Three-body resonance in the KNN-πＹN coupled system Y. Ikeda and T.Sato (Osaka Univ.) Table of contents 1. Motivation 2. Formalism (3-body equation) 3. Results (KNN resonance state) 4. Summary

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

Our Investigation P K- K-pp system S=-1, B=2, Q=+1 Jπ=0- We investigate the possible [KNN](I=1/2,J=0) 3-body resonance state. Λ(1405) -> the resonance in the KN-πΣ coupled channel system It will be very important to take into account the dynamics of KN-πΣ system in order to investigate whether KNN resonance may exist. -> Coupled channel Faddeev equation Solve -> KNN 3-body resonance Find P K- K-pp system S=-1, B=2, Q=+1 Jπ=0- (3-body s-wave state) We consider s-wave state. We expect most strong attractive interaction in this configure. L=0 (s-wave interaction)

2. Formalism 2-body Meson-Baryon Potential Chiral effective Lagrangian φ : Meson field , B : Baryon field

The ＫＮＮ-πΣＮ resonance NN散乱 反対称化を考慮 ＫＮＮ-πＹＮ 共鳴状態を理解するための全体の目標 本研究での枠組み->KN interaction に注目 : 1-particle exchange term π Ｎ Σ : 2-body scattering term KN-πY(I=0, 1) πN(I=1/2,3/2) NN散乱 反対称化を考慮

fit : Martin’s analysis and Kaonic hydrogen data Parameter fit Our parameter -> cut-off of dipole form factor fit : Martin’s analysis and Kaonic hydrogen data Non relativistic Relativistic I=0 (-1.70 + i0.68 fm) KN =946 MeV πΣ=988 MeV ------------------------ I=1 (0.72 + i0.59 fm) KN =920 MeV πΣ=960 MeV πΛ=640 MeV I=0 (-1.70 + i0.68 fm) KN =1095 MeV πΣ=1450 MeV ------------------------ I=1 (0.68 + i0.60 fm) KN =1100 MeV πΣ=850 MeV πΛ=1250 MeV

-> Fit to the scattering length and phase shift. πN scattering (S11 and S31) -> Fit to the scattering length and phase shift. (S11) (S31) Rel. Rel. Non-rel. Non-rel. Phys. Lett. B 469 (1999) 25. NN potential -> 2-term Yamaguchi type Phys. Rev. 178 (1969) 1597.

Pole of 3-body amplitude AGS equation for 3-body amplitude K, N,π KN-πＹ, NN, πN Eigenvalue equation for Fredholm kernel Pole of 3-body amplitude Wp = -B –iΓ/2 Similar to πNN, ηNN, K-d analyses.　　(Matsuyama, Yazaki, ……)

3. Numerical Results 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!! KN amplitude bellow threshold spectator energy WKN (MeV)

The pole trajectories of three-body system a:KN only b:+NN c:+πＹ in τ d:π exchange

The three-body resonance poles (other parameters) Rel. model -1.70-i0.68 fm Martin -1.60-i0.68 fm -1.70-i0.59 fm -1.80-i0.68 fm -1.70-i0.78 fm

Summary In the future We solve 3-body equation directly. We can find the resonance pole in the KNN physical and πΣN unphysical energy plane. (Wpole = -79.7-i36.4 MeV using relativistic kinematics) In the future The pole position strongly depends on KN interaction. -> Form factor (dipole -> monopole) -> Structure dependence on Λ(1405) Effects of kaon absorption (p-wave interaction)