Quark mass dependence of the nucleon axial-vector coupling constant

Abstract

We study the quark mass expansion of the axial-vector coupling constant ${g}_{A}$ of the nucleon. The aim is to explore the feasibility of chiral effective field theory methods for extrapolation of lattice QCD results---so far determined at relatively large quark masses corresponding to pion masses ${m}_{\ensuremath{\pi}}\ensuremath{\gtrsim}0.6\mathrm{GeV}$---down to physical values of ${m}_{\ensuremath{\pi}}.$ We compare two versions of non-relativistic chiral effective field theory: One scheme restricted to pion and nucleon degrees of freedom only, and an alternative approach which incorporates explicit $\ensuremath{\Delta}(1230)$ resonance degrees of freedom. It turns out that, in order to approach the physical value of ${g}_{A}$ in a leading-one-loop calculation, the inclusion of the explicit $\ensuremath{\Delta}(1230)$ degrees of freedom is crucial. With information on important higher order couplings constrained from analyses of the $\ensuremath{\pi}\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\pi}\ensuremath{\pi}N$ reaction, a chiral extrapolation function ${g}_{A}{(m}_{\ensuremath{\pi}})$ is obtained, which works well from the chiral limit across the physical point into the region of present lattice data. The resulting enhancement of ${g}_{A}{(m}_{\ensuremath{\pi}})$ near the physical pion mass is found to arise from an interplay between long- and short-distance physics.