Determining the Nucleon's Neutral Weak Axial Form Factor $G^{e(T=1)}_{A}$ Using Quasi-Elastic Electron Scattering from a Deuterium Target

The $G^{0}$ collaboration has taken data using the Jefferson Lab high- luminosity polarized electron beam to measure the parity-violating asymmetry of elastically and quasi-elastically scattered electrons from cryogenic proton and deuterium targets. This asymmetry, arising from the interference between the electromagnetic and neutral weak interactions and which may be as small as a few ppm, provides a means to determine the strange quark contribution to the proton electric and magnetic form factors, $G^{s}_{E}$ and $G^{s}_{M}$, and the neutron's neutral weak axial form factor, $G^{e(T=1)}_{A}$. The asymmetry seen in quasi-elastic electron scattering from deuterium is predominantly sensitive to the isovector part of $G^{e}_{A}$, which is one of the dominant uncertainties in the present experimental determination of $G^{s}_{E}$ and $G^{s}_{M}$ at lower momentum transfer. The status, method, and on-going analysis of the data quality, behavior of asymmetries, and systemic errors involved in the determination of $G^{e}_{A}$ at $Q^{2}$ of 0.23 $GeV^{2}$ and 0.63 $GeV^{2}$ will be presented.