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

TL;DR

This paper uses baryon chiral perturbation theory to analyze lattice QCD data, extracting the nucleon axial charge and radius, and demonstrating the significance of the $ riangle(1232)$ resonance contributions.

Contribution

It provides a leading one-loop order calculation including the $ riangle(1232)$ resonance, fitting lattice data to determine low-energy constants and extract nucleon axial properties.

Findings

Lattice QCD data up to 400 MeV pion mass fit well with the model.

Extracted axial charge $g_A=1.237(74)$ consistent with experimental values.

Axial radius $ angle=0.263(38)~{ m fm}^2$ agrees with recent neutrino scattering data.

Abstract

We calculate the nucleon axial form factor up to the leading one-loop order in a covariant chiral effective field theory with the $\Delta(1232)$ 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 $\sim 0.6$ GeV. The $\Delta(1232)$ 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 $\langle r_A^2\rangle =0.263(38)~{\rm fm}^2$. 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 quasi-elastic 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., one-loop level. A more precise determination might need terms of $\mathcal{O}(p^5)$.