Weak neutral current axial form factor using (ν ¯)ν -nucleon scattering and lattice QCD inputs

We present a determination of the neutral current weak axial charge G_A^Z(0 )=-0.654 (3_)stat(5_)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(Q²) 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(Q²) 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(Q²) 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.