Non-Resonant Inelastic $\vec{e}p$ Scattering as a Probe of Hadron Structure*

The $Q_{weak}$ experiment at Jefferson Lab made the first direct measurement of the proton's weak charge, $Q^p_W$, via a measurement of the parity-violating asymmetry in elastic $\vec{e}p$ scattering with low four-momentum transfer. Energy-dependent electroweak radiative corrections must be applied to the measured asymmetry. The $\gamma Z$ box, where a photon and a Z-boson are simultaneously exchanged, is the most problematic correction. It cannot be calculated through the same perturbative methods as the rest of the corrections. The asymmetry arising from the $\gamma Z$ box depends on the $\gamma Z$ interference structure functions, $F_{1,3}^{\gamma Z}$, for which there is almost no data. Using the $Q_{weak}$ apparatus, with modifications, a measurement of the parity-violating asymmetry of non-resonant inelastic $\vec{e}p$ scattering was made with \SI{3.35}{GeV} incident electrons. The asymmetry of inelastically scattered electrons with $Q^2 \approx \SI{0.09}{(GeV/c)^2}$ and $W \approx \SI{2.23}{ GeV}$ was measured to experimentally validate and constrain theoretical predictions of the $\gamma Z$ box correction to the proton's weak charge and to probe the $F_{1,3}^{\gamma Z}$ structure functions. Final results will be presented and compared with theoretical predictions.