Axial coupling constant of the nucleon for two flavors of dynamical quarks in finite and infinite volume

Abstract

We present data for the axial coupling constant ${g}_{A}$ of the nucleon obtained in lattice QCD with two degenerate flavors of dynamical nonperturbatively improved Wilson quarks. The renormalization is also performed nonperturbatively. For the analysis we give a chiral extrapolation formula for ${g}_{A}$ based on the small scale expansion scheme of chiral effective field theory for two degenerate quark flavors. Applying this formalism in a finite volume, we derive a formula that allows us to extrapolate our data simultaneously to the infinite volume and to the chiral limit. Using the additional lattice data in finite volume, we are able to determine the axial coupling of the nucleon in the chiral limit without imposing the known value at the physical point.