Hyperon-nucleon force from lattice QCD

Abstract

We calculate potentials between a proton and a ${\Xi }^0$ (hyperon with strangeness -2) through the equal-time Bethe-Salpeter wave function, employing quenched lattice QCD simulations with the plaquette gauge action and the Wilson quark action on (4.5 fm)^4 lattice at the lattice spacing $a\simeq 0.14$ fm. The ud quark mass in our study corresponds to $m_{\pi }\simeq 0.37$ and 0.51 GeV, while the s quark mass corresponds to the physical value of $m_K$. The central $p{\Xi }^0$ potential has a strong (weak) repulsive core in the ${}^1{S}_0$ (${}^3{S}_1$) channel for $r \lsim 0.6$ fm, while the potential has attractive well at the medium and long distances (0.6 fm $\lsim r \lsim 1.2$ fm) in both channels. The sign of the $p{\Xi }^0$ scattering length and its quark mass dependence indicate a net attraction in both channels at low energies.

10 gages, 4 figures, version accepted for publication in Physics Letters B

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