HYPERON-NUCLEON FORCES CALCULATED FROM LATTICE QCD

Abstract

We study the hyperon-nucleon (YN) forces by using quenched lattice QCD. The Bethe-Salpeter amplitudes are calculated for the lowest scattering state of the systems so as to obtain the YN potentials. The numerical calculation is twofold: (i) The pΞ0 potentials and scattering lengths are obtained by using lattice QCD with β = 5.7, the lattice spacing of a = 0.1416(9) fm , on the 323 × 32 lattice. Two kinds of ud quark mass are used, corresponding to mπ ≃ 0.37 GeV and 0.51 GeV. The spatial lattice volume is (4.5 fm)3. The scattering lengths obtained from Lüscher's formula show that the pΞ0 interactions are both attractive at 1S0 and 3S1 channels, and the interaction in the 3S1 is more attractive than in the 1S0. These attractive forces become stronger as the u, d quark mass decreases. (ii) The pΛ potentials are calculated. The lattice setup is almost same as the former calculation except for the temporal part. The calculation is performed on 323 × 48 lattice. Two kinds of ud quark mass are used, corresponding to mπ ≃ 0.47 GeV and 0.51 GeV. The lowest scattering energies in the finite lattice volume are calculated.