On finite volume effects in the chiral extrapolation of baryon masses

We perform an analysis of the QCD lattice data on the baryon octet and decuplet masses based on the relativistic chiral Lagrangian. The baryon self energies are computed in a finite volume at next-to-next-to-next-to leading order (N$^3$LO), where the dependence on the physical meson and baryon masses is kept. The number of free parameters is reduced significantly down to 12 by relying on large-$N_c$ sum rules. Altogether we describe accurately more than 220 data points from six different lattice groups, BMW, PACS-CS, HSC, LHPC, QCDSF-UKQCD and NPLQCD. Values for all counter terms relevant at N$^3$LO are predicted. In particular we extract a pion-nucleon sigma term of 39$_{-1}^{+2}$ MeV and a strangeness sigma term of the nucleon of $\sigma_{sN} = 84^{+ 28}_{-\;4}$ MeV. The flavour SU(3) chiral limit of the baryon octet and decuplet masses is determined with $(802 \pm 4)$ MeV and $(1103 \pm 6)$ MeV. Detailed predictions for the baryon masses as currently evaluated by the ETM lattice QCD group are made.