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”

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

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) 262-268. T. Koike & T. Harada, Nucl. Phys. A804 (2008) 231-273. T. Koike & T. Harada, Phys, Rev. C80 (2009) 055208-1~14. c.f. J. Yamagata-Sekihara et al., Phys, Rev. C80 (2009) 045204.

( ) 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

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) 055204. 　　 J. Yamagata, H. Nagahiro, S. Hirenzaki, PRC74 (2006) 014604.

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

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:1112.2823 [nucl-th]

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).

Coupled-channel model Single- vs. Coupled-channel DWIA calculation Single-channel model W0 is changed. V0 = -360 MeV, B1 = 0.8, B2 = 0.2 (pSN) (pY) Coupled-channel model V2 is changed. V1 = -360 MeV, VC = +100 MeV, W1 = -10 MeV.

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

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

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

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.

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

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

Consideration by analytically solvable model  d-type coupling potential

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

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

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

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)

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.