1. 少数体ケイオン核の課題
August 7, 2008
Y. Akaishi
T. Yamazaki, M. Obu, M. Wada

2. Super strong nuclear force
Super strong nuclear force
Revival of
Heitler-London-Heisenberg picture
K-pp as decaying state

3. KbarN scattering amplitude
T. Hyodo and W. Weise, Phys. Rev. C 77 (2008)
Effective KbarN interaction based on chiral SU(3) dynamics
Akaishi-Yamazaki
Chiral Im
1420

4. Chiral unitary model L = 630 MeV/c Weinberg- Tomozawa Virtually
Unitarized
L = 630 MeV/c
Virtually
Resonance / bound states

5. Step form factor and resonance width
VWT
　M. Obu
L = 630 MeV/c iL
Potential
Slow damping
Rapid oscillation
kR+ikI
Resonance
High excitation
Narrow width

6. Wave function of L(1405) Effective local K-p potential rms r KE PE
r [fm]
SC i16
SC i20
G i20
rms r KE PE
[fm] [MeV] [MeV]
Effective local K-p potential
[MeV]
Imaginary
Real

7. Dimensional regularization
Feynman's identity
Analytic continuation
Wick rotation
Laurent expansion
Regularization

8. Two-step cutoff potential model
Step function
m =140 MeV/c, M =1189 MeV/c
Loop integral
Non-relativistic reduction of G4Dim
-0.6 for M=1189 MeV/c
-1.0 for M= 800 MeV/c
with m = 630 MeV/c & a(m)=-1.96

9. Trajectory of pS poles as a function of s22
K + N _
s22
E=0
Im E
Re E
-1.6
-2.0
-1.0
s22= -0.6
-200 MeV
-0.4
-100 MeV
"Shape"
resonance
L(1405)
Bound state
Anti-resonance / virtual state
[ + ] sheet
pS physical
Feshbach
-1.3
-1.2
-0.8 x
Poles which characterize
the potential shape
Re k
Im k m
m =270 MeV/c2
[ - ] sheet
pS unphysical

10. p+ p + S p+ p+ p L* L* p S TSp,Sp S TSp,NK S+(1660) K- + p S+(1660)
R.J. Hemingway,
Nucl. Phys. B253 (1985) 742
Interference
MSp [MeV/c2]

11. S-p invariant-mass distributions
R.J. Hemingway
From K-4He atom
B. Riley et al.
Pseudo-invariant mass
T. Yamazaki & Y. Akaishi,
Phys. Lett. B 453 (1999) 1

12. P. Kienle, Y. Akaishi & T. Yamazaki, Phys. Lett. B 632 (2006) 187
S-p invariant mass / D-momentum distributions
P. Kienle, Y. Akaishi & T. Yamazaki, Phys. Lett. B 632 (2006) 187
1420 MeV/c2
1405 MeV/c2
with G = 40 MeV
Quasi-free
D-momentum [MeV/c]

13. S-p partial invariant-mass spectraY Y
S-p partial invariant-mass spectra
from stopped K- on 4He, 3He and D
S-wave abs.
1420 MeV/c2
1405 MeV/c2
with G = 40 MeV
MSp [MeV/c2]

14. Acknowledgements:
O. Morimatsu, K. Yazaki
Thank you very much!