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3 He (In-flight K - , N) 反応による K - pp 生成スペクトル

ＫＥＫ「原子核・ハドロン物理：横断研究会」　２００７年 11 月 19 日　 KEK. 3 He (In-flight K - , N) 反応による K - pp 生成スペクトル. 小池　貴久 理研　仁科センター 原田　融 大阪電気通信大学. Many calculations support the existence of K - pp deeply-bound state, although B.E. and G are not converged theoretically.

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3 He (In-flight K - , N) 反応による K - pp 生成スペクトル

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  1. ＫＥＫ「原子核・ハドロン物理：横断研究会」　２００７年11月19日　KEKＫＥＫ「原子核・ハドロン物理：横断研究会」　２００７年11月19日　KEK 3He (In-flight K-, N) 反応によるK-pp生成スペクトル 小池　貴久 理研　仁科センター 原田　融 大阪電気通信大学

  2. Many calculations support the existence of K-pp deeply-bound state, although B.E. and G are not converged theoretically. ◆ Theoretical works for K-pp deeply-bound state ・ Nogami: First prediction Phys. Lett. 7 (1963) 288. ・ Yamazaki & Akaishi: First quantitative few-body calculation by ATMS method B.E. = 48 MeV, G = 61 MeV PLB535(2002)70. ・Shevchenko, Gal & Mares (+ Revai): KNN-pSN coupled channel Faddeev calculation B.E. = 55-70 MeV, G = 95-110 PRL 98(2007)082301, PRC76(2007)044004. ・ Ikeda & Sato: KNN-pSN c.c. Faddeev calculation B.E. = 79 MeV, G = 74 MeV PRC 76(2007)035203. ・ Dote & Weise (+Hyodo): AMD / Simple corralated. model arXiv:nucl-th/070150. ・ Nishikawa & Kondo: Skyrmion model arXiv:hep-ph/0703100. ・Arai, Yasui & Oka: L* N model arXiv:0705. 3936[nucl-th] ・ Yamagata, Hirenzaki et al.: Chiral unitary model talk atJPS 2007Spring, Chiral07 ・ Noda, Hirenzaki et al.: Rearrangement-channel Gaussian talk at JPS 2007Autum

  3. ◆ Experimental search for K-pp deeply-bound state ・ FINUDA collaboration at DAFNE: “K-pp” → L + p invariant-mass spectroscopy using stopped K- reaction on 6Li, 7Li, 12C. Reported: B.E. = 115 MeV G = 67 MeV PRL94 (2005) 212303. ・ Magas, Oset, Ramos & Toki : critical view; NOT “K-pp” bound state, BUTFSI after two-nucleon absorption. K- + ”pp” → L + p p + N → p’ + N’ PRC74 (2006)025206. … still controversial.

  4. 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 spectroscopy + “K-pp” →Lp → p-pp invariant-mass spectroscopy Our purpose: Theoretical calculation of 3He(In-flight K-, n) inclusive/semi-exclusive spectra within the DWIA framework using Green’s function method. Ref: T. Koike and T. Harada, Phys. Lett. B652 (2007)262-268.

  5. ◆Distorted-Wave Impulse Approximation (DWIA) Strength function Kinematical factor Fermi-averaged ementary cross-section n(K-,n)K- in lab. system Morimatsu & Yazaki’s Green function method Green’s function with K--“pp” optical potential recoil effect Distorted wave for incoming(+)/outgoing(-) particles → Eikonal app. neutron hole wave function → (0s)3 h.o. model

  6. ◆ Momentum transfar ◆ Kinematical Factor pK- pn(>pK-) K- n n K- p p q p p

  7. ; K- escape ; K- conversion When , K- conversion into channel 1 ; ◆ Decomposition of strength function the conversion part can be further decomposed as . . . etc.

  8. ; Pole contribution e.g. pole contribution ; of conversion part into channel 1 . . . etc. ◆ Decomposition of Green’s function Then, another decomposition of the strength fucntion can be made;

  9. ◆ Yamazaki-Akaishi’sK--”pp” optical potential Ref. PLB535 (2002) 70. V0 = -300 MeV W0 = -70 MeV b = 1.09 fm Schordinger Energy → B.E. = 51 MeV, G = 68 MeV ( Klein-Gordon Energy)

  10. Energy-independent pot. Energy -dependent pot. ◆ Phase space factor f (E) Ref. J. Mares, E. Friedman, A. Gal, PLB606 (2005) 295. ・ f1(E) : 1-body abs. K + N → S /L + p ・ f2(E) :2-body abs. K + “NN” → S /L +N ・ f(E) = 0.8 f1(E) + 0.2 f2(E) Ref. J. Yamagata, H. Nagahiro, S. Hirenzaki, PRC74 (2006) 014604.

