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

TL;DR

This paper combines lattice QCD calculations and neutrino scattering data to precisely determine the weak axial form factor of the nucleon, improving understanding of neutral current interactions.

Contribution

It introduces a novel combined analysis using lattice QCD inputs and experimental data to accurately determine the neutral current weak axial form factor $G^Z_A(Q^2)$.

Findings

Determined $G^Z_A(0)$ with improved precision using lattice QCD.

Provided a phenomenological fit for $G^Z_A(Q^2)$ consistent with data.

Showed the importance of strange quark contributions in modeling neutrino-nucleon scattering.

Abstract

We present a determination of the neutral current weak axial charge $G^Z_A(0)=-0.654(3)_{\rm stat}(5)_{\rm sys}$ using the strange quark axial charge $G^s_A(0)$ 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 $G^Z_A(Q^2)$ in the range of $0\lesssim Q^2\leq 1$ GeV$^2$. This yields a phenomenological value of $G^Z_A(0)=-0.687(89)_{\rm stat}(40)_{\rm sys}$. The value of $G^Z_A(0)$ constrained by the lattice QCD calculation of $G^s_A(0)$, 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 $G^Z_A(Q^2)$ 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 $G^Z_A(Q^2)$ 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.