1. 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

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

3. 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)

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

6. 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

7. 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 ( i0.68 fm)
KN =946 MeV
πΣ=988 MeV
I=1 ( i0.59 fm)
KN =920 MeV
πΣ=960 MeV
πΛ=640 MeV
I=0 ( i0.68 fm)
KN =1095 MeV
πΣ=1450 MeV
I=1 ( i0.60 fm)
KN =1100 MeV
πΣ=850 MeV
πΛ=1250 MeV

9. -> 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.

10. 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, ……)

11. 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)

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

13. 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

14. 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 = 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)