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 $m_{\pi }\gtrsim 0.6\mathrm{GeV}$—down to physical values of $m_{\pi }.$ 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 $\Delta \mathrm{}\left(1230\right)\mathrm{}$ 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 $\Delta \mathrm{}\left(1230\right)\mathrm{}$ degrees of freedom is crucial. With information on important higher order couplings constrained from analyses of the $\pi \overrightarrow{N}\pi \pi N$ reaction, a chiral extrapolation function $g_A{(m}_{\pi })$ is obtained, which works well from the chiral limit across the physical point into the region of present lattice data. The resulting enhancement of $g_A{(m}_{\pi })$ near the physical pion mass is found to arise from an interplay between long- and short-distance physics.