Sigma term and strangeness content of octet baryons

Abstract

By using lattice QCD computations we determine the sigma terms and strangeness content of all octet baryons by means of an application of the Hellmann-Feynman theorem. In addition to polynomial and rational expressions for the quark-mass dependence of octet members, we use $SU(3)$ covariant baryon chiral perturbation theory to perform the extrapolation to the physical up and down quark masses. Our ${N}_{f}=2+1$ lattice ensembles include pion masses down to about 190 MeV in large volumes (${M}_{\ensuremath{\pi}}L\ensuremath{\gtrsim}4$), and three values of the lattice spacing. Our main results are the nucleon sigma term ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}=39(4){(}_{\ensuremath{-}7}^{+18})$ and the strangeness content ${y}_{N}=0.20(7){(}_{\ensuremath{-}17}^{+13})$. Under the assumption of validity of covariant baryon $\ensuremath{\chi}\mathrm{PT}$ in our range of masses one finds ${y}_{N}=0.276(77){(}_{\ensuremath{-}62}^{+90})$.