ΛN and Ξ N Interactions Studied with Lattice QCD

Department of Physics, Tohoku University, Sendai, 980-8578, Japan

^a e-mail: nemura@nucl.phys.tohoku.ac.jp

Abstract

We present our recent studies of Lambda-Nucleon (ΛN) as well as Cascade-Nucleon (ΞN) interactions by using lattice QCD. The equal-time Bethe-Salpeter (BS) amplitude of the lowest energy scattering state of baryon number B = 2 system (proton-Λ and proton-Ξ⁰) is calculated from lattice QCD. For the calculation of the ΛN potential, two different types of gauge configurations are employed: (i) 2+1 flavor full QCD configurations generated by the PACS-CS collaboration at β = 1.9 (a = 0.0907(13) fm) on a 32³ × 64 lattice, whose spatial volume is (2.90 fm)³ . (ii) Quenched QCD configurations at β = 5.7 (a = 0.1416(9) fm) on a 32³ × 48 lattice, whose spatial volume is (4.5 fm)³ . The spin-singlet central potential is calculated from the BS wave function for the spin J = 0 state, whereas the spin-triplet central potential as well as the tensor potential are deduced simultaneously from the BS wave function for the spin J = 1 state by dividing it into the S-wave and the D-wave components. For the calculation of the Ξ N potential, we employ quenched QCD configurations, at β = 5.7 (a = 0.1416(9) fm) on a 32³ × 32 lattice, whose spatial volume is (4.5 fm)³ . The effective central potential in the spin triplet channel as well as the central potential in the spin singlet channel are calculated for the ΞN . The scattering lengths are obtained from the asymptotic behavior of the BS wave function by using the Lüscher’s formula.