Extraction of nucleon axial charge and radius from lattice QCD results using baryon chiral perturbation theory

We calculate the nucleon axial form factor up to the leading one-loop order in a covariant chiral effective field theory with the Δ (1232 ) resonance as an explicit degree of freedom. We fit the axial form factor to the latest lattice QCD data and pin down the relevant low-energy constants. The lattice QCD data, for various pion masses below 400 MeV, can be well described up to a momentum transfer of ∼0.6 GeV . The Δ (1232 ) loops contribute significantly to this agreement. Furthermore, we extract the axial charge and radius based on the fitted values of the low-energy constants. The results are g_A=1.237 (74 ) and ⟨r_A²⟩=0.263 (38 ) fm² . The obtained coupling g_A is consistent with the experimental value if the uncertainty is taken into account. The axial radius is below but in agreement with the recent extraction from neutrino quasielastic scattering data on deuterium, which has large error bars. Up to our current working accuracy, r_A is predicted only at leading order, i.e., the one-loop level. A more precise determination might need terms of O (p⁵).