Confronting axial-vector form factor from lattice QCD with MINERvA antineutrino-proton data

We compare recent MINERvA antineutrino-hydrogen charged-current measurements to phenomenological predictions of the axial-vector form factor based on fits to all available electron scattering and deuterium bubble-chamber data and to representative lattice-QCD (LQCD) determination by the PNDME Collaboration. While there is $1$--$2\sigma$ agreement in the cross section with MINERvA data for each bin in $Q^2$, we identify three regions with different relevance and opportunity for LQCD predictions. For $Q^2 \lesssim 0.2~\mathrm{GeV}^2$, the phenomenological extractions have large number of data points and LQCD is competitive, while MINERvA data have large errors. For $0.2~\mathrm{GeV}^2 \lesssim Q^2 \lesssim 1~\mathrm{GeV}^2$, LQCD is competitive with the MINERvA determination, and both give values larger than from phenomenological extraction. For $Q^2 > 1~\mathrm{GeV}^2$, the MINERvA data are the most precise. Our analysis indicates that with improving precision of MINERvA-like experiments and LQCD data, the uncertainty in the nucleon axial-vector form factor will be steadily reduced.