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.
Highlights
The proton radius puzzle, the discrepancy between extractions of the proton charge radius from electron scattering or electronic hydrogen spectroscopy on the one hand and from muonic hydrogen spectroscopy on the other hand, has not been solved yet
To test for a scenario of broken universality at the percent level, of the size that 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 extend our calculation of the QED corrections in the soft-photon approximation and present a full one-loop QED calculation, keeping all terms in the lepton mass
Summary
The proton radius puzzle, the discrepancy between extractions of the proton charge radius from electron scattering or electronic hydrogen spectroscopy on the one hand and from muonic hydrogen spectroscopy on the other hand, has not been solved yet. The initial discrepancy amounted to around 5.6σ when comparing both values: the extraction using elastic electron scattering, from which the A1@MAMI Collaboration reported the value RE 1⁄4 0.879ð8Þ fm [1,2], and the muonic hydrogen spectroscopy, which reported the value RE 1⁄4 0.84087ð39Þ fm [3,4], with more than an order of magnitude higher precision This puzzle has spurred a lot of activity, resulting in a new round of experiments in the field, which are crucial for scrutinizing and improving our understanding of systematic errors in such precision measurements. It was found that the difference between both values for the extracted proton charge radius amounts to an effect of 0.2% on this cross section ratio Such a measurement would allow one to test lepton universality at a significance level of three. Several technical details are discussed in five Appendixes
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