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

TL;DR

This paper discusses modifications to electromagnetic structure functions used in calculating the $ Z$-box diagram for parity-violating electron-proton scattering, aiming to resolve discrepancies among different research groups.

Contribution

It introduces new modification procedures for structure functions $F_{1,2,3}^{ Z}(x,Q^2)$, compares them with previous methods, and analyzes their impact on the $ Z$-box diagram calculations.

Findings

Different modifications lead to variations in the $ Z$-box diagram results.

The new $F_3^{ Z}(x,Q^2)$ modification improves resonance region modeling.

Discrepancies among groups are linked to structure function treatment at low $Q^2$ and $W^2$.

Abstract

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 $F_3^{\gamma Z}(x,Q^2)$ in the resonance region and calculate the axial contribution to the $\gamma Z$-box diagram. Details of these modifications will illuminate where discrepancies between the groups arise and where future improvements can be made.