ΛN and ΞN Interactions Studied with Lattice QCD

Abstract. We present our recent studies of Lambda-Nucleon (ΛN) as well as Cascade-Nucleon (ΞN) interac-tions 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 vol-ume 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 ΞN 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.