ストレンジ・ダイバリオンの 質量と崩壊幅の研究

1. ストレンジ・ダイバリオンの質量と崩壊幅の研究ストレンジ・ダイバリオンの質量と崩壊幅の研究 Y. Ikeda and T. Sato (Osaka Univ.) • KNN resonance (Recent theoretical progress) • Faddeev approach and variational approach • Numerical Results • Summary

2. KNN resonance -- Recent theoretical progress --

3. Large meson-baryon components -> S-wave resonance in the KN-pS coupled channel system (Chiral unitary model) • KNN resonance – L(1405) - Structure of L(1405) • Multi-quark state? • Bound state of KN? • Chiral SU(3) dynamics • It will be very important • to take into account the full dynamics of KN-pS system • in order to investigate whether KNN resonance may exist.

4. Phenomenological Chiral SU(3) KN interaction 3 body Method Variational Method (B, G) Akaishi, Yamazaki (48, 60)MeV Dote, Hyodo, Weise (17-23, 40-70)MeV Faddeev equation (B, G) Shevchenko et al. (55-70, 90-110)MeV Ikeda, Sato (45-80, 45-75)MeV • KNN resonance – Theoretical progress - • Faddeev equation -> Full dynamics of KNN-pSN system • Variational approach -> pSN system is effectively included.

5. Faddeev approach and Variational approach

6. Faddeev approach Faddeev Equation • W : 3-body scattering energy • i(j) = 1, 2, 3 (Spectator particles) • T(W)=T1(W)+T2(W)+T3(W) (T : 3-body amplitude) • ti(W) : 2-body t-matrix with spectator particlei • G0 : 3-body Green’s function (relativistic kinematics)

7. Alt-Grassberger-Sandhas(AGS) Equation tn j i i i Two-body t-matrix : Xij = + Xij n j j Separable potential : AGS and Faddeev eqs. are equivalent within separable potential model.

8. K K K K K K p ・・・ N N N N N S N • Faddeev approach v.s. Variational approach • Effective KN interaction Hyodo, Weise PRC77(2008). • Effective KN interaction in KNN system N -> Faddeev approach -> Variational approach At least, the spectator momentum is neglected in the pSN Fock space.

9. KN potential model Weinberg-Tomozawa interaction F: Meson field , B : Baryon field S-wave Weinberg-Tomozawa potential Coupling const. Form factor

10. K- p- p+ p S+(1660) L(1405) p S • Parameter fit (KN interaction) Our parameters -> cut-off of dipole form factor Fit 1 : L(1405) pole position given by Dalitz (Model Dalitz) Fit 2 : Hemingway’s experiment (Model Hemingway) NPB253, 742(1985) Invariant mass

11. Parameter fit (KN interaction) with assumption Dalitz and Deloff JPG17, 289 (1991)., Nacher et al., PLB461, 299 (1999).

12. Experimental data (total cross section) (I=0 channel) (I=1 channel)

13. Alt-Grassberger-Sandhas(AGS) Equation Eigenvalue equation for Fredholm kernel tn j i i i 3-body resonance pole at Wpole Xij = + Xij Wpole = -B –iG/2 j j Similar to πNN, ηNN, K-d analyses.(Matsuyama, Yazaki, ……) • Summary of our framework K, N KN-pY, NN

14. Numerical results

15. Dalitz (Approx.) Wpole=-42-i35 Hemingway (Approx.) Wpole=-32-i26 • The pole position of three-body KNN system KNN physical pYN unphysical sheet Dalitz Wpole=-67-i22 Hemingway Wpole=-47-i25

16. The reason of less binding energies Model Dalitz (W=-67 MeV) Model Hemingway (W=-47 MeV)

17. KN interaction dependences of KNN poles Model Dalitz Model Hemingway

18. Summary • We compare variational approach with Faddeev approach • by using the approximate 2-body KN amplitude. • We find the different pole energies • corresponding to KNN state for each approach. • KNN state becomes the bound state • as increasing KN interaction. In the future • reaction This production mechanism will be investigated by LEPS and CLAS collaborations. @SPring8, Jlab