workman, Phys. Rev. C 53 (1996) 430. 11. I.G. Aznauryan, Phys. Rev. C 67 (2003) 015209. 12. A. Waluyo, C. Bennhold, private communication (for model details, see also T. Feuster, U. Mosel, Phys. Rev. C 59 (1999) 460). 13. T.-S.H. Lee, A. Matsuyama and T. Sato, these proceedings, nucl-th/0406050. 14. B. Krusche and S. Schadmand, Prog. Part. Nucl. Phys. 51 (2003) 399.
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SCIENTIFIC PROGRAM Wednesday, March 24, 2004 Focus Session on Exotic Baryons Chair F.Klein
9:00 Experimental Review on Exotic Baryons - T . Nakano
- V . Burkert 1O:OO KN Scattering Data and Exotic O+ Baryon - W . Briscoe
9:30 Studies of Pentaquark Baryons at JLab
10:20 Break
Chair J.-M.Richards 10:45 Pentaquarks in the Chiral Soliton Model
- M . Polyakov
11:30 Status of Quark Model Approaches to Pentaquark States - K . Maltman 12:15 Pentaquarks in Lattice QCD - T . Kovacs 13:OO Lunch
Chair V.Burkert 14:30 Search for Pentaquark States on Proton Target at CLAS - R . de Vita
- S . Nicollai 15:lO Study of the Exotic 0' in Polarization Reactions - Q. Zhao 14:50 Search for the 0'
Exotic Baryon in 3He to PRO+
15:30 Determining the O+ Quantum Numbers from K'p + r r K * n Reactions; Checking the Possible Nature of the O+ as a K?rN Bound State - E . Oset
Break Chair K.Maltman 16:30 Mass Spectrum and Magnetic Moments of Pentaquark States topinto 16:50 Pentaquark Spectra in the Diquark Picture - C. Sernay 17:lO Pentaquarks and Radially Excited Baryons 17:30 Discussion
393
- H.
Weigel
- E.
San-
394
Thursday, March 25, 2004 Chair K.A.Svarc
- T.S.H. Lee 9:15 Experimental Review on Strangeness Production - K . Glander
8:30 Review on Coupled-Channel Calculations
9:45 Interpretation of Results on Strangeness Production - B . Saghai 10:15Break
Chair L.Tiator 10:45 S11 Resonances in
7r
and 9 Channels - S. Kamalov
11:15 Experimental Review on w Production - P . Cole 11:45 In Search of Missing Resonances
- S . Capstick
12:30 Lunch 14:OO Excursion in Chartreuse 20:OO Conference Banquet
Friday, March 26, 2004 Chair C.Papanicolas 8:30 Recent Results from GDH Collaboration at MAMI - H . - J . Arends 9:00 Double-Polarization Experiments with Polarized HD at LEGS - A . Sandorfi 9:30 CLAS Results on Delta and Roper Resonances - C. Smith
10:OO Break
Focus Session on the nature of resonances in the region 1.41,7 GeV 10:30 Experimental Review on Double-Pion Production
- M . Ripani
Chair H.Lee 11:15 A Partial Wave Decomposition of y p
+ p7r+7r- - M .
