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Faddeev 計算による K 中間子原子核

Faddeev 計算による K 中間子原子核. based on PRC76, 035203 (2007). 池田 陽一，佐藤 透（阪大理・原子核理論）. 原子核・ハドロン物理：横断研究会＠ KEK 2007 年 11 月 19 日 -21 日. Contents Our motivation KNN system with coupled channel Numerical results Summary and future work. Our motivation. Akaishi and Yamazaki, PRC65(2002).

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Faddeev 計算による K 中間子原子核

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  1. Faddeev計算によるK中間子原子核 based on PRC76, 035203 (2007). 池田 陽一，佐藤 透（阪大理・原子核理論） 原子核・ハドロン物理：横断研究会＠KEK2007年11月19日-21日

  2. Contents • Our motivation • KNN system with coupled channel • Numerical results • Summary and future work

  3. Our motivation

  4. Akaishi and Yamazaki, PRC65(2002) Agnello et al., PRL94(2005) Kaon absorption?? (Magas et al.)

  5. Λ(1405) K-pp system -> the resonance in the KN-πΣ coupled channel system P P S=-1, B=2, Q=+1 L=0 (s-wave interaction) Jπ=0- (3-body s-wave state) • It will be very important • to take into account the dynamics of KN-πΣ system • in order to investigate whether KNN resonance may exist. Solve K- -> Coupled channel Faddeev equation Find • We consider s-wave state. • We expect most strong attractive interaction • in this configure. -> KNN 3-body resonance Our Investigation • We investigate the possible • [KNN](I=1/2,J=0) 3-body resonance state.

  6. KNN system with coupled channel

  7. Separable interaction : Two-body t-matrix :

  8. g τ g ＝ g τ g Kernel Kernel 例えば、一部のダイアグラムは… ｔ ｔ

  9. Formal solution of AGS equation AGS Equation Fredholm type kernel Eigenvalue equation for Fredholm kernel Formal solution for 3-boby amplitude 3-body resonance pole at Wpole

  10. KN-πY(I=0, 1) πN(I=1/2,3/2) NN scattering (Anti-symmetrized) The ＫＮＮ-πＹＮ resonance 本研究での枠組み：KN相互作用に注目 : 1-particle exchange term π N N N N π N N K Σ,Λ Σ,Λ Σ,Λ π N K : 2-body scattering term Meson-Baryon scattering Baryon-Baryon scattering

  11. 2-body Meson-Baryon Potential Chiral effective Lagrangian φ : Meson field , B : Baryon field S-wave separable potential Coupling const. Form factor

  12. Parameter fit (KN interaction) Our parameters -> cut-off of dipole form factor Fit ① : Scattering length given by Martin Fit ② : Λ(1405) pole position given by Dalitz

  13. Experimental data (total cross section)

  14. Experimental data (total cross section) (I=1 channel) (I=0 channel)

  15. πN scattering (S11 and S31) S11 phase shift S31 phase shift Our scattering length Our scattering length Exp. Exp.

  16. NN potential -> 2-term Yamaguchi type Attractive Repulsive core

  17. AGS equation for 3-body amplitude Eigenvalue equation for Fredholm kernel Pole of 3-body amplitude Wp = -B –iΓ/2 Similar to πNN, ηNN, K-d analyses.(Matsuyama, Yazaki, ……) K, N,π KN-πＹ, NN, πN

  18. Numerical results

  19. Fit to Dalitz pole The pole trajectories of three-body system KNN physical πΣN unphysical energy plane a:KN only b:+NN c:+πＹin τ d:π exchange

  20. The three-body resonance pole KNN physical πΣN unphysical energy plane -1.70-i0.68 fm Martin -1.60-i0.68 fm -1.70-i0.59 fm -1.80-i0.68 fm -1.70-i0.78 fm

  21. Nishikawa, Kondo -1.70-i0.68 fm Martin Dalitz Dote et al. Akaishi, Yamazaki DAΦNE Shevchenko et al. K-pp研究の現状 KNN physical πΣN unphysical energy plane

  22. Summary • We solve 3-body equation directly. • We can find the resonance pole • in the KNN physical and πＹN unphysical energy plane. In the future • The pole position strongly depends on KN interaction. • -> Structure dependence on Λ(1405) Arai, Oka, Yasui • reaction • Effects of KNN --> ＹN (p-wave interaction)

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