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 Letter 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→l^{-}l^{+}p reaction, we show that a measurement of a ratio of e^{-}e^{+}+μ^{-}μ^{+} over e^{-}e^{+} cross sections with an absolute precision of 7×10^{-4} would allow for a test to distinguish, at the 3σ level, between the two different proton charge radii currently extracted from muonic and electronic observables.