Abstract
We report on the calculation of first-order QED corrections for the $\gamma p\rightarrow l^+l^-p^{\prime}$ process. An upcoming experiment at MAMI (Mainz) aims to compare the cross sections of muon- and electron-pair production in this reaction to test lepton universality. Precise knowledge of the electromagnetic radiative corrections is needed for these measurements. As a first step, we present the leading QED radiative corrections in the soft-photon approximation when accounting for the finite lepton mass. For the kinematics at MAMI, we find corrections of the percent level for muons, and of order $10\%$ for electrons.
Highlights
Recent experiments found a significant difference in the proton charge radius, comparing measurements with electrons and muons
The reported value of the muonic hydrogen experiments is RE 1⁄4 0.84087ð39Þ fm [4]. This discrepancy, often referred to as the proton radius puzzle, has triggered a lot of activity in recent years. Explanations for this puzzle reach from systematic errors in the extraction, see Refs. [5,6,7,8,9,10,11,12], to physics beyond the standard model, see for example in Refs. [13,14,15,16,17,18,19,20,21,22]
If one tries to explain this puzzle by new physics, one has to give up lepton universality as a consequence, since this requires the same, universal coupling for all leptons
Summary
Recent experiments found a significant difference in the proton charge radius, comparing measurements with electrons and muons. The reported value of the muonic hydrogen experiments is RE 1⁄4 0.84087ð39Þ fm [4] This discrepancy, often referred to as the proton radius puzzle, has triggered a lot of activity in recent years. To shed further light on this puzzle and test lepton universality, the MUSE experiment has been proposed, which aims at comparing the scattering of muons and electrons on a proton target [23,24]. Experiment only requires a relative measurement through the ratio of electron- and muon-pair production cross sections slightly above dimuon production threshold.
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