  The ratio of di-lepton production cross sections on a proton, using the
$\gamma p\rightarrow l^+ l^- p$ process, above and below di-muon production
threshold allows to extract the effective lepton-proton interaction, which is
required to be identical for electrons and muons if lepton universality is
exact. To test for a scenario of broken universality at the percent level, of
the size which could explain the different proton charge radii extracted from
electron scattering and from muonic hydrogen spectroscopy, we evaluate all
one-loop QED corrections to this process, including the full lepton mass
dependencies. We furthermore show that two-photon exchange processes with both
photons attached to the proton line vanish after averaging over di-lepton
angles, and estimate the relatively small radiation off the proton. We compare
the full one-loop calculation with a soft-photon approximation of the same
order, and present estimates for a planned experiment.
