Light-quark mass dependence of the nucleon axial charge and pion-nucleon scattering phenomenology

TL;DR

This study investigates how the nucleon axial charge depends on light-quark mass using chiral perturbation theory, highlighting the importance of including the $$ degree of freedom for accurate lattice QCD data description.

Contribution

It demonstrates that including the $$ resonance is essential to accurately model the light-quark mass dependence of the nucleon axial charge in chiral perturbation theory.

Findings

Including $$ improves fit to lattice QCD data.

Reported $g_A$ at physical pion mass is 1.260 ± 0.012.

Determined $d_{16}$ value consistent with empirical data.

Abstract

The light-quark mass dependence of the nucleon axial isovector charge ($g_A$) has been studied up to next-to-next-to-leading order, $O(p^4)$, in relativistic chiral perturbation theory using extended-on-mass-shell renormalization, without and with explicit $\Delta (1232)$ degrees of freedom. We show that in the $\Delta$-less case, at this order, the flat trend of $g_A (M_{\pi})$ exhibited by state-of-the-art lattice QCD (LQCD) results cannot be reproduced using low energy constants (LECs) extracted from pion-nucleon elastic and inelastic scattering. A satisfactory description of these LQCD data is only achieved in the theory with $\Delta$. From this fit we report $g_A (M_{\pi\rm{(phys)}}) = 1.260 \pm 0.012$, close to the experimental result, and $d_{16}= -0.88\pm 0.88$ GeV$^{-2}$, in agreement with its empirical value. The large uncertainties are of theoretical origin, reflecting the difference between $O(p^3)$ and $O(p^4)$ that still persists at large $M_{\pi}$ in presence of the $\Delta$.