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

Abstract

The pion mass dependence of the nucleon mass within the covariant $SU(2)$ baryon chiral perturbation theory both without and with explicit $\ensuremath{\Delta}(1232)$ 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 ${M}_{\ensuremath{\pi}}<420\text{ }\text{ }\mathrm{MeV}$, 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 ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}$ data. As a result of our analysis, which encompasses the study of finite volume corrections and discretization effects, we report a value of ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}=41(5)(4)\text{ }\text{ }\mathrm{MeV}$ in the 2 flavor case and ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}=52(3)(8)\text{ }\text{ }\mathrm{MeV}$ for $2+1$ flavors, where the inclusion of the $\ensuremath{\Delta}(1232)$ 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 ${r}_{0}=0.493(23)\text{ }\text{ }\mathrm{fm}$.