Lambda-nucleon force from lattice QCD

We study the Λ-nucleon (ΛN) force by using lattice QCD. The Bethe-Salpeter amplitude is calculated for the lowest scattering state of the ΛN so as to obtain the ΛN potential. The numerical calculation is twofold: (i) Full lattice QCD by using 2 + 1 flavor PACS-CS gauge configurations with, β = 1.9, corresponding to the lattice spacing of a = 0.0907(13) fm, on a 323 × 64 lattice. A set of parameter (κud ,κs) = (0.13770,0.13640) is used, which corresponds to mπ ≈ 300 MeV and mK ≈ 594 MeV. The spatial lattice volume corresponds to (2.86 fm)3. (ii) Quenched lattice QCD with β = 5.7, the lattice spacing of a = 0.1416(9) fm, on the 323 × 48 lattice. Two sets of hopping parameters (κud,κs) = (0.1665,0.1643),(0.1670,0.1643) are used. The spatial lattice volume is (4.5 fm)3. For the full QCD, we find that the Λp has a relatively strong (weak) repulsive core in the S0 (S1) channel at short distance, while the potential has slight attractive region at medium distance. The lowest scattering energy in the finite lattice volume is calculated; Slightly negative values obtained in both spin channels. For the quenched QCD, we find that the results are qualitatively in agreement with those in the full QCD calculation.