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

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

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

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

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

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

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

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)

 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

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

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

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

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).

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

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.

Numerical results Numerical results

 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, i93.3) MeV ： -B-i G/2 = (-13.7-i29.0, 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 Jlab