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

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 $Δ(1232)$ degrees of freedom. We show that in the $Δ$-less case, at this order, the flat trend of $g_A (M_π)$ 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 $Δ$. From this fit we report $g_A (M_{π\rm{(phys)}}) = 1.260 \pm 0.012$, 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 $M_π$ in presence of the $Δ$.