Modification of electromagnetic structure functions for the $\gamma Z$-box diagram

The $\gamma Z$-box diagram for parity violating elastic $e$-$p$ scattering has recently undergone a thorough analysis by several research groups. Though all now agree on the analytic form of the diagram, the numerical results differ due to the treatment of the structure functions, $F_{1,2,3}^{\gamma Z}(x,Q^2)$. Currently, $F_{1,2,3}^{\gamma Z}(x,Q^2)$ at low $Q^2$ and $W^2$ must be approximated through the modification of existing fits to electromagnetic structure function data. We motivate and describe the modification used to obtain $F_{1,2}^{\gamma Z}(x,Q^2)$ in our previous work. We also describe an alternative modification and compare the result to our original calculation. Finally, we present a new modification procedure to acquire $F_3^{\gamma Z}(x,Q^2)$intheresonanceregionandcalculatetheaxialcontributiontothe$\gamma Z$-box diagram. Details of these modifications will illuminate where discrepancies between the groups arise and where future improvements can be made.