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

TL;DR

The paper addresses the nucleon axial coupling $g_A$ in two-flavor dynamical QCD by combining lattice simulations with non-perturbative renormalization of the axial current and a small-scale expansion (SSE) based extrapolation framework. The forward matrix elements of the isovector axial current are computed on ensembles with two degenerate Wilson quarks, with $Z_A$ determined non-perturbatively (RI$^\prime$-MOM and $\overline{MS}$ matching) and $g_A$ renormalized, while finite-volume effects are modeled within SSE to allow simultaneous extrapolations to infinite volume and the chiral limit. In SSE, the ${\mathcal{O}}(\epsilon^3)$ expansion includes explicit $\pi$, $N$, and $\Delta(1232)$ degrees of freedom, with eight diagrams $BFHM$ that contribute; the formalism also addresses cancellations of $\Delta_0$-dependent renormalizations to avoid scheme dependence. The study shows that the axial coupling in the chiral limit can be determined from finite-volume data without enforcing the physical-point value and provides a principled route to connect lattice results to the physical $g_A$, including controlled treatment of renormalization and finite-size effects.

Abstract

We present data for the axial coupling constant g_A of the nucleon obtained in lattice QCD with two degenerate flavours of dynamical non-perturbatively improved Wilson quarks. The renormalisation is also performed non-perturbatively. 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 flavours. 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.

Figures (3)

• Figure 1: The renormalization constant $Z_A$ plotted versus the square of the renormalization scale $\mu$.
• Figure 2: Results for $g_A$. For $(\beta,\kappa) = (5.29,0.1355)$ and $(5.29,0.1359)$ we show the results obtained on three different spatial volumes. The smallest box size $L$, leading to the smallest $g_A$, is about $1.0 \, \hbox{fm}$, while the middle size is approximately $1.3 \, \hbox{fm}$. All other volumes are larger. The star represents the physical point.
• Figure :