We calculate the nucleon axial form factor up to the leading one-loop orderin a covariant chiral effective field theory with the $\Delta(1232)$ resonanceas an explicit degree of freedom. We fit the axial form factor to the latestlattice QCD data and pin down the relevant low-energy constants. The latticeQCD data, for various pion masses below $400$ MeV, can be well described up toa momentum transfer of $\sim 0.6$ GeV. The $\Delta(1232)$ loops contributesignificantly to this agreement. Furthermore, we extract the axial charge andradius 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 obtainedcoupling $g_A$ is consistent with the experimental value if the uncertainty istaken into account. The axial radius is below but in agreement with the recentextraction from neutrino quasi-elastic scattering data on deuterium, which haslarge error bars. Up to our current working accuracy, $r_A$ is predicted onlyat leading order, i.e., one-loop level. A more precise determination might needterms of $\mathcal{O}(p^5)$.
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