1. Yoichi Ikeda (Osaka Univ.) in collaboration with Hiroyuki Kamano (JLab) and Toru Sato (Osaka Univ.) Introduction Introduction Our model of KN interaction Our model of KN interaction Coupled-channel Faddeev equations Coupled-channel Faddeev equations Numerical Results Numerical Results Summary Summary Introduction Introduction Our model of KN interaction Our model of KN interaction Coupled-channel Faddeev equations Coupled-channel Faddeev equations Numerical Results Numerical Results Summary Summary The resonance pole of strange dibaryon in KNN – pYN system

2. Introduction Introduction KN interaction in isospin I=0 channel Strong attraction The L (1405) resonance  Quasi-bound state of KN state  CDD pole coupling with mesons  Multi-quark state  Quasi-bound state of KN state  CDD pole coupling with mesons  Multi-quark state KN - pS coupled system KNpS L(1 405) Strange dibaryon resonance KNNpSN KNN - pSN(?) KNN – pYN coupled system

3. Introduction Introduction  Two poles on KN physical and pS unphysical sheet (chiral unitary model) taken form Jido et al. NPA725 (2003). taken form Hyodo and Weise. PRC77 (2008). Structure of the L (1405) Structure of strange dibaryon

4. We investigate We investigate possible strange dibaryon resonance poles. S=-1, B=2, Q=+1 J π =0 - (3-body s-wave state) We consider s-wave state. We consider s-wave state. We can expect most strong attractive interaction We can expect most strong attractive interaction in this configure. in this configure. L=0 (s-wave interaction) N K N Introduction Introduction

5. Potential derived from Weinberg-Tomozawa term F : Meson field, B : Baryon field Chiral effective Lagrangian … on-shell factorization Our model of KN interaction Our model of KN interaction

6. Unitarized by Lippmann-Schwinger equation Unitarized by Lippmann-Schwinger equation Our model of KN interaction Our model of KN interaction E-dep. potential Cutoff parameters

7. Our model of KN interaction Our model of KN interaction Poles of the amplitude Poles of the amplitude (KN bound state) 1428.8-i15.3(MeV) (pS resonance) 1344.0-i49.0(MeV) Hyodo, Weise PRC77(2008). Consistent with chiral unitary model (coupled-channel chiral dynamics)

8. Faddeev Equations  W : 3-body scattering energy  i(j) = 1, 2, 3 (Spectator particles)  T(W)=T 1 (W)+T 2 (W)+T 3 (W) (T : 3-body amplitude) t i (W, E(p i )) : 2-body t-matrix with spectator particle i  t i (W, E(p i )) : 2-body t-matrix with spectator particle i  G 0 (W) : 3-body Green’s function (relativistic kinematics)  W : 3-body scattering energy  i(j) = 1, 2, 3 (Spectator particles)  T(W)=T 1 (W)+T 2 (W)+T 3 (W) (T : 3-body amplitude) t i (W, E(p i )) : 2-body t-matrix with spectator particle i  t i (W, E(p i )) : 2-body t-matrix with spectator particle i  G 0 (W) : 3-body Green’s function (relativistic kinematics)

9.  W : 3-body scattering energy  i(j) = 1, 2, 3 (Spectator particles)  Z(p i,p j ;W) : Particle exchange potentials  t (p n ;W) : Isobar propagators Faddeev equation with separable potentials Faddeev equation with separable potentials i j i j = X ij i j tntntntn + n Alt-Grassberger-Sandhas(AGS) Equation

10. KNN-pYN coupled-channel system KNN-pYN coupled-channel system Alt-Grassberger-Sandhas(AGS) Equation i j i j = X ij i j tntntntn + n : 1-particle exchange term π Σ,Λ N N K N N K N π Σ,Λ N π Σ,Λ N

11. NN potential -> Two-term separable potential Attraction Repulsive core X ij Two-body potentials –NN interaction- Two-body potentials –NN interaction- N N K NN

12. Two-body potentials – pN interaction- Two-body potentials – pN interaction- X ij Σ,Λ π N pNpNpNpN E-dep. potential I=1/2I=3/2 L=500 (MeV) Scattering length

13. YN potential -> One-term separable potential X ij Σ,Λ π N YN Two-body potentials –YN interaction- Two-body potentials –YN interaction- I=1/2 I=3/2 Scattering length Torres, Dalitz, Deloff, PLB174 (1986).

14. Pole of the AGS amplitudes Pole of the AGS amplitudes W pole = -B –iG/2 Eigenvalue equation for Fredholm kernel three-body resonance pole at W pole Formal solution for three-boby amplitudes Fredholm kernel

15. Possible singularities of the amplitudes Possible singularities of the amplitudes  Z(p i,p j ;W) : Particle exchange potentials  t(p n ;W) : Isobar propagators We search for three-body resonance poles on KNN physical, pYN unphysical, and “………” sheet.

16. Numerical results Numerical results

17.  We construct the model of energy-dependent KN interaction. (chiral unitary approach)  We solve the Faddeev equations. ： We found two poles of strange dibaryon. ： We found two poles of strange dibaryon. ： -B-i G/2 = (-13.7-i29.0, -37.2-i93.3) MeV ： -B-i G/2 = (-13.7-i29.0, -37.2-i93.3) MeV  Pole I -> KNN physical, pYN unphysical, L*N physical sheet  Pole II -> KNN physical, pYN unphysical, L*N unphysical sheet Summary Summary Future Future reaction This production mechanism will be investigated by LEPS and CLAS collaborations. @SPring8, Jlab