11:35 7 Photoproduction off the Neutron - V. Kouznetsov
Bellis
395 11:55 Discussion 1230 Lunch
Chair G.Bali
14:OO Baryon Resonances from Lattice QCD - F . Lee 14:40 N* Properties from the l / N c Expansion - C. Schat 15:20 Dynamical Baryon Resonances from Chiral Unitarity - A . Rarnos 16:OO Break 16:30 Paralell Sessions
Saturday, March 27, 2004
Focus Session on Relativity Chair: E.Oset 8:30 Form Factors of Hadronic Systems in Various Approaches of Relativistic Quantum Mechanics - B. Desplanques 8:50 Hadron Structure from the Salpeter Equation 9:lO Point Form Approach to Baryon Structure
-
- B. Metsch
W. Plessas
9:30 Light Front Approach to Hadron Form Factors - S. Sirnula
9:50 Discussion 10:30 Break
Chair: M.Giannini 11:OO Baryon Resonances from J/!P Decays - B . Zou
11:30 BRAG Summary - M . Manley 12:OO Conference Summary - V . Vento
Parallel session A Chair: A .D'Angel0 16:30 New CLAS Measurements of Pion Electroproduction in the A(1232) Region at Q2=0.16 GeV2 - L.C.Srnith
396 16:45 Analysis of Single Pion Electroproduction Data from CLAS - L . C.Smith 17:OO 7 and T O Photoproduction on Deuteron: Beam Asymmetries and Total Cross Section - A . Fantini 17:20 Photoproduction of
- 0. Bartolomy
and 7 Mesons at CB-ELSA
17:40 Double and Target asymmetries for the A'(1232)
Resonance
- A . Biselli
18:OO Combined Analysis of Single Meson Photoproduction with the Operator Expansion Method - A . Anisovich 18:20 Compton Scattering of Polarized Photons on the Proton at GRAAL - A. Giusa 18:40 Total Photoabsorption off the Proton and Deuteron at Intermediate Energies - V . Nedorezov 19:OO Study of Nucleon Resonances in ( y , r ) N + @X within a Coupled-Channel Lagrangian Model - V. Shklyar
Parallel session B Chair: B.Krusche 16:3O Helicity Asymmetries In Double Charged Pion Photoproduction from Hydrogen with Circularly Polarized Photons - S . Strauch 16:50 Search for New Baryon States in Analysis of the Recent CLAS Data on Double Charged Pion Photo- and Electroproduction - V. Burkert 17:lO 2xa Photoproduction and the Second Resonance Region - M . Kotulla 17:30 N* Photoproduction from Nuclei
- S. Schadmand
17:50 Multi Resonance Contribution to the 7 Production in p-p Scattering - S. Ceci 18:lO Nucleon Resonances and Processes Involving Strange Particles
18:3O Multichannel KN Scattering and Hyperon Resonances
- A . Svarc
- M . Manley
18:50 Renormalization of N-N Scattering with Pion Exchanges and Boundary Conditions - M . Pavon- Valderrama
Parallel session C Chair: WPlessas 16:30 Further Evidence for the Breathing Mode of the Nucleon - H.P. Morsch 17:lO Electromagnetic Form Factors in the Hypercentral Constituant Quark Model - M.M. Giannini
397 17:30 Generalized Sum Rules of the Nucleon in the Hypercentral Constituant Quark Model - M . Gorshteyn 17:50 Strong Decay of Baryons in the Point Form Formalism - T . Melde 18:lO Chiral Dynamics of the Two A(1405) States
- D . Jido
18;30 Baryon Form Factors of Relativistic Constituant Quark Models - B . JuliaDiaz 18:50 Electromagnetic Form Factors of Hyperons in Relativistic Quark Models T . Van Cauteren
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List of Participants Alexandrou Constantia
Anisovich Alexey
Department of Physics
Helmholtz-Institut fur
University of Cyprus
Strahlen -und Kernphysik
P.O. Box 20537
Nussallee 14-16
Nicosia CY-1678
53115 Bonn
CYPRUS
GERMANY
[email protected]. cy
alexei@iskp. m i - b o n n . de
Arends Hans-Jurgen
Bali Gunnar S
Institut fur Kernphysik
Department of Physics and Astronomy
Universitat Mainz
University of Glasgow
J.-J.-Becherweg 45
University Avenue
D-55099 Mainz
Glasgow G12
GERMANY
UNITED KINDOM
arends @kph.uni-mainz.de
g .
[email protected]. uk
Bartholomy Olivia
Bellis Matthew
Helmholtz-Institut
Dept. of Physics
fuer Strahlen- und Kernphysik
Applied Physics and Astronomy
Universitaet Bonn Nussallee 14-16
Rensselaer Polytechnic Institute
Nussallee 14-16
110 8th St.
53111 Bonn
Troy, NY 12180
GERMANY
U.S.A.
