Manifestly Covariant Analysis of the QED Compton Process in $e p\to e γp$ and $e p \to e γX$

TL;DR

This work develops a manifestly covariant tensor framework to compute unpolarized QED Compton scattering cross sections in $ep$ collisions, directly incorporating experimental cuts and contrasting exact cross sections (via $F_1,F_2$ and proton form factors) with the EPA. The elastic channel is shown to agree with EPA at the sub-percent level, while the inelastic channel drives the overall difference, highlighting the importance of nonzero $Q^2$ contributions. Using H1 cuts and the ALLM97 $F_2$, the authors find $\,\sigma_{el}=1.7346$ pb and $\sigma_{inel}=1.1719$ pb (EPA: $1.7296$ pb and $1.5969$ pb), with total agreement around 14%; bin-by-bin comparisons reveal better EPA alignment in $x_\gamma$ than in $x_l$ bins. The method provides a robust platform for extracting the proton’s photon content and can be extended to polarized processes and other photon-induced reactions.

Abstract

We calculate the unpolarized QED Compton scattering cross section in a manifestly covariant way. Our approach allows a direct implementation of the specific kinematical cuts imposed in the experiments, {\it e. g.} HERA-H1. We compare the 'exact' cross section in terms of the structure functions $F_{1,2} (x_B,Q^2)$, assuming the Callan-Gross relation, with the one obtained using the equivalent photon approximation (EPA) as well as with the experimental results. We find that the agreement with the EPA is better in $x_γ$ bins, where $x_γ$ is the fraction of the longitudinal momentum of the proton carried by the virtual photon, compared to the bins in the leptonic variable $x_l$.