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L(1405) の光発生反応

L(1405) の光発生反応. Prog . Theor . Exp. Phys. (2014) 023D01. 中村　聡　（阪大理）. 共同研究者：　慈道　大介 ( 首都大）. Introduction. L(1405) : 1st excited state of L. 1330. Alston et al., PRL 6 (1961). 1430. K - p  pppS. E. (MeV). _. pS. K N. (1405, -25). L(1405).

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L(1405) の光発生反応

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  1. L(1405)の光発生反応 Prog. Theor. Exp. Phys. (2014) 023D01 中村　聡　（阪大理） 共同研究者：　慈道　大介 (首都大）

  2. Introduction L(1405) : 1st excited state of L 1330 Alston et al., PRL 6 (1961) 1430 K -ppppS E (MeV) _ pS KN (1405, -25) L(1405) * Existence “predicted” by Dalitz and Tuan (1960) in analysis of KN scattering length with KN-pSmodel * First experimental evidence in K -ppppS(1961) _ _

  3. Too light to interpret as naïve 3-quark state Controversial L(1405) structure • 3-quark + mass splitting term Collins & Georgi, PRD 59 (1999) • Schat et al., PRL 88 (2002) • 5-quark Strottman, PRD 20 (1979) • Zou, NPA 835 (2010) • too many states • Meson-baryon molecule Dalitz & Tuan, PRL 2(1959) • Oset & Ramos, NPA 635(1998)

  4. L(1405) as pole of Scattering amplitude Coupled-channel scattering equation for T-matrix (scattering amplitude) (i,j,k: meson-baryon channel) T-matrix for real energy W is used to calculate observables (cross sections, etc.) Analytic continuation to complex energy W Near pole position : Resonance is identified by : mass width Resonance pole can be extracted from analyzing data

  5. Why want to know L(1405) pole(s) ? • Internal structure of L(1405) • constraint on hadron structure models • Nuclear structure of deeply bound kaonic nuclei (e.g., K-pp) • K-p - pSamplitude is essential input • current status for K-pp : rather large model dependence • B.E. = 10 – 100 MeV, Width = 35 – 110 MeV

  6. Pole structure of L(1405) • Two-pole cloudy bag model Veit et al. PRD 31, 1033 (1985) chiral unitary model Jidoet al. NPA 725, 181 (2002) • Single-pole potential models Fink et al., PRC 41, 2720 (1990) Akaishi-Yamazaki model PRC 65, 044005 (2002) Still, pole structure has not been established

  7. Ideal experiment p S p S Attempt to determine L(1405) pole from data 1330 1430 E (MeV) _ pS KN (1405, -25) L(1405) Impossible ! difficulty in determining L(1405) pole structure Two-meson production experiment K+ g, p } p Energy at L(1405) N S

  8. How to extract L(1405) pole from two-meson production data • Construct a model that consists of production mechanism + final state interaction (FSI) • FSI contains MB p S amplitude • Fit data with adjustable parameters in production mechanism and MB  p S amplitude • Extract poles from MB  p S amplitude But, good data had not been available until recently

  9. Photo-production of L(1405) gp  K+ L(1405)K+p S • LEPS/Spring-8 Ahnet al., NPA 721, 715 (2003) • LEPS/Spring-8 Niiyama et al., PRC 78, 035202 (2008) • CLAS/JLabMoriya et al., PRC 87, 035206 (2013) (p S invariant mass distribution) PRC 88, 045201 (2013) (K+ angular distribution) Experiments

  10. p S line-shape data from CLAS/JLab gp  K+ L(1405)K+p S Moriya et al., PRC 87, 035206 (2013) Cleanest data for L(1405) progress toward pole extraction

  11. What to do here ? • Production mechanism + s-wave rescattering • Gauge invariance at tree level • Fit data Develop cUM-based model for gp  K+ p S

  12. MODEL • Chiral unitary model • Photo-production mechanism

  13. Chiral Unitary Model (cUM) Oset& Ramos, NPA (1998) Oset et al., PLB (2002) Coupled-channel scattering equation : Weinberg-Tomozawa interaction

  14. Chiral Unitary Model (cUM) (W : total energy) _ On-shell factorization (m : renormalization scale ) Dimensional regularization Subtraction constant, fitted to data

  15. Chiral Unitary Model (cUM) _ Good description of K-p  KN, pS, pLdata above and near K-p threshold

  16. Chiral Unitary Model (cUM) Two-pole structure Jido et al. NPA 725, 181 (2002) 1390 - 66i 1426 - 16i pS2.9 1.5 KN 2.1 2.7 pole position Coupling strength -

  17. Photo-production Model Minimal substitution

  18. Photo-production Model Minimal substitution

  19. Photo-production Model Minimal substitution

  20. Photo-production Model

  21. Photo-production Model Rescattering cUMs-wave amplitude ( L(1405) )

  22. Fit data • Subtraction constants (10 parameters) • contact production mechanism (30 parameters) (total energy (W) dependent complex couplings, gauge invariant) • Form factors (1 parameters)

  23. Results * Good description of line-shape data * Different peak position for different charge states  Two-pole structure plays a role ??

