$\gamma Z$-exchange contribution in elastic $ep$ scattering by perturbative QCD

TL;DR

This paper calculates the $b3 Z$-exchange contribution to elastic electron-proton scattering at high momentum transfer using perturbative QCD, revealing the need to modify dispersion relations at high energies.

Contribution

It provides analytical expressions for the $b3 Z$-exchange amplitudes and shows that the commonly used dispersion relation for the axial-vector part is invalid at high $Q^2$, requiring a modification.

Findings

The $b3 Z$-exchange amplitude contributions are analytically derived.

The usual dispersion relation for the axial-vector amplitude is invalid at high $Q^2$.

High-energy behavior constrains low-energy dispersion relation assumptions.

Abstract

In this study, we calculate the $\gamma Z$-exchange contribution to elastic $ep$ scattering at large momentum transfer within perturbative QCD. We present analytical expressions for the $\gamma Z$-exchange contributions to the amplitudes. We also estimate the asymptotic behaviors of the amplitude contributions and of the physical quantity $A_{\text{PV}}$ at high momentum transfer. These asymptotic behaviors determine the subtraction order in the dispersion relations (DRs) satisfied by the amplitudes. We find that the DR usually used in the literature for the axial-vector part of the amplitude is not valid at high $Q^2$ and should be modified to a once-subtracted form. Within the present pQCD framework and the adopted proton distribution amplitudes, these high-energy properties also provide nontrivial constraints on low-energy DR assumptions.