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Lepton universality test in the photoproduction of $e^- e^+$ versus $μ^- μ^+$ pairs on a proton target

In view of the significantly different proton charge radius extracted from muonic hydrogen Lamb shift measurements as compared to electronic hydrogen spectroscopy or electron scattering experiments, we study in this work the photoproduction of a lepton pair on a proton target in the limit of very small momentum transfer as a way to provide a test of the lepton universality when extracting the proton charge form factor. By detecting the recoiling proton in the $γp \to l^- l^+ p$ reaction, we show that a measurement of a ratio of $e^-e^+ + μ^-μ^+$ over $e^-e^+$ cross sections with a relative precision of around 2%, would allow for a test to distinguish between the two different proton charge radii currently extracted from muonic and electronic observables.