[email protected]. de
[email protected]
399
400
Biselli Angela
Bocquet Jean-Paul
Carnegie Mellon University
Laboratoire de Physique Subatomique
5000 FORBES AVE
et de Cosmologie (LPSC)
PITTSBURGH PA 15213
53,Avenue des Martyrs
U.S.A
38026 Grenoble Cedex
biselli@jlab. org
FRANCE
[email protected]
Briscoe William
Bur ker t Volker
The George Washington University
Jefferson Lab
Washington, DC 20052
12000 Jefferson Avenue
U.S.A
Newport News, VA 23606
[email protected]
U.S.A
burkert@jlab. org
Capstick Simon
C a r b o n n e l Jaume
Department of Physics
Laboratoire de Physique Subatomique
Florida State University
et de Cosmologie (LPSC)
Tallahassee
53,Avenue des Martyrs
FL 32306-4350
38026 Grenoble Cedex
U.S.A
FRANCE
capstickaphy. fsu.edu
[email protected]
Ceci Sasa
Cole Philip
Rudjer Boskovic Institute
Jefferson Lab
Bijenicka cesta 54
Bldg 16 Room 144
10000 Zagreb
12000 Jefferson Ave
CROATIA
Newport News, VA 23606
[email protected]
U.S.A.
Cole @jlab.org
401
Corthal Tamara
D’Angelo Annalisa
Ghent University
Universita’ di Roma, Tor Vergata
Proeftuinstraat 86
Via della Ricerca Scientifica 1
B-9000 Gent
00133 Roma
BELGIUM
ITALY
Tamara. Corthals @ UGent. be
[email protected]
De Vita Raffaella
Di Salvo Rachele
INFN
INFN Rome
via Dodecaneso 33
Via della Ricerca Scientifica 1
16146 Genova
00133 Roma
ITALY
ITALY
devitaage. infn.it
rachele.
[email protected]
Desplanques Bertrand
Djalali Chaden
Laboratoire de Physique Subatomique
University of South Carolina
et de Cosmologie (LPSC)
Physics Department
53, Av. des Martyrs
712 Main Street
38026 Grenoble Cedex
Columbia, SC 29208
FRANCE
U.S.A.
[email protected]. fr
[email protected]
Fantini Alessia
Giannini Mauro
University of Roma2, Tor Vergata
Dipartimento di Fisica and INFN
Via Della Ricerca Scientifica 1
via Dodecaneso 33
00173 Rome
1-16146 Genova
ITALY
ITALY
alessia.fantini@romaZ. infn.it
giannini@ge. infn.at
402 Giusa Antonio
Glander Karl-Heinz
Dipartimento di Fisica e Astronomia
Saphir (Elsa)
Universith di Catania
Physikalisches Institut
Viale A. Doria, 6
Nussallee 12
Catania
53115 Bonn
ITALY
GERMANY
[email protected]. it
[email protected]
Gorshteyn Mikhail
Jido Daisuke
University of Genova
ECT*
Dipartimento di Fisica
Villa Tambosi
via Dodecaneso 33
Strada delle Tabarelle 286
16146 Genova
1-38050 Villazzano (Trento)
ITALY
ITALY
[email protected]
j i d o @ect.it
Julia Diaz Bruno
Kamalov Sabit
Helsinki Institute of Physics (HIP)
Institut fur Kernphysik
University of Helsinki
Universitat Mainz
Gustaf Hallstromin katu 2
D-55099 Mainz
00014 Helsinki P.O. Box 64
GERMANY
FINLAND
[email protected]. de
bruno.julia @helsinki.fi
Klasen Michael
Klein Friedrich
Laboratoire de Physique
Physikalisches Institut
Subatomique et Cosmologie
University of Bonn
53, Av des Martyrs
Nussallee 12
Grenoble 38330
D-53115 Bonn
FRANCE
GERMANY
[email protected]
[email protected] bonn. de
403 Kotulla Martin
Kovacs Tamas G.
Institut fuer Physik
Department of Physics
University of Basel
University of Pecs
Klingenbergstr. 82
Ifjusag u. 6.
CH-4056 Basel
H-7624 Pecs
SWITZERLAND
HUNGARY
Martin.
