Pion-Nucleon Sigma Term in Lattice QCD

Abstract

We calculate both connected and disconnected contribution to the $\pi$-$N$ $\sigma$-term in quenched lattice QCD with Wilson quark action on a $12^3\times 20$ lattice at $\beta =5.7$. The latter is evaluated with the aid of the variant wall source method, which was previously applied successfully for extraction of $\pi$-$\pi$ scattering lengths and ${\eta }^{\prime }$ meson mass. We found that the disconnected contribution is about twice larger than the connected one. The value for the full $\pi$-$N$ $\sigma$ term $\sigma =40-60$ MeV is consistent with the experimental estimates. The nucleon matrix element of the strange quark density $\bar{s}s$ is fairly large in our result.

Comments: 11 pages. Latex file. Figures are also included as ps files