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ハドロン分光 Hadron spectroscopy

ハドロン分光 Hadron spectroscopy. 構成クォークとメソンダイナミックス. 保坂　淳　 Hosaka, Atsushi, RCNP Osaka Univ. Contents. 1. General discussions Quark model Mathematical tool or realistic Quark excitation, minimal+qq, pentaquarks 2. Meson(s) in a baryon (1)Virtual, (2)Almost “real” mesons

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ハドロン分光 Hadron spectroscopy

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  1. ハドロン分光Hadron spectroscopy 構成クォークとメソンダイナミックス 保坂　淳　 Hosaka, Atsushi, RCNP Osaka Univ WS@KEK

  2. Contents 1. General discussions Quark model Mathematical tool or realistic Quark excitation, minimal+qq, pentaquarks 2. Meson(s) in a baryon (1)Virtual, (2)Almost “real” mesons 3. Multiquarks 4. Summary WS@KEK

  3. 1. General discussions WS@KEK

  4. QCD At high energies = Asymptotic freedom Success of perturbative QCD Quarks at deep inside hadrons are well understood At low energies = Infrared slavery • Quarks are confined • Hadron masses (~1 GeV) >> Quark masses (~10 MeV) • Chiral symmetry is spontaneously broken WS@KEK

  5. Scale Energy scale of hadrons is similar to that of nuclei Thus Hadron structure is very important to (Hyper) Nuclei Historically: Constituent quark model seems to work well WS@KEK

  6. Quark model Convenient method for flavor & spin symmetry SU(3) SU(2) WS@KEK

  7. • Success of Gell-Mann Okubo mass formula • Magnetic moments Minimal Anomalous D/(F+D) ratio of SU(6) = 3/5 = 0.6 fit ~ 0.58 So far quarks are convenient tool for realization of SU(3)/SU(6) algebra WS@KEK

  8. Lattice calculation for mBB Erkol-Takahashi-Oka, 0805.3068[hep-lat] D/(F+D) = 0.616 ~ 0.6 WS@KEK

  9. Constituent quarks seem at work for qq and qqqground states minimal What about other states? • Quark excitation (single particle levels) • Minimal + qq • Multiquarks genuinenonminimal, tetra, penta, … WS@KEK

  10. Excitation of a quark Effective dynamical degrees of freedom Realistic Excited Ground R R WS@KEK

  11. • Measured from the ground state • 8MS states are shifted downward by 200 MeV Positive parity baryons Takayama-Toki-Hosaka, PTP101, 1271(1999) WS@KEK

  12. Negative parity baryons WS@KEK

  13. の第１励起状態が軽すぎる (1405)が軽すぎる 負パリティー状態にばらつきがある 光の結合もよくわかっていない（東北） S11(1535, 1650), D13(1520, 1700) WS@KEK

  14. Minimal + qq ~ m, m 1/0.5 ~ 400 MeV WS@KEK

  15. Minimal + qq ~ m, m 1/0.5 ~ 400 MeV  Penta(multi)quark But Nonmimimal Constituent model WS@KEK

  16. For one quanta (hbar omega) ~ one qq pair (0+), a1(1+) … mesons 1/2–, 3/2–, … baryons WS@KEK

  17. Virtual mesons • Neutron charge radius • Nuclear force • Nucleon spin l = 0 l = 1 l = 0 WS@KEK

  18. Almost real mesons m m E,a q* M M Free Correlated E* EB E(m+M) WS@KEK

  19. Open channels P-wave S-wave GeV N(1710) K N(1650) K  N(1535) (1520) N 1.5 N(1440) KN (1405)  (1232) N 1 N(940) WS@KEK

  20. 2. Meson(s) in a baryon 2-1. Virtual mesons A problem in Photoproduction N -> K Ozaki-Nagahiro-Hosaka Phys.Lett.B665:178-181,2008. e-Print: arXiv:0710.5581 [hep-ph] WS@KEK

  21.  N Y, Q, … A problem in Photoproduction N -> K Effective Lagrangian approach K*-exchange Too strong? WS@KEK

  22. Strong K* ? Bennhold et al. NPA695 (2001) 237 Also discussed by Guidal et al. NPA627 (1997) 645 WS@KEK

  23. + Magnetic – Electric = g Asymmetry K Magnetic Electric K* K WS@KEK

  24. + Magnetic – Electric = SU(3) g Asymmetry K Magnetic Electric K* K LEPS data Sumihama et al. PRC73,035214 (2006) WS@KEK