  11. ◆ Optical potential strength parameter ・Set 1: Yamazaki-Akaishi’s optical potential: 1-a. Energy-independent 1-b. Energy-dependent V0 = -300 MeVV0 = -300 MeV W0 = -70 MeV W0 = -93 MeV× f (E) → B.E. = 51 MeV, G = 68 MeVRef. PLB535(2002)70. ・Set 2: simulate Shevcenko-Gal-Mares’s Faddeev cal.: 2-a. Energy-independent 2-b. Energy-dependent V0 = -350 MeVV0 = -350 MeV W0 = -100 MeV W0 = -165 MeV× f (E) → B.E. = 72 MeV, G = 115 MeVRef. PRL 98(2007)082301. c.f.similar Faddeev cal. by Ikeda-Sato B.E. = 79 MeV, G = 74 MeV Ref. PRC 76(2007)035203

  12. 3He(In-flight K-,n), pK-= 1.0 GeV/c, qn = 0o V0 = -300 MeV W0 = -70 MeV B.E. = 51 MeV, G = 68 MeV using Yamazaki-Akaishi’s optical potential

  13. ◆ Enegy-indep. vs. energy-dep. potential : YA case pK = 1 GeV/c qn = 0o S p decay threshold

  14. ◆ Decomposiiton of spectrum: YA case pK = 1 GeV/c qn = 0o K- conversion 1-body abs. K- escape 2-body abs. from bound state 2-body abs.

  15. 3He(In-flight K-,n), pK-= 1.0 GeV/c, qn = 0o V0 = -350 MeV W0 = -100 MeV B.E. = 72 MeV, G = 115 MeV simulate Shevcenko-Gal-Mares’s Faddeev calculation. Ref: PRL 98(2007)082301.

  16. ◆ Enegy-indep. vs. energy-dep. pot. : SGM case pK = 1 GeV/c qn = 0o S p decay threshold

  17. ◆ Decomposiiton of spectrum : SGM case pK = 1 GeV/c qn = 0o K- conversion 1-body abs. K- escape 2-body abs. from bound state 2-body abs.

  18. Energy-independentpotential

  19. V0 = -300 MeV V0 = -340 MeV V0 = -360 MeV V0 = -380 MeV V0 = -400 MeV W0 = -93 MeV (fix) 1.0 0.0 Energy-dependent potential EK-pp (MeV)

  20. V0 = -300 MeV V0 = -340 MeV V0 = -360 MeV V0 = -380 MeV V0 = -400 MeV W0 = -93 MeV (fix) 0.8 0.2 Energy-dependent potential EK-pp (MeV)

  21. V0 = -300 MeV V0 = -340 MeV V0 = -360 MeV V0 = -380 MeV V0 = -400 MeV W0 = -93 MeV (fix) Dashed lines: 1-body abs. Solid lines: 2-body abs. 0.8 0.2 Energy-dependent potential EK-pp (MeV)

  22. W0 = -60 MeV W0 = -100 MeV W0 = -140 MeV W0 = -180 MeV V0 = -360 MeV (fix) 1.0 0.0 Energy-dependent potential EK-pp (MeV)

  23. W0 = -60 MeV W0 = -100 MeV W0 = -140 MeV W0 = -180 MeV V0 = -360 MeV (fix) 0.8 0.2 Energy-dependent potential EK-pp (MeV)

  24. W0 = -60 MeV W0 = -100 MeV W0 = -140 MeV W0 = -180 MeV V0 = -360 MeV (fix) Dashed lines: 1-body abs. Solid lines: 2-body abs. 0.8 0.2 Energy-dependent potential EK-pp (MeV)

  25. 1.00 f1(E) + 0.00 f2(E) 0.95 f1(E) + 0.05 f2(E) 0.90 f1(E) + 0.10 f2(E) 0.80 f1(E) + 0.20 f2(E) V0 = -350 MeV (fix) W0 = -165 MeV (fix) a b Energy-dependent potential EK-pp (MeV)

  26. Dashed lines: 1-body abs. Solid lines: 2-body abs. 1.00 f1(E) + 0.00 f2(E) 0.95 f1(E) + 0.05 f2(E) 0.90 f1(E) + 0.10 f2(E) 0.80 f1(E) + 0.20 f2(E) V0 = -350 MeV (fix) W0 = -165 MeV (fix) a b Energy-dependent potential EK-pp (MeV)

  27. ◆ Summary ・ 山崎・赤石の計算 (B.E. ~ 50 MeV) に従えば、K-pp 生成ピーク がはっきりと観測できることが期待される。 この場合、 B.E. が KN → p S崩壊しきい値 (~100 MeV) より 十分小さいので、スペクトルのピーク構造はしきい値効果の 影響を受けない。 ・Shevchenko-Gal-Mares （及び池田・佐藤）の Faddeev 計算が 示唆するように、 B.E.が p S崩壊しきい値に近づく場合、 K-pp 生成シグナルはしきい値におけるカスプ的構造として現れる。 幅が小さく、かつ２体吸収過程への分岐比が小さければ、 　１体吸収過程がカスプ的構造を形成する。 幅が大きい時 and/or ２体吸収過程への分岐比が大きい時は ２体吸収過程がカスプ的構造を形成する。 幅が非常に大きくても、 ２体吸収過程のカスプ的構造は残る。

  28. ◆今後の課題 ・ Phase space factor を用いた single-channel ポテンシャルモデル　 　は coupled-channel モデルと consistent か？ → Coupled-channel DWIA の枠組による計算で確かめる必要 　　　がある。 ・ ２体吸収過程に関して、K中間子原子で測定された約 20%の 　分岐比をこの反応にそのまま適用することは適切か？ 　→ ２体吸収過程のエネルギー依存性、密度依存性を調べる 　　　必要がある。

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