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

TL;DR

This study uses chiral perturbation theory to analyze lattice QCD data, determining the nucleon mass dependence on pion mass and extracting the pion-nucleon sigma term with high precision, considering finite volume and discretization effects.

Contribution

It provides a comprehensive chiral analysis of lattice QCD data, including explicit Delta(1232) degrees of freedom, to accurately determine the pion-nucleon sigma term and nucleon mass dependence.

Findings

Pion-nucleon sigma term is 41(5)(4) MeV for 2 flavors.

Sigma term is 52(3)(8) MeV for 2+1 flavors.

Including Delta(1232) shifts results by about 9 MeV.

Abstract

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 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 and 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 the nucleon mass and pion-nucleon sigma-term data. As a result of our analysis, which encompasses the study of finite volume corrections and discretization effects, we report a value for the pion-nucleon sigma-term of 41(5)(4) MeV in the 2 flavor case and 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 lQCD data, given by a Sommer scale of r_0=0.493(23) fm.