[email protected]
[email protected]. hu
Krusche Bernd
Kuznetsov Viacheslav
Inst it ut e of Physics
Institute for Nuclear Research
University of Basel
7a, Prosp. 60th Anniversary of October,
Klingelbergstrasse 82
117312 Moscow
CH-4056 Basel
RUSSIA
SWITZERLAND
[email protected]
Bernd.
[email protected]
Laveissiere Geraud
Lee Frank X.
Laboratoire de Physique Corpusculaire
Physics Department
de Clermont-Ferrand
George Washington University
Universitk Blaise Pascal
725 21st Street
24 av des Landais, 63177 AUBIERE
NW Washington, DC 20052
FRANCE
U.S.A.
[email protected] r
fxlee@gwu. edu
Lee T.-S. Harry
Levi Sandri Paolo
Physics Division
INFN-LNF
Argonne National Laboratory
Via Enrico Fermi 40
Argonne, Illinois 60439
00044 Fkascati
U.S.A.
ITALY
[email protected]. anl.gov
Paolo.
[email protected]
404 Lleres Annick
Maltman Kim
Laboratoire de Physique
Dept. Math and Statistics
Subatomique et Cosmologie
York University and CSSM
53, Av des Martyrs
York Univ. 4700 Keele St
Grenoble 38330
Toronto On Canada M3J 1P3
FRANCE
CANADA
lleres @Ipsc.in2p3.f r
k m a l t m a n @yorku.ca
Manley Mark
Melde Thomas
Department of Physics
Institute for Theoretical Physics
Kent State University
Universit aetsplatz
OHIO 44242
A-8010 Graz
U.S.A.
AUSTRIA
m a n l e y a k e n t . edu
[email protected]
Metsch Bernard
Morsch Hans-Peter
Helmholtz-Institut fuer Strahlen
Institut fuer Kernphysik
und Kernphysik
Forschungszentrum Juelich
Universitaet Bonn
D-52425 Juelich
Nussallee 14-16 D-53115 Bonn
GERMANY
GERMANY
morsch@fz-juelich. de
m e t s c h @itkp.uni-bonn. de
Nakano Takashi
Nedorezov Vladimir
RCNP, Osaka University
Institute for Nuclear Researches RAS
10-1 Mihogaoka, Ibaraki
7A, 60-th October anniversary prospect
Osaka 567-0047
Moscow 117312
JAPAN
RUSSIA
nakano@rcnp. Osaka-u. ac.jp
[email protected]. ac. ru
405 Niccolai Silvia
Oset Eulogio
IPN Orsay
Departemento de Fisica teorica
15, rue Georges Clemenceau
Universidad de Valencia
91406 Orsay Cedex
A P T 0 22085- 46071 Valencia
FRANCE
SPAIN
silvia@jlab. oTg
[email protected]
Ostrick Michael
Papanicolas Costas
Physiklaisches Institut Univ. Bonn
Institute of Accelerating
Nussallee 1 2
Systems and Applications
D-53115 Bonn
P.O.Box 17214 GR-10024 Athens
GERMANY
GREECE
[email protected] e
[email protected]
Pavon Valderrama Manuel
Plessas Willibald
Universidad de Granada
Inst. f. Theor. Phys.
Avenida F’uentenueva S/N
Univ. Graz
18071, Granada
Universitaetsplatz 5
SPAIN
A-8010 Graz
[email protected]
AUSTRIA
[email protected]
Polyakov Maxim
Ramos Angels
Institut de Physique
Departament E.C.M.
