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Kaon-Nucleon potential from lattice QCD

S. Aoki (Univ. of Tsukuba), T. Doi (Univ. of Tsukuba), T. Hatsuda (Univ. of Tokyo), T. Inoue (Univ. of Tsukuba), N. Ishii (Univ. of Tokyo), K. Murano (Univ. of Tokyo), H. Nemura (Tohoku Univ.), K. Sasaki (Univ. of Tsukuba).

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Kaon-Nucleon potential from lattice QCD

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  1. S. Aoki (Univ. of Tsukuba),T. Doi (Univ. of Tsukuba),T. Hatsuda (Univ. of Tokyo),T. Inoue (Univ. of Tsukuba), N. Ishii (Univ. of Tokyo), K. Murano (Univ. of Tokyo),H. Nemura (Tohoku Univ.),K. Sasaki (Univ. of Tsukuba) Kaon-Nucleon potential from lattice QCD Yoichi Ikeda (Univ. of Tokyo) for HAL QCD collaboration

  2. Plan of this talk • Introduction and our motivation • Formalism • Numerical results and discussions • Summary and future plans

  3. Open problems Many experiments at high energy show negative results. No narrow peak was observed by CLAS collaboration. Reaction-dependent production mechanism? • Introduction Experimental study of Q+ state by LEPS collaboration • nK+ invariant mass distribution shows a narrow peak around 1.524 GeV • Statistical significance of the peak is 5.1 s • The obtained results support the evidence of the Q+ state

  4. Current status from LQCD • Penta-quark might be allowed, but most probably NK scattering state. • One possible explanation of Q+ state  Hadronic molecule (NK) or bound state (NpK) Need precise information on NK interaction • Introduction LQCD studies for signal of Q+ state • Quenched LQCD for energy of penta-quark (J=1/2, 3/2) (e.g., Csikor, Sasaki, Chiu, Mathur, Ishii, Takahashi, Alexandrou, Lasscock, Holland)

  5. I=1 Potential from Quark model Barnes-Swanson, PRC49. No attraction in any range were found. I=0 Consistent with meson-exchange model? e.g.,) Julich group, NPA506. • Introduction NK (I=0, 1) scattering phase shifts S01 Hashimoto, PRC 29. S11 NK scattering phase shift  repulsive LQCD simulations solve the ambiguities of the NK potential.

  6. PACS-CS config. (2+1 flavors) Previous LQCD studies of the Q+ are all quenched. PRD79(2009). Full LQCD simulation is necessary. We are almost on the “physical point”. • Our motivation

  7. Production mechanism of Q+ state might be reaction dependent. The nK+ potential derived from QCD powerful tool to analyze the nature of the Q+. Previous LQCD studies of the Q+ are all quenched. Full LQCD simulation is necessary. This study We derive the nK+ potential from Full LQCD simulation. • Our motivation

  8. 1) Define interpolating operators 2) Calculate the equal-time BS amplitude 3) Derive the potential from Schrodinger Eq. • Formalism (HAL procedure) Wave func.  Potential  Observable • Developed by Ishii, Aoki, and Hatsuda for NN system PRL99, 022001(2007).

  9. This work • Formalism (This work) Schrodinger Eq. We investigate the s-wave nK+ potential. S-wave projected nK+ wave function and potential

  10. Numerical set-up • 2+1 flavor full QCD configuration by CP-PACS/JLQCD • RG improved gauge action & O(a) improved Wilson-clover quark action • Lattice spacing : a=0.1209 [fm] • Size of Lattice : 163×32  L=1.93 [fm] • Hopping parameters : , • # of conf. = 700 • Flat wall source to provide NK state.

  11. Numerical results (Hadron effective masses) G2(t) : 2-point function Dirichlet B.C. Wall source NK threshold 2707(8) MeV

  12. nK+ effective mass in J=1/2- channel G4(t) : NK temporal correlator NK threshold (s-wave) Plateau Wall source Dirichlet B.C. • Single state saturation is achieved. • The best fit in the plateau gives Meff=2723(10) MeV.

  13. Potential I=1 I=0 • S-wave nK+ BS wave function and potential Wave function • Repulsive core at short distance ( r<0.5[fm] ) • Attractive pocket in middle range ( 0.5<r<1.2 [fm] )

  14. Fitting function Gaussian core + (Yukawa x form factor)2 S01 • The range of Yukawa-type potential = 805 MeV S11 • Qualitatively consistent with experimental data • Pion mass is 871 MeV in our set-up • Note • S-wave nK+ scattering phase shift

  15. Summary • S-wave nK+ potential derived from full LQCD is studied. - We found repulsive core at short distance and weak attractive pocket in the middle range. • We calculate the scattering phase shift - Qualitatively consistent with experimental data • We also study the effective mass of the nK+ state in J=1/2- channel. - The low-lying state is consistent with nK+ threshold. • Future plans • We will study the quark mass dependence of the s-wave nK+ potential. • P and D-wave nK+ potentials  The small width of the Q+ might be explained due to the centrifugal barrier.

  16. back up

  17. Convergence of nK+ potential

  18. Potential fit Gaussian core + (Yukawa x form factor)2 • The range of Yukawa-type potential = 805 MeV

  19. Scattering length ry(r) fit Very weak interaction at threshold Calculated from LS eq. with fitted potential

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