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Table of contents 1. Motivation 2. Formalism (3-body equation)

Table of contents 1. Motivation 2. Formalism (3-body equation) 3. Results (KNN resonance state) 4. Summary. 1. Motivation. Kaon absorption?? (Magas et al.). K - pp system. P. P. S=-1, B=2, Q=+1. L=0 (s-wave interaction). Solve. K -. -> Coupled channel Faddeev equation.

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Table of contents 1. Motivation 2. Formalism (3-body equation)

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

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

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

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

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

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

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

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

  9. = 2-body Meson-Baryon Potential φ : Meson field , B : Baryon field

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

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

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

  13. 1 particle exchange term -> Logarithmically singularity

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