Weak neutral current axial form factor using $ \left(\overline{\nu}\right)\nu $-nucleon scattering and lattice QCD inputs

We present a determination of the neutral current weak axial charge $$ {G}_A^Z(0)=-0.654{(3)}_{\mathrm{stat}}{(5)}_{\mathrm{sys}} $$ using the strange quark axial charge $$ {G}_A^s(0) $$ calculated with lattice QCD. We then perform a phenomenological analysis, where we combine the strange quark electromagnetic form factor from lattice QCD with (anti)neutrino-nucleon scattering differential cross section from MiniBooNE experiments in a momentum transfer region 0.24 ≲ Q2 ≲ 0.71 GeV2 to determine the neutral current weak axial form factor $$ {G}_A^Z\left({Q}^2\right) $$ in the range of 0 ≲ Q2 ≤ 1 GeV2. This yields a phenomenological value of $$ {G}_A^Z(0) $$ = −0.687(89)stat(40)sys. The value of $$ {G}_A^Z(0) $$ constrained by the lattice QCD calculation of $$ {G}_A^s(0) $$, when compared to its phenomenological determination, provides a significant improvement in precision and accuracy and can be used to provide a constraint on the fit to $$ {G}_A^Z\left({Q}^2\right) $$ for Q2> 0. This constrained fit leads to an unambiguous determination of (anti)neutrino-nucleon neutral current elastic scattering differential cross section near Q2 = 0 and can play an important role in numerically isolating nuclear effects in this region. We show a consistent description of $$ {G}_A^Z\left({Q}^2\right) $$ obtained from the (anti)neutrino-nucleon scattering cross section data requires a nonzero contribution of the strange quark electromagnetic form factor. We demonstrate the robustness of our analysis by providing a post-diction of the BNL E734 experimental data.