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

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.