1. Osaka Electro-Communication Univ.
Workshop on “Future Prospect of Hadron Physics at J-PARC and Large Scale Computation Physics”, IQBRC, Ibaraki, Feb. 9, 2012.
Kbar-(NN) equivalent local potential from Kbar(NN) - p(SN) coupled channel model
Takahisa Koike
RIKEN Nishina center
Toru Harada
Osaka Electro-Communication Univ.　 K- p
“K-pp”

2. Present Status of “K-pp” = [ Kbar×{NN} I=1 ] I=1/2
Theoretical calculations disagree with each other.
Experimental observations disagree with each other.
Theories and experiments disagree with each other.
Theory
YA: Yamazaki, Akaishi
SGM: Shevchenko, Gal, Mares
IS: Ikeda, Sato
DHW: Dote, Hyodo, Weise
IKMW: Ivanov, Kienle et al.
NK: Nishikawa, Kondo
AYO: Arai, Yasui, Oka
YJNH: Yamagata, Jido et al.
WG: Wycech, Green
Experiment
FINUDA
OBELIX
DISTO
pSN decay
threshold

3. J-PARC E15 experiment for searching “K-pp”
M. Iwasaki, T. Nagae et al. ,
3He(In-flight K-, n) “K-pp” missing-mass 　
at pK- = 1 GeV/c and qn=0o 　　 spectroscopy
　　　　　　　　　　　+　　　　
“K-pp”  Lp invariant-mass
spectroscopy
Simultaneous measurement
Our purpose: theoretical calculation of 3He(In-flight K-, n) inclusive/semi-exclusive spectra within the DWIA framework
using Green’s function method.
T. Koike & T. Harada, Phys. Lett. B652 (2007)
T. Koike & T. Harada, Nucl. Phys. A804 (2008)
T. Koike & T. Harada, Phys, Rev. C80 (2009) ~14.
c.f. J. Yamagata-Sekihara et al., Phys, Rev. C80 (2009)

4. ( ) Calculated results of inclusive spectrum A: DHW B: YA C: SGM
( )
Energy-dependent
potential
L = 0 component
Energy-independent
potential omitting
phase space factor
C: SGM
D2: FINUDA
pSN decay
threshold

5. Phenomenological K--”pp” effective potential
Phase space factor
pSN
pLN SN
E-dependence
f (E) = B1(pSN) f1S (E)
0.7
+ B1(pLN) f1L (E)
0.1
+ B2(YN) f2 (E)
0.2
Refs. J. Mares, E. Friedman, A. Gal, PLB606 (2005) 295.
D. Gazda, E. Friedman, A. Gal and J. Mares, PRC76 (2007)
　　 J. Yamagata, H. Nagahiro, S. Hirenzaki, PRC74 (2006)

6. “Moving pole” picture of spectrum shape
B: YA
C: SGM

7. Purpose of this talk In the KbarNN single-channel picture,
the phenomenological Kbar – (NN) effective potential
has been employed.
 “Moving pole” in complex E-plane
i.e. Energy-dependent Breit-Wignar
 Threshold effect e.g. cusp peak
Q: How to justify the energy dependence of
our phenomenological potential?
Purpose of this talk
Kbar – (NN) single-channel effective potential is derived from
Kbar(NN) – p (SN) coupled channel model.
 Find the conditions that the phenomenological potential
can be apply.　　　
Ref. T. Koike, T. Harada, arXiv: [nucl-th]

8. Kbar (NN) –p (SN) coupled-channel Green’s function
Channel 1 = Kbar(NN); assuming stiff “NN” core
Channel 2 = p (SN); assuming stiff “SN” core
Use the energy-independent Gaussian potentials
Imaginary parts W1 , W2 describe the effect of other decay
channels (pLN, YN).

9. Coupled-channel model
Single- vs. Coupled-channel DWIA calculation
Single-channel model
W0 is changed.
V0 = -360 MeV,
B = 0.8,
B = 0.2
(pSN)
(pY)
Coupled-channel model
V2 is changed.
V1 = -360 MeV,
VC = +100 MeV,
W1 = -10 MeV.

10. Derivation of equivalent local potential
Definition of equivalent local effective potential in channel 1 :
(1,1) component of coupled-channel Green’s function:
By comparing above two eqs.,
Multiplying wave function f 1(r’), and integrating over r’ ;
　　f 1(r’)  Kbar(NN) bound state wave function

11. Calculated results of Ueff
V1 = -300 MeV, Vc = +100 MeV, V2 = -150 MeV; W1 =W2= 0 MeV; b=1.09fm
(corresponding to YA)

12. ◆ Calculated results of Ueff
V1 = -350 MeV, Vc = +100 MeV, V2 = -150 MeV; W1 =W2= 0 MeV; b=1.09fm
(corresponding to SGM)

13. Comparison with the phenomenological potential
Phenomenological potential form
The effective potential depth corresponding to Gaussian potential is defined as;
 If ,
the phenomenological potential is good approximation.

14. Effective potential depth
V1 = -350 MeV
V2 = -150 MeV
Vc = +100 MeV
“SGM”
V1 = -300 MeV
V2 = -150 MeV
Vc = +100 MeV
“YA”

15. Effective potential depth
V1 = -400 MeV
V2 = -150 MeV
Vc = +100 MeV
V1 = -300 MeV
V2 = -300 MeV
Vc = +100 MeV
Kbar(NN) bound
below Eth(pSN)
p(SN) bound

16. Consideration by analytically solvable model
 d-type coupling potential

17. Solvable model (2) --- wave functions
where,

18. Solvable model (3) --- effective potential
Here,

19. Plot of Ueff(E) ; V1 = -300 MeV, Vc = +100 MeV
This simple analytical model well reproduce the V2 dependence of numerical results.
V2 = -300 MeV

20. Condition that phase-space-like E-dependence can be held.
In the energy region which satisfy;
but, E
c.f.
To make
a bound state,
Im Ueff ~ const.× (phase space factor)

21. Summary Future Problems
We have numerically derived the Kbar-(NN) single-channel
effctive potential Ueff from Kbar(NN) - p(SN) CC Green’s
function method, and confirmed the following features;
bound
above Eth(pSN)
below Eth(pSN)
unbound
Can Im Ueff be approximated
by the phase space factor?
Kbar(NN)
p(SN)
Yes No
Future Problems
Multi-channel case; KbarNN- pSN-YN
Case of energy-dependent potential in CC scheme.