  25. WZW induced process Meson clouds g K WZW term • Strength is determined by QCD • Contains => Magnetic • Triangle can not be K* • Energy dependent, raising p K p L Actual computation (Ozaki) Covariant loop integral Cutoff ~ 1 GeV WS@KEK

  26. Asymmetry 0.5 0 LEPS data, Sumihama et al – 0.5 1 0.9 0.8 0.6 0.7 WS@KEK

  27. g K p K p L g K As energy is increased p K p 2-2. Almost real mesons WS@KEK

  28. Dynamically generated resonance Weakly bound system of mB Example: (1405) and N(1535) WS@KEK

  29. KN- scattering for (1405) Oset and Ramos, NPA635, 99 (1998) Chiral Unitary model S-channel unitarity Approx. cross. symm. + • • • + + V V G V V G V G V 散乱方程式を解く • Input V and • Suitably renormalize G(√s) WS@KEK

  30. V: WT interaction Contact, S-wave WS@KEK

  31. G(√s): Loop function G is divergent for the contact interactionVWT a-parameter, subtraction constant is chosen suitably => apheno WS@KEK

  32. Mass spectrum  Oset and Ramos, NPA635, 99 (1998) K–p) ) WS@KEK

  33. pS -> pS KN -> pS Two poles Jido-Oller-Oset-Ramos-Meissner, Nucl.Phys.A725:181-200,2003: nucl-th/0303062 Im Re 1426 + 16i (KN) 1390 + 66i (pS) WS@KEK

  34. 疑問: メソンとバリオンの成分だけで記述できるか 他の成分（３ｑ）は要らない？ WS@KEK

  35. To answer these questions: We use the ambiguity (a-parameter) in G(E) a-parameterの決め方 データ から決める WS@KEK

  36. Determination of anatural (2) (1) Thereshold m WS@KEK

  37. (1) Physics of MB scattering (2) Boundary condition (matching) Near the threshold Choose this point at  = M for LET WS@KEK

  38. aphenoneqanatural How to interpret the difference WS@KEK

  39. Modify the interaction • The deviation from the natural value (different a) is absorbed into the interaction as a pole term (1) of mass Meff and (2) of higher order • If a is small (close to natural), Meff –> large a is large (different from natural), Meff ~ MT WS@KEK

  40. (1405) N(1535) with realistic parameters Coupled channel S = -1, I = 0 Channel i is a matrix equation. Pole in √s are complex. j i WS@KEK

  41. Subtraction constants (1405) N*(1535) For S =-1 (~(1405)), apheno ~ anaturalMeff ~ 8 GeV For S = 0 (~N(1535)), apheno ≠anatural Meff ~ 1.6 GeV WS@KEK

  42. Full Pole Couplings of N*(1535) Full amplitude = Pole + Dynamical (phenomenological) (Meson Cloud) = + Dynamical WS@KEK

  43. 4. Multiquarks WS@KEK

  44. 4. Multiquarks • Large impact on hadron physics • New form of matter • Very difficult to observe and predict (and explain) Maybe as difficult as solving the problems of QCD? • So far candidates are 1(1400, 1600, 2000) ~ can be hybrid +(1520), Z+(4430) WS@KEK

  45. Pentaquarks  n → K–+ LEPS (Nakano et al) exp. SPring-8, 2002 Q = + 1, S = +1 => Minimally 5 quarks In the quark model M ~ 1.7 MeV, Fall apart width ~ very wide Fall apart BUT exp M ~ 1.52 MeV, Width ~ very narrow < ~10 MeV WS@KEK

  46. 2003 Current status Exp: • Many positive results until ~ 2004 • Many negative results appear CLAS WS@KEK

  47. 2003 Current status Exp: • Many positive results until ~ 2004 • Many negative results appear CLAS The peak here disappears in 2006 PRL 97, 032001 WS@KEK

  48. New LEPS exp Deuteron target • Fermi motion => Minimal momentum prescription • Optimal  cut • No reflection from (1520) WS@KEK

  49. Tohoku N*(1675) neutron proton WS@KEK

  50. Theory Accumulated properties of  in various models • No explanation everybody agrees • Chiral soliton model can predict the mass and width JP = 1/2+ • In the quark model, JP = 3/2– is likely, but light mass seems difficult to explain Color singlet vs. colored correlations Must be in multiquarks states WS@KEK

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