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Exotics in Meson-Baryon Dynamics with Chiral Symmetry

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Exotics in Meson-Baryon Dynamics with Chiral Symmetry Version 2.1 Dissertation Submitted to Graduate School of Science of Osaka University for the Degree of Doctor of Physics Exotics in meson-baryon dynamics with chiral symmetry Tetsuo Hyodo A) ∼ 2006 ∼ Research Center for Nuclear Physics (RCNP), Osaka University Mihogaoka 10-1, Ibaraki, Osaka 567-0047, Japan A)Email address: [email protected] ii Acknowledgement First of all, I would like to sincerely express my gratitude to the supervisor, Professor At- sushi Hosaka for enlightening discussions, helpful suggestions and continuous encouragements over the past five years. I have been instructed about plenty of things in hadron physics from fundamental facts to recent developments, which are reflected throughout this dissertation. I wish to thank Professor Eulogio Oset (IFIC, Valencia Univ.) for providing many excit- ing ideas and stimulating discussions. He has been giving me a lot of interesting subjects and beautiful hand-writing notes on them. Doctor Daisuke Jido (YITP) is acknowledged for collaboration and help from the beginning of the master course, which have provided funda- mental tools for researches. I appreciate Doctor Seung-il Nam (Pusan National Univ.) for his friendship and interesting discussions. Without their affectionate support, I would never complete this dissertation. The work presented in this thesis has been done with my collaborators, Professor Hyun Chul Kim (Pusan National Univ.), Doctor Felipe J. Llanes-Estrada (Madrid Univ.), Professor Jose R. Pel´aez (Madrid Univ.), Professor Angels Ramos (Barcelona Univ.), Doctor Sourav Sarkar (IFIC, Valencia Univ.), and Professor Manolo J. Vicente Vacas (IFIC, Valencia Univ.). I would like to thank them all again for the fruitful collaborations. I am very grateful to Professor Takashi Nakano (RCNP), Mister Koji Miwa (Kyoto Univ.), and people of LEPS collaboration for letting me know the latest experimental situation and suggestions for the theoretical studies from experimental point of view. It is my great pleasure to visit Valencia, where many collaborators and friends of mine are studying. I thank them for their kind hospitality during my stays. I express my thankfulness to my wife Kana for generous understanding of my study and support for healthy life. The work presented here is supported in part by the Japan Society for the Promotion of Science (JSPS) the Grant for Scientific Research ((C) No.17959600). I would like to thank all the members of theory group of Research Center for Nuclear Physics (RCNP) for their kind helps. I am very happy to study at RCNP where I have had exciting discussions with experimentalists and many opportunities to visit foreign coun- tries. Finally, I wish to acknowledge Professor Hiroshi Toki for providing such a comfortable environment, collaborators and colleagues. iii Abstract Quantum chromodynamics (QCD) governs the strong interaction among quarks and glu- ons, which compose hadrons in the non-perturbative vacuum. Since hadrons are elementary excitations of the QCD vacuum, it is important to study their properties in order to under- stand the whole dynamics of QCD. The field of the hadron spectroscopy is being stimulated by recent experimental results, namely, evidences of new states and observation of various quantities to extract properties of excited states. In this thesis, we study the exotics appearing in the meson-baryon dynamics. We consider not only the manifestly exotic states such as pentaquarks, but also the states which are considered to contain a large amount ofqq ¯ components in addition to the valence quarks. We study the properties of these exotics in effective models with hadronic degrees of freedom. These models are constructed based on the chiral and flavor symmetries of QCD, and the results are compared with experimental data. There are two main subjects to be pursued in this thesis. One is the study of baryon resonances using the chiral unitary model, and the other is the study of pentaquarks. A key issue common for both subjects is the investigation of multi-quark components. We adopt a model which utilizes the meson-baryon interaction derived from the chiral perturbation theory. Imposing the unitarity condition, the model describes the baryon reso- nances as meson-baryon molecule states. Hence, the resonances may be regarded as five-quark states in contrast to conventional approaches with three quarks. The model has been referred to as the chiral unitary model. Within this model, we study the flavor SU(3) breaking effect at the interaction level. An interesting two-pole structure of the Λ(1405) resonance is stud- ied through the production reactions in order to clarify the structure in experiments. The amplitude of the chiral unitary model