Nucleon mass, sigma term, and lattice QCD

Abstract

We investigate the quark mass dependence of the nucleon mass $M_N.$ An interpolation of this observable, between a selected set of fully dynamical two-flavor lattice QCD data and its physical value, is studied using relativistic baryon chiral perturbation theory up to order $p^4.$ In order to minimize uncertainties due to lattice discretization and finite volume effects our numerical analysis takes into account only simulations performed with lattice spacings $a<\mathrm{}0.15\mathrm{}\mathrm{fm}$ and $m_{\pi }L>\mathrm{}5.\mathrm{}$ We have also restricted ourselves to data with $m_{\pi }<600\mathrm{}\mathrm{MeV}$ and $m_{\mathrm{sea}}{=m}_{\mathrm{val}}.$ A good interpolation function is found already at the one-loop level and chiral order $p^3.$ We show that the next-to-leading one-loop corrections are small. From the $p^4$ numerical analysis we deduce the nucleon mass in the chiral limit $M_0\approx 0.88\mathrm{GeV}$ and the pion-nucleon sigma term ${\sigma }_N=(49\mathrm{}\pm 3)\mathrm{MeV}$ at the physical value of the pion mass.