Quark mass dependence of the nucleon axial-vector coupling constant

TL;DR

This work analyzes how the nucleon axial-vector coupling $g_A$ depends on the light-quark (pion) mass and evaluates chiral EFT extrapolations from lattice QCD data at large $m_\pi$ down to the physical point. It compares two SU(2) frameworks: HBChPT with only pions and nucleons, and SSE with explicit $\Delta(1232)$ degrees of freedom, finding that including the $\Delta$ is crucial for a realistic leading-one-loop extrapolation. The authors show that short-distance counterterms, constrained by $\pi N\to\pi\pi N$ analyses, are essential to counterbalance chiral logs and produce an extrapolation that agrees with the physical $g_A$ while matching lattice data. The resulting extrapolation is relatively flat across the explored $m_\pi$ range, with a mild enhancement near the physical point, demonstrating that a consistent interplay between long- and short-distance physics underpins the observed trend. This work underscores the necessity of the $\Delta$ degree of freedom in chiral extrapolations of axial observables and provides a framework for integrating lattice results with phenomenological constraints to predict $g_A$ across quark masses.

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 larger than 0.6 GeV - down to the physical value of the pion mass. 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(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 Delta(1230) degrees of freedom is crucial. With information on important higher order couplings constrained from analyses of inelastic pion production processes, a chiral extrapolation function for g_A is obtained, which works well from the chiral limit across the physical point into the region of present lattice data. The resulting enhancement of our extrapolation function near the physical pion mass is found to arise from an interplay between long- and short- distance physics.

Figures (7)

• Figure 1: Diagrams contributing to the nucleon axial-vector coupling constant $g_A$ at leading-one-loop order. The wiggly line denotes an external (isovector) axial-vector background field, interacting with a nucleon (solid lines).
• Figure 2: The long-dashed curve represents the free fit to the QCDSF lattice data below $m_\pi=750$ MeV, utilizing the leading-one-loop SSE (Fit Ib) results of Eq.(\ref{['gasse']}). The analogous leading-one-loop HBChPT result (fit Ia) originating from Eq.(\ref{['gAA']}) is shown as the short-dashed curve. The solid line represents fit II for the SSE extrapolation with the additional SU(6) quark model constraint $g_1=9/5\,g_A^0$. The indicated error band results from the 95% confidence ellipse shown in Fig.\ref{['su6confidence']}, while the solid dot indicates the physical value of $g_A$.
• Figure 3: Confidence ellipse for the SU(6)-constrained leading-one-loop SSE fit II shown in Fig.\ref{['su6fit']}. The two parameters shown denote the nucleon coupling constant $g_A^0$ in the chiral limit versus the parameter $C(\lambda)$ discussed in the text, evaluated at the regularization scale $\lambda=1$ GeV.
• Figure 4: Fit III: Incorporating known information from $\pi N\rightarrow\pi\pi N$ differential cross sections into the leading-one-loop SSE analysis. The solid line shows the central value, whereas the dashed curves denote the upper and lower error bar from Eq.(\ref{['GeVcouplings']}). The matching of the coupling constants was performed at $\lambda=0.54$ GeV as discussed in the text.
• Figure 5: Confidence ellipses for the constrained leading-one-loop SSE fit III shown in Fig.\ref{['cfit']}. The 2 parameters shown denote the nucleon coupling constant $g_A^0$ in the chiral limit versus the axial $\Delta \Delta$ coupling $g_1$. The three ellipses shown correspond to central, upper and lower values for the short distance couplings determined in Eq.(\ref{['GeVcouplings']}) at a scale of $\lambda=1$ GeV.