Pion-nucleon σ term in lattice QCD

We calculate both the connected and disconnected contributions to the π-N σ term in quenched lattice QCD with the Wilson quark action on a ${12}^3$×20 lattice at β=5.7 with the lattice spacing a≊0.14 fm. The latter is evaluated with the variant wall source method, previously applied successfully for π-π scattering lengths and the η’ meson mass. We found the disconnected contribution to be about twice as large as the connected one. The value for the full π-N σ term σ=40–60 MeV is consistent with the experimental estimates. The nucleon matrix element of the strange quark density s¯s is fairly large in our result.