Kaonic Nuclei : Formation

1. NFQCD10, Mini-Symposium (Hadrons in Nuclei), YITP, Kyoto, Feb. 23, 2010 Kaonic Nuclei : Formation --- 3He(in-flight K-, n) spectrum Takahisa Koike RIKEN, Nishina Center Toru Harada Osaka Electro-Communication Univ.

2. “K-pp”is suggested to be the lightest and most fundamental kaonic nuclei,but the theoretically-calculated and experimentally- measured B.E. and G are not converged! 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

3. Simultaneous mesurement ◆ New measurement for searching “K-pp” M. Iwasaki, T. Nagae et al. , J-PARC E15 experiment 3He(in-flight K-, n) “K-pp” missing-mass at pK- = 1 GeV/c and qn=0ospectroscopy + “K-pp” →Lp → p-pp invariant-mass detecting all charged particles spectroscopy from the decay of “K-pp” Our purpose: Theoretical calculation of 3He(In-flight K-, n) inclusive/ semi-exclusive spectra within the DWIA framework using Green’s function method.

4. ◆ Theoretical calculations of 3He(In-flight K-, n)reaction spectrum for J-PARC E15 experiment ・ Our approach: IntroducingK- -nucleus phenomenological potential → Explore possible senarios for various cases. Refs. 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. ・ Other approach within a similar framework: Optical potential model based on chiral unitary approach Ref. J. Yamagata-Sekihara et al., Phys, Rev. C80 (2009) 045204.

5. pK =1 GeV/c n K- p p pn K- n p q p ◆Distorted-Wave Impulse Approximation (DWIA) Strength function Kinematical factor Fermi-averaged ementary cross-section K- + n → N + Kbar in lab. system forward backward (q=0o ) q = pK - pn < 0

6. In charge basis, n K- K- K-+n → n+K- n K- p p p 3He p p - 3He n K0n p - p K0 K- n K-+p → n+Kbar0 ◆Distorted-Wave Impulse Approximation (DWIA) Strength function Kinematical factor Fermi-averaged ementary cross-section K- + n → N + Kbar in lab. system

7. In isospin basis, N - K K- p p - K N N N N N N - - K0n p - [ K×{NN} I=1 ] I=1/2 ◆Distorted-Wave Impulse Approximation (DWIA) Strength function Kinematical factor Fermi-averaged ementary cross-section K- + n → N + Kbar in lab. system = 16.4 mb/sr DI = 0 now used

8. ◆Distorted-Wave Impulse Approximation (DWIA) Strength function Kinematical factor Fermi-averaged ementary cross-section K- + n → N + Kbar in lab. system Morimatsu & Yazaki’s Green function method Prog.Part.Nucl.Phys.33(1994)679. Green’s function K-pp system → employing K--“pp” effective potential recoil effect Distorted wave for incoming(+)/outgoing(-) particles → Eikonal approximation neutron wave function → (0s)3 harmonic oscillator model

9. P-space: K-pp Q-space: pSN, pLN, YN ◆ K--”pp” effective potential Phase space factor E-dependence Phenomenological parametrization single-channel effective potential

10. SN pSN pLN ◆ K--”pp” effective potential ・ 1-nucleon K- absorption K-pp → “K-p” + p → p + S + N : f1S(E) K-pp → “K-p” + p → p + L + N : f1L(E) ・ 2-nucleon K- absorption K-pp → K- + “pp” → Y + N: f2 (E) ・ Total phase space factor f(E) = B1(pSN)f1S(E) + B1(pLN) f1L(E) + B2(YN)f2 (E) = 0.7 = 0.1 = 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.

11. ◆ Validity of E-dependence of our potential V0 is made deeper in our potential. KbarN attraction is artificially enhanced in coupled-channel Faddeev calculation. pSN decay only pSN decay only + pLN decay +YNdecay Ikeda&Sato, Phys. Rev. C79 (2009) 035201.

12. Real Complex ◆ Single-channel Green’s function ◆ Determing pole position The Klein-Gordon equation is solved self-consistently in complex E-plane; B.E. and G are determined from these relations.

13. We consider the following 4 cases of the calculations/experiment; B: variational cal. with phenomenological KbarN int. by Yamazaki-Akaishi (YA) C: Faddeev cal. with phenomenological KbarN int. by Shevchenko-Gal-Mares (SGM) A: variational cal. with Chiral SU(3) based KbarN int. D: fitting to experimental data by Dote-Hyodo-Weise (DHW)

14. ◆ Parameters of our optical potentials B2(YN) = 0.0 B2(YN) = 0.2 Fitted values ＊b = 1.09 fm for all potentials; the range effect is small.

15. ◆ Employed K--”pp” optical potentials A: DHW B: YA C: SGM D2: FINUDA

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

17. Decomposition of strength function into K- escape / K- conversion part , where ; Free Green’s function , ; K-escape ; K- conversion complex potential K- conversion spectrum is actually measured in J-PARC experiment.

18. ◆ Decomposition into semi-exclusive spectra A: DHW B: YA p S N decay via 1-nucleon K- abs. p L N decay via 1-nucleon K- abs. Y N decay via 2-nucleon K- abs. K- escape C: SGM D2: FINUDA

19. Moving-pole in complex E-plane ◆ Definition of D (E) E-dependent complex eigenvalue

20. ◆ Examples of the relation between D (E) and w (E) C: SGM B: YA

21. ◆ Pole trajectory w (E) in complex E-plane ×= (-B.E. , -G /2 )

22. ◆ Summary ・ Within the KbarNN single channel picture, the spectrum shape can be understood by relating to the trajectory of the moving pole in the complex E-plane, rather than the static values of B.E. and G . ・ The E-dependence of the effective potential determines the trajectory of the moving pole. ◆ Next works ・ Construct the more quantitative effective potential in single-channel calculation. ・ Interpretaion of the spectrum shape in coupled-channel scheme.