Nucleon mass and pion-nucleon sigma term from a chiral analysis of lattice QCD data

The pion mass dependence of the nucleon mass within the covariant SU(2) baryon chiral perturbation theory both without and with explicit Delta(1232) degrees of freedom up to order p(4) is investigated. By fitting to a comprehensive set of lattice QCD data in 2 and 2 + 1 flavors from several collaborations, for pion masses M-pi < 420 MeV, we obtain low energy constants of natural size that are compatible with pion-nucleon scattering data. Our results are consistent with the rather linear pion mass dependence showed by lattice QCD. In the 2 flavor case we have also performed simultaneous fits to nucleon mass and sigma(pi N) data. As a result of our analysis, which encompasses the study of finite volume corrections and discretization effects, we report a value of sigma(pi N) = 41(5)(4) MeV in the 2 flavor case and sigma(pi N) = 52(3)(8) MeV for 2 + 1 flavors, where the inclusion of the Delta(1232) resonance changes the results by around 9 MeV. In the 2 flavor case we are able to set independently the scale for lattice QCD data, given by a Sommer scale of r(0) = 0.493(23) fm.