  24. Resonant and non-resonant contributions Non-resonant Resonant

  25. Resonant and non-resonant contributions • * Significant non-resonant contribution •  Shifting peak positions • Same resonance peak position •  2nd pole (1426– 16i) seems dominant •  Single-pole model works as well ??

  26. Isospin decomposition • I=0 (L(1405)) dominance • Small but nonnegligible effect of I=2 contribution

  27. Single Breit-Wigner model Single Breit-Wigner model works ! 1 pole solution is still not excluded

  28. K+ angular distribution New data from CLAS/JLab for gp K+ p S Moriya et al, PRC 88, 045201 (2013) Fitting only lineshape very different angular distributions is still possible  K+ angle data are important to constrain production mechanism

  29. K+ angular distribution (not fitted) • Overall trend is captured in our model • More fit will be done • L(1405)pole structure will be extracted

  30. Summary • Pole structure of L(1405)has not been well confirmed by data • New CLAS data forgp  K+ p S ; cleanest data in L(1405) region  hope to extract L(1405)pole structure • gp  K+ p S model is developed with cUM amplitude -- meson-exchange + contact production mechanism (gauge invariant @ tree level) -- Line-shape data are well fitted -- Single Breit-Wigner model also can fit line-shape data

  31. Future work • Fit K+angle data from CLAS cUM amplitude (subtraction constant) is also varied  extraction of L(1405)pole structure • Use different contact interactions, form factors  study model dependence of extracted poles

  32. Future work One- or two-pole structure ? Very new data from CLAS (yesterday) for electroproduction of L(1405) PRC 88, 045202 (2013) 1.6 (GeV/c)2 < Q2 < 3.0 (GeV/c)2 • Fairly clear two peaks ! • two-pole solution ? • Higher statistics data hoped !

  33. Possible ideas for L(1405)photoproduction experiments at ELPH, LEPS, LEPS2 Data wanted for less model-dependent determination of L(1405) properties • Double-differential cross sections • Polarization observable • Multi-channel data • K*, S*(1385) unsubtracted data (cf. CLAS data) gp K+p S K+K N K+p L … -

  34. Backups

  35. Attempt to determine pole structure of L(1405) Confront theory with data below KN threshold • p-p K0L(1405) K0 p S Thomas et al., NPB 56, 15 (1973) • K-p p0L(1405) p0 p0 S0 • Crystall Ball, PRC 70, 034605 (2004) • K-d nL(1405) n p S J-PARC proposal Hadron beam experiments

  36. cUM-based calculation for p-p K0p S Hyodo et al., PRC 68, 065203 (2003) p- K0 p … Data: Thomas et al., NPB (1973)

  37. cUM-based calculation for K-p p0 p0 S0 Magas et al., PRL 95, 052301 (2005) d s/d MI(arbitrary scale) + the peak is due to second pole Data: Crystall Ball, PRC (2004)

  38. K+ angular distribution Very new data from CLAS/JLab for gp K+ p S Moriya et al, arXiv:1305.6776

  39. LEPS/SPring8 data Niiyama et al., PRC (2008) Forward K+ kinematics of gp K+Y* Comparison with CLAS data for gp  K+Y* (Moriya et al, arXiv:1305.6776) • CLAS • LEPS • LEPS and CLAS data are consistent at low energies • No LEPS data for normalized line shape for gp  K+ p S •  We analyze only CLAS data

  40. Lagrangians

  41. fixed by V gMdecay width; relative phase by SU(3) Hidden local symmetry model

  42. Tensor coupling SU(3) relation for magnetic coupling

  43. Niiyama et al., PRC (2008) Nacher et al., PLB (1999) Nacher et al., PLB 455, 55 (1999) • Calculated line shape is : • Wrong in ordering p-S+ and p+S- • Too small cross section ?

  44. P-wave scattering model(cUM) Jido et al., PRC 66, 055203 (2002) + (relativistic correction to WT term)

  45. Is L(1405) exotic ? Naïve 3-quark picture is not likely Nucleon (1/2+) N(1535) (1/2- ) 940 MeV 1535 MeV Radial excitation to L=1 costs ~ 600 MeV L(1405) (1/2-) L (1/2+) 1116 MeV 1405 MeV ~ 300 MeV

  46. cUM-based calculation for gp K+ p S Nacher et al., PLB 455, 55 (1999) W=2.02 GeV

  47. L(1405) in Lattice QCD operator M L(1405) Quench 3-quark ~ 1.7 GeVNemotoet al., PRD (2003) Quench 5-quark ~ 1.89 GeVIshii et al., PTP (2007) Full 3-quark ~ 1.6 GeV Takahashi et al., PRD (2010) Full 3-quark ~ 1.45 GeV Menadue et al., PRL (2012) (variational analysis)

  48. cUM-based calculation for gp K+ p S Nacher et al., PLB 455, 55 (1999) Contact photo-production (WT term) + s-wave cUMrescattering

  49. Comparison with CLAS data Nacher et al., PLB (1999) W=2.02 GeV • Calculated line-shape is : • wrong in ordering • p-S+ and p+S- • Overestimate in magnitude K. Moriya et al.PRC (2013)

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