enables us to extract various coupling constants of the generated resonance. Using this method, we calculate the magnetic moments of the N(1535) resonance and K∗ vector meson coupling to the Λ(1520) resonance. The Θ+ baryon has strangeness S = +1. Therefore the minimal number of quarks to construct the Θ+ is five, which is manifestly exotic. We study a K induced reaction to de- termine the Θ+ quantum numbers in experiments. Inspired by the πKN molecule picture, we estimate the two-meson clouds around antidecuplet baryons using phenomenological in- teraction Lagrangians based on flavor SU(3) symmetry. A possibility of spin 3/2fortheΘ+ is examined in the 8-10 representation mixing scheme, analyzing the SU(3) relations for the mass spectra and the decay widths of known baryon resonances. This scheme is extended to determine two-meson couplings of the Θ+. The resulting interactions are applied to the meson-induced productions of the Θ+. iv Contents I Introduction and review 1 1 Introduction 3 1.1Hadronicdescriptionofexotics.......................... 3 1.2Baryonresonancesinchiralunitarymodel.................... 5 1.3Pentaquarks..................................... 6 2 Effective field theory and symmetries 9 2.1Quantumchromodynamics............................ 9 2.2Introductiontoeffectivefieldtheory....................... 10 2.3SymmetriesofQCDLagrangian.......................... 11 2.3.1 Chiralsymmetry.............................. 11 2.3.2 Spontaneouschiralsymmetrybreaking.................. 12 2.3.3 Flavorsymmetryandexplicitsymmetrybreaking............ 13 2.4Chiralperturbationtheory............................. 14 2.4.1 Mesonsystem................................ 14 2.4.2 Meson-baryonsystem........................... 18 3 Overview of pentaquarks 21 3.1Researchesbeforethefirstevidence........................ 21 3.2Experiments..................................... 23 3.2.1 Evidences for the Θ(uudds¯)state..................... 24 3.2.2 Restrictiononthedecaywidth...................... 28 3.2.3 Searchesforotherexoticcandidates................... 30 3.2.4 Negative results for the Θ+ and interpretation of experimental results 31 3.3Theoreticalstudiesonreactionmechanism.................... 33 3.3.1 Photoproduction.............................. 33 3.3.2 Hadron-inducedreactions......................... 36 3.3.3 Highenergyreaction............................ 37 v Contents 3.3.4 Otherstudiesonreactionmechanisms.................. 38 3.4Analysisbasedonthesymmetryprinciple.................... 39 3.4.1 Flavorsymmetry.............................. 39 3.4.2 Chiralsymmetry.............................. 40 3.4.3 Large Nc analysis.............................. 40 3.5Chiralsolitonmodels................................ 41 3.5.1 RigidrotatorquantizationinflavorSU(3)................ 41 3.5.2 Predictionsandrelatedstudies...................... 43 3.5.3 Skyrmionmodel.............................. 45 3.5.4 Othercalculations............................. 46 3.6Constituentquarkmodels............................. 48 3.6.1 Generalfeaturesandinteractions..................... 48 3.6.2 Hyperfineinteractionsinfive-quarksystem............... 49 3.6.3 Quarkcorrelations............................. 50 3.6.4 Diquarkeffectivemodels.......................... 52 3.6.5 Calculationsinquarkmodels....................... 53 3.7Othermodelsandapproaches........................... 55 3.7.1 Hadronicmolecule............................. 55 3.7.2 Fluxtubepicture.............................. 56 3.7.3 Miscellaneousstudies............................ 57 3.8 In-medium properties and Θ+ hypernuclei.................... 58 3.9QCDsumruleapproaches............................. 60 3.9.1 Mass of spin 1/2Θ+ state......................... 61 3.9.2 Studiesforotherpentaquarks....................... 62 3.9.3 Estimationofcouplingconstants..................... 62 3.10LatticeQCDsimulation.............................. 63 3.10.1Massofthepentaquarkstates....................... 63 3.10.2Pentaquarkpotential............................ 66 II Baryon resonances in chiral unitary model 69 4 Chiral unitary model and flavor SU(3) breaking effect 71 4.1Introduction..................................... 71 4.2Formulationofchiralunitarymodel....................... 72 4.2.1 Kernelinteraction............................. 73 vi T. Hyodo (Ver:2.1, August 10, 2006) Contents 4.2.2 UnitarizationoftheamplitudebytheN/Dmethod........... 74 4.3Calculationwithacommonsubtractionconstant................ 77 4.3.1 Subtraction constants in the SU(3) limit . .......... 77 4.3.2 The S = −1 channel (KN¯ scattering).................. 78 4.3.3 The S = 0 channel (πN scattering).................... 81 4.4Resonancesinthescatteringamplitude..................... 83 4.4.1 Generalbehavioroftheamplitude.................... 83 4.4.2 PolesinthesecondRiemannsheet.................... 84 4.5FlavorSU(3)breakinginteractions.......................
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