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 $M_{\pi }<420\mathrm{MeV}$, 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 ${\sigma }_{\pi N}=41(5)(4)\mathrm{MeV}$ in the 2 flavor case and ${\sigma }_{\pi N}=52(3)(8)\mathrm{MeV}$ 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 $r_0=0.493(23)\mathrm{fm}$.

• Received 5 April 2013

DOI:https://doi.org/10.1103/PhysRevD.88.054507