# Leading order corrections to the Bethe-Heitler process in the $\gamma p\rightarrow l^+l^-p$ reaction

## TL;DR

This paper calculates one-loop QED corrections to the gamma p to l+ l- p process to test lepton universality and explore potential explanations for proton radius discrepancies, providing theoretical predictions for upcoming experiments.

## Contribution

It provides the first complete one-loop QED correction calculation including lepton mass effects for the gamma p to l+ l- p process, relevant for testing lepton universality.

## Key findings

- Two-photon exchange processes with both photons attached to the proton vanish after angle averaging.
- The full one-loop correction differs from soft-photon approximation results.
- Estimated small proton radiation effects are included.

## Abstract

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.