Universite de Liege
University of Barcelona
Universitk de Liege au Sart Tilman
Facultat de Fisica, Diagonal 647
B4000 Liege 1
Barcelona
BELGIUM
SPAIN
[email protected]. be
Tamos @ecm.ub. es
406 Rebreyend Dominique
Richard Jean-Marc
Laboratoire de Physique Subatomique
Laboratoire de Physique Subatomique
et de Cosmologie (LPSC)
et de Cosmologie (LPSC)
53, avenue des Martyrs
53, avenue des Martyrs
38026 Grenoble
38026 Grenoble
FRANCE
FRANCE
[email protected]. f r
jean-marc. richard@lpsc. in2p3.f r
Ripani Marco
Russo Giuseppe
INFN - Genova
Dipartimento di Fisica e Astronomia
V. Dodecaneso 33
Univ. Catania and INFN sezione di Catania
1-16143 Genova
Viale A. Doria 6
ITALY
95125 Catania
ripani @ge.infn.it
ITALY
[email protected]
Sadler Michael
Saghai Bijan
Abilene Christian University
CEA
ACU Box 27963 Abilene
DAPNIA/DIR CEA/Saclay
TX 79699
91191 Gif-sur-Yvette cedex
U.S.A.
FRANCE
[email protected]. edu
[email protected] r
Sandorfi Andrew
Santopinto Elena
Physics Department
Infn and Universita di Genova
Brookhaven National Laboratory
V. Dodecaneso 33
Bldg. 510
1-16143 Genova
Upton, NY 11973-5000
ITALY
U.S.A.
[email protected]
[email protected]
407 S c h a d m a n Susan
Schat Carlos
Giessen University
CNEA
11. Physikalisches Institut
Av. del Libertador 8250
Justus-Liebig-Universitaet
1429 Buenos Aires
Heinrich-Buff-Ring 16
ARGENTINA
D-35392 Giessen
schat@phy. duke.edu
- CONICET
GERMANY
[email protected]
Schmieden Hartmut
Semay Claude
Physikalisches Institut
Groupe de Physique Nuclkaire ThCorique
University of Bonn
Universitk de Mons-Hainaut
Nussallee 12
Place du Parc, 20
D-53115 Bonn
B-7000, Mons
GERMANY
BELGIUM
[email protected] bonn.de
claude.semay@umh. ac.be
Shklyar Vitaliy
Silvestre-Brac Bernard
Institute for theoretical physics I
Laboratoire de Physique Subatomique
Heinrich-Buff-Ring 16
et de Cosmologie (LPSC)
D-35392 Giessen
53 Avenue des martyrs
GERMANY
38026 Grenoble-Cedex
[email protected]
FRANCE silvestre @lpsc. in2p3.f r
Simula Silvano
Sirunyan A l b e r t
INFN - Roma I11
Yerevan Physics Institute
Via della Vasca Navale 84
2,Alikhanian Brothers str.
1-00146 Roma
375036,Yerevan
ITALY
ARMENIA
simula@roma3. infn.at
sirunian@uniphi. yerphi.a m
408
Smith Cole
Strauch Steffen
Physics Dept.
Department of Physics
University of Virginia
The George Washington University
McCormick Road
725 21st Street
Charlottesville VA 22901
N.W. Washington, D.C. 20052
U.S.A.
U.S.A.
coleOnstar.phys. Virginia.edu
strauch@gwu. edu
Svarc Alfred
Tiator Lothar
Rudjer Boskovic Institute
Institut fur Kernphysik
Bijenicka c. 54
Universitat Mainz
10 000 Zagreb
D-55099 Mainz
CROATIA
GERMANY
[email protected]
[email protected]
Van Cauteren Tim
Vent0 Vicente
Ghent University
Departamento de Fisica Teorica
INW Proeftuinstraat 86
Universidad de Valencia
B-9000 Gent
C. Dr. Moliner, 50
BELGIUM
E-46100 Burjassot (Valencia)
tim.vancauteren0ugent. be
SPAIN Vicente.
[email protected]
Voutier Eric
Weigel Herbert
Laboratoire de Physique Subatomique
Fachbereich Physik
et de Cosmologie (LPSC)
Siegen University
53 Avenue des martyrs
Walter-Flex Strape 3
38026 Grenoble-Cedex
D 57068 Siegen
FRANCE
GERMANY
eric.
[email protected]
[email protected]. de
409
Zhao Qiang
Zou Bingsong
Department of Physics
Institute of High Energy Physics
University of Surrey
P.O.Box 918(4)
Guildford, Surrey, GU2 7XH
Beijing 100039
UNITED KINDOM
CHINA
qiang.zhao @surrey.ac.uk
[email protected]
