Kaon Absorption from Kaonic Atoms and Formation Spectra

Kaon Absorption from Kaonic Atoms and Formation Spectra of Kaonic Nuclei J. Yamagata (Nara Women’s Univ. ) H. Nagahiro (RCNP, Osaka Univ. ) D. Jido (YITP, Kyoto Univ. ) S. Hirenzaki (Nara Women’s Univ. )

Introduction Kaonic Nuclei J-PARC target -- Signals for kaonic nuclei even with large width? width ( only a few subcomponents ) Theoretical Study ( Kpp bound states ) 3 He Structure : Akaishi, Yamazaki, Dote ; N. V. Shevchenko, A. Gal, J. Mares； Ikeda, Sato; Dote, Weise Reaction : Yamagata, Nagahiro, Jido, Hirenzaki ; Koike, Harada (cf: K-pp system : FINUDA. Interpretation by known process ; Oset, Toki) Our study 1. 2. 3. 4. Kaonic Nuclei : He, t targets Yamagata, Nagahiro, Okumura, Hirenzaki, 16 PTP 114(05)301 ; Errata 114(05)905 Kaonic Nuclei : O targets Yamagata, Nagahiro, Hirenzaki, Deeply bound Kaonic Atoms PRC 74(06)014604 Hirenzaki, EPJA 31(07)255 Comments on Kaon Absorption Yamagata, Nagahiro, Kimura, Hirenzaki in preparation

Our Theoretical Tools Formation spectra in Green function method O. Morimatsu, K. Yazaki, NPA 435(85)727, NPA 483(88)493 Bound state by solving Klein-Gordon equation E. Oset and L. L. Salcedo, J. Comput. Phys. 57 (85) 361 Optical potential Chiral Unitary Model (1) T(r, E)r(r) Higher order medium modifications (2) T(r=0, E)r(r) Linear density [A. Ramos, E. Oset, NPA 671(00)481] [Hirenzaki, Okumura, Toki, Oset, Ramos, PRC 61(00)055205] [ E. Oset, A. Ramos, Nucl. Phys. A 635 (98)99] [ E. Oset, A. Ramos, C. Bennhold, Phys. Lett. B 527(02)99] Phenomenological Model (1) [Batty, Friedman, Gal, Phys. Rep. 287(97)385] (2) [T. Yamazaki, Y. Akaishi, PLB 535(02)70]

1. Kaonic Nuclei - Light nuclear targets Optical Potential E. Oset, A. Ramos, Nucl. Phys. A 635 (98)99 E. Oset, A. Ramos, C. Bennhold, Phys. Lett. B 527(02)99 Chiral Unitary -- T(r=0, E)r(r) K-pn E= K-nn 0 [Me. V] -50 [Me. V] -100[Me. V] Im Vopt [Me. V] Re Vopt [Me. V] K-pp Linear density r [fm]

1. Kaonic Nuclei - Light nuclear targets Formation Spectra -- Chiral Unitary -- T(r=0, E)r(r) 3 He (K-, n) K－pp 1 s : 42. 0 Tn Me. V (41. 1 Me. V) [Me. V] 2 p ; 19. 1 Me. V(46. 3 Me. V) 3 d : 11. 6 Me. V(40. 0 Me. V) 3 He (K-, p) K－pn 1 s : 22. 6 Tp Me. V (40. 4 Me. V) [Me. V] 2 p ; 11. 2 Me. V(38. 4 Me. V) Linear density t (K-, p) K－nn Tp [Me. V] B. E. (Width)

1. Kaonic Nuclei - Light nuclear targets Linear density vs. Higher order medium modifications K-pn(T(r, E)r(r)) Im Vopt [Me. V] Re Vopt [Me. V] K-pn(T(r=0, E)r(r)) E= r [fm] 0 [Me. V] -50 [Me. V] -100[Me. V]

1. Kaonic Nuclei K－pn Linear density vs. Higher order medium modifications Kpn(T(r=0, E)r(r)) Tp [Me. V] Kpn(T(r, E)r(r)) Tp [Me. V] Real Kpn : Expected to be in between

1. Kaonic Nuclei Chiral Unitary (T(r=0, E)r(r)) K－pp AY type T. Yamazaki, Y. Akaishi, PLB 535(02)70 Koike, Harada ; nucl-th/0703037 Different origin ! Tn [Me. V]

1. Kaonic Nuclei ( KNN systems ) – Comments on our calculation We don’t calculate structure as few body systems. We need to evaluate 2 body absorption correctly. Chiral Unitary Model T(r=0, E) --- only 1 body absorption T(r, E) --- more than 3 body absorption Real KNN states (only 1 and 2 body absorption) We assume density distribution of pp and nn system.

2. Kaonic Nuclei (16 O) Optical Potential Chiral Unitary Model [A. Ramos, E. Oset, NPA 671(00)481] [Hirenzaki, Okumura, Toki, Oset, Ramos, PRC 61(00)055205] Phenomenological Model [Batty, Friedman, Gal, Phys. Rep. 287(97)385] E= 0 [Me. V] -50 [Me. V] -100[Me. V]

Energy dependent 2. Kaonic Nuclei (16 O) 16 O(In-flight Chiral Unitary K, n) PK = 930 Me. V/c Please ask Kishimoto group for experimental data. Phenomenology Comparison with Kishimoto group’s data [ T. Kishimoto et al. , Prog. Theor. Phys. Suppl. 149 (2003)264 ] [ Fig. taken from the seminar slide @NWU by Dr. Hayakawa ] 80%: 20%

3. Deeply bound Kaonic Atoms -- 12 C(K-, p) Chiral Unitary Model Atomic State

3. Deeply bound Kaonic Atoms Proton hole state – 12 C Chiral Unitary 1 s 2 p Phenomenology 1 s 2 s 2 p Dip !! 1 s 2 p 2 s 120 Sn 1 s 2 p These are very interesting structures !! 2 s 2 s

4. Comments on Kaon Absorption Kaon absorption from Kaonic Atoms What the data mean? Observed ratio 1 body : 2 body = 80 : 20 for 12 C The density probed by the Kaonic Atoms : Overlapping density p N K 12 C K Chiral Unitary T. Yamazaki, S. Hirenzaki PLB 557 (03)20 Phenomenology

Im Vopt : 1 body abs. (r term) 2 body abs. (r 2 term) • 80 : 20 Absorption (a) from 2 p state (b) from 3 d state -100 -50 E=0 Me. V Formation Spectra

Summary We have studied 1. Kaonic Nuclei (for light nuclear targets) Kpp and Kpn (T(r=0, E)r(r)) -- Bound state exist in complex E plane -- Peak positions are not corresponding to the binding energy Knn (T(r=0, E)r(r)) no bound states Kpn (T(r, E)r(r)) -- Smooth spectra, no peak. 2. Kaonic Nuclei ( for 16 O) We have found smooth slope in spectra. (good agreement with the latest experimental analysis) 3. Deeply bound Kaonic Atoms We have found very interesting structure. (no experimental evidence so far) 4. Comments on Kaon Absorption The strong K-atomic state dependence of the nuclear density probed by atomic kaon. (meanings of the observed ratio of 1 to 2 body abs. ) evaluation of 2 body absorption is very important!!