Weak Neutral Current Axial Form Factor Using $(\bar{\nu })\nu$-Nucleon Scattering and Lattice QCD Inputs

We present a determination of the neutral current weak axial charge $G_A^Z(0)=-0.654(3{)}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}(5{)}_{\mathrm{s}\mathrm{y}\mathrm{s}}$ 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 $0.24\lesssim Q^2\lesssim 0.71$ GeV${}^2$ to determine the neutral current weak axial form factor $G_A^Z(Q^2)$ in the range of $0\lesssim Q^2\leq 1$GeV$^2$\mathrm{.}Thisyieldsaphenomenologicalvalueof$G^Z_A(0)=-0.687(89){\rm stat}(40){\rm sys}$\mathrm{.}Thevalueof$G^Z_A(0)$ 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 $G_A^Z(Q^2)$ for $Q^2>0$. This constrained fit leads to an unambiguous determination of (anti)neutrino-nucleon neutral current elastic scattering differential cross section near $Q^2=0$ and can play an important role in numerically isolating nuclear effects in this region. We show a consistent description of $G_A^Z(Q^2)$ 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.