We report an analysis of the impressive new lattice simulation results for octet baryon masses in $2+1$-flavor QCD. The analysis is based on a low-order expansion about the chiral SU(3) limit in which the symmetry breaking arises from terms linear in the quark masses plus the variation of the Goldstone boson masses in the leading chiral loops. The baryon masses evaluated at the physical light-quark masses are in remarkable agreement with the experimental values, with a model dependence considerably smaller than the rather small statistical uncertainty. From the mass formulas one can evaluate the sigma commutators for all octet baryons. This yields an accurate value for the pion-nucleon sigma commutator. It also yields the first determination of the strangeness sigma term based on $2+1$-flavor lattice QCD and, in general, the sigma commutators provide a resolution to the difficult issue of fine-tuning the strange-quark mass.

• Received 27 January 2009

DOI:https://doi.org/10.1103/PhysRevD.81.014503