Pion-nucleon σ term with dynamical Wilson fermions

Abstract

We calculate connected and disconnected contributions to the flavour singlet scalar density amplitude of the nucleon in a full QCD lattice simulation with $n_f=2$ dynamical Wilson fermions at $\beta=5.6$ on a $16^3 \times 32$ lattice. We find that both contributions are of similar size at the light quark mass. We arrive at the estimate $\sigma_{\pi N} = 18(5)$MeV. Its smallness is directly related to the apparent decrease of $u$, $d$ quark masses when unquenching QCD lattice simulations. The $y$ parameter can be estimated from a semi-quenched analysis, in which there are no strange quarks in the sea, the result being $y=0.59(13)$.}