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
 We investigate the possible
[KNN](I=1/2,J=0) 3-body resonance state.
Λ(1405)
P
-
-> the resonance
K pp system
P
in the KN-πΣ coupled channel system
L=0 (s-wave interaction)
 It will be very important
S=-1, B=2, Q=+1
π
-
J =0
(3-body
s-wave state)
to take into account
the dynamics of KN-πΣ
system
K
in order to investigate whether KNN resonance may exist.
Solve
 We consider
s-wave state.
-> Coupled
channel Faddeev
equation
 We expect
most strong
attractive
interaction
Find
in this configure.
-> KNN 3-body resonance
2. Formalism
2-body Meson-Baryon Potential
Chiral effective Lagrangian
φ : Meson field , B : Baryon field
The ＫＮＮ-πΣＮ resonance
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
Parameter fit
Our parameter
-> cut-off of dipole form factor
fit : Martin’s analysis and Kaonic hydrogen data
Non 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
Relativistic
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
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.
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
How
this
attractive
KN 3-body
interaction
2-body
T-matrix
in the
system
contributes to 3-body binding system
:spectator energy
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
 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)

K-中間子原子核研究の現状

Document 7287941

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