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

Abstract

The light-quark mass dependence of the nucleon axial isovector charge (gA) has been studied up to next-to-next-to-leading order, O(p 4 ), in relativistic chiral perturbation theory using extendedon-mass-shell renormalization, without and with explicit ∆(1232) degrees of freedom. We show that in the ∆-less case, at this order, the flat trend of gA(Mπ) 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 ∆. From this fit we report gA(M π(phys) ) = 1.260 ± 0.012, close to the experimental result, and d16 = −0.88 ± 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 Mπ in presence of the ∆.I.