Pion-Nucleon Sigma Term in Lattice QCD

TL;DR

This paper computes the pion-nucleon sigma term using quenched lattice QCD, revealing the significant role of disconnected contributions and providing results consistent with experimental estimates.

Contribution

First lattice QCD calculation of both connected and disconnected contributions to the pion-nucleon sigma term using Wilson quarks on a small lattice.

Findings

Disconnected contribution is about twice the connected one.

Full sigma term is estimated to be 40-60 MeV.

Strange quark density in the nucleon is found to be large.

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.