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

Kaon absorption??(Magas et al.)

Kaon absorption??(Magas et al.)

1. Motivation1. Motivation

Our Our InvestigationInvestigation We investigate the possible We investigate the possible

[KNN][KNN](I=1/2,J=0)(I=1/2,J=0) 3-body resonance 3-body resonance state.state.

PP

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 We expect most strong attractive interactionmost strong attractive interaction in this in this configure.configure.

L=0 (s-wave interaction)

-> Coupled channel Faddeev equation-> Coupled channel Faddeev equation

Solve

-> KNN 3-body resonance-> KNN 3-body resonanceFind

Meson-Baryon interactionMeson-Baryon interaction

2. Formalism2. Formalism

We employ the dipole form factor.

Cut-off parameterCut-off parameter

-> fit scattering length (Kaonic hydrogen, Martin’s analysis)

Chiral effective LagrangianChiral effective Lagrangian

AGS equation for 3-body AGS equation for 3-body amplitudeamplitude

Eigenvalue equation for Fredholm kernelEigenvalue equation for Fredholm kernel

Pole of 3-body Pole of 3-body amplitudeamplitude

spectator energyspectator energy

3. Numerical 3. Numerical ResultsResults

KN amplitude bellow threshold

WKN (MeV)

2-body T-matrix in the 3-body 2-body T-matrix in the 3-body systemsystem 　　 :spectator

energy

How this attractive KN interaction How this attractive KN interaction contributes to 3-body binding system contributes to 3-body binding system is determined by solving dynamical 3-body eq. directly!!is determined by solving dynamical 3-body eq. directly!!

-44.9-i21.0 (MeV)-44.9-i21.0 (MeV)

-59.2-i15.9 (MeV)-59.2-i15.9 (MeV)

4. Summary4. 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 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(Wpolepole = -59.2-i15.9 MeV using relativistic kinematics) = -59.2-i15.9 MeV using relativistic kinematics)

Future worksFuture works

φ : Meson field , B : Baryon field

=

2-body Meson-Baryon Potential

Yamaguchi type NN interaction

attractiverepulsive

We take an attractive term only.

phas

e sh

ift (

degr

ee)

TLab

Strong attraction!?

repulsive

attractive

attractive only

Formal solution of AGS equation

Fredholm type kernel

Eigenvalue equation for Fredholm kernel

Formal solution for 3-boby amplitude

・ Pearce and Gibson PRC 40 902.

2-body scattering term

Complex q Complex q planeplane

Pole of scattering state

Pole of resonance state

=Pole of resonance state

Physical Physical branchbranch

Unphysical Unphysical branchbranch

Singularity of tau

-> Logarithmically singularity

1 particle exchange term