1. Table of contents 1. Motivation 2. Formalism (3-body equation) 3. Results (KNN resonance state) 4. Summary Table of contents 1. Motivation 2. Formalism (3-body equation) 3. Results (KNN resonance state) 4. Summary

2. Kaon absorption?? (Magas et al.) Kaon absorption?? (Magas et al.) 1. Motivation

3. Our Investigation We investigate the possible We investigate the possible [KNN] (I=1/2,J=0) 3-body resonance state. [KNN] (I=1/2,J=0) 3-body resonance state. P P K-K- K - pp system S=-1, B=2, Q=+1 We consider s-wave 3-body KNN state. We consider s-wave 3-body KNN state. We expect most strong attractive interaction We expect most strong attractive interaction in this configure. in this configure. L=0 (s-wave interaction) -> Coupled channel Faddeev equation Solve -> KNN 3-body resonance Find

4. Meson-Baryon interaction 2. Formalism We employ the dipole form factor. Cut-off parameter -> fit scattering length (Kaonic hydrogen, Martin’s analysis) Chiral effective Lagrangian

5. AGS equation for 3-body amplitude Eigenvalue equation for Fredholm kernel Pole of 3-body amplitude

6. spectator energy 3. Numerical Results KN amplitude bellow threshold W KN (MeV) 2-body T-matrix in the 3-body system 2-body T-matrix in the 3-body system :spectator energy How this attractive KN interaction contributes to 3-body binding system is determined by solving dynamical 3-body eq. directly!!

7. -44.9-i21.0 (MeV) -59.2-i15.9 (MeV)

8. 4. Summary The pole position strongly depends on KN interaction. The pole position strongly depends on KN interaction. -> form factor (dipole -> monopole) -> form factor (dipole -> monopole) -> explicit resonance model (3-quark ) -> explicit resonance model (3-quark ) Effects of kaon absorption (p-wave interaction) Effects of kaon absorption (p-wave interaction) We solve 3-body equation directly. We can find the resonance pole We can find the resonance pole in the and energy plane. in the and energy plane. (W pole = -59.2-i15.9 MeV using relativistic kinematics) (W pole = -59.2-i15.9 MeV using relativistic kinematics) Future works

10. φ : Meson field, B : Baryon field = 2-body Meson-Baryon Potential

12. Yamaguchi type NN interaction attractive repulsive We take an attractive term only. phase shift (degree) T Lab Strong attraction!? repulsive attractive attractive only

14. Formal solution of AGS equation Fredholm type kernel Eigenvalue equation for Fredholm kernel Formal solution for 3-boby amplitude

15. ・ Pearce and Gibson PRC 40 902. 2-body scattering term Complex q plane Pole of scattering state Pole of resonance state = Physical branch Unphysical branch Singularity of tau

16. -> Logarithmically singularity 1 particle exchange term