Manifestly covariant analysis of the QED Compton processin ep→eγp and ep→eγX

We calculate the unpolarized QED Compton scattering cross section in a manifestly covariant way. Our approach allows a direct implementation to be made of the specific kinematical cuts imposed in the experiments, e.g. HERA-H1. We compare the 'exact' cross section in terms of the structure functions F-1,F-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(gamma) bins, where x(gamma) 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).