The Pion-Nucleon sigma-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 $y=0.59(13)$.}

Comments: Final version, accepted for publication in Phys. Rev. D, minor changes to the text, 1 new figure, 17 pages