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# Hyperon-nucleon force from lattice QCD

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### 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 $$^1S_0$$ ($$^3S_1$$) 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.

### Author and article information

###### Journal
06 June 2008
2009-02-05
###### Article
10.1016/j.physletb.2009.02.003
0806.1094