Yoichi Ikeda (Osaka Univ.) in collaboration with

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

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

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

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

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

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

8. Faddeev Equations • 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, E(pi)) : 2-body t-matrix with spectator particle i • G0(W) : 3-body Green’s function (relativistic kinematics)

9. Alt-Grassberger-Sandhas(AGS) Equation tn j i i i Xij = + Xij n j j • Faddeev equation with separable potentials • W : 3-body scattering energy • i(j) = 1, 2, 3 (Spectator particles) • Z(pi,pj;W) : Particle exchange potentials • t(pn;W) : Isobar propagators

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

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

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

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

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

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

16. Numerical results

17. Summary • We construct the model of energy-dependent KN interaction. (chiral unitary approach) • We solve the Faddeev equations. 　　　：We found two poles of strange dibaryon. 　　　：-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 • Future reaction This production mechanism will be investigated by LEPS and CLAS collaborations. @SPring8, Jlab