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

TL;DR

This paper proposes a method to test lepton universality by comparing electron and muon pair photoproduction on protons, aiming to clarify discrepancies in proton charge radius measurements from different experiments.

Contribution

It introduces a novel experimental approach to compare lepton pair production cross sections, providing a potential way to resolve proton radius discrepancies.

Findings

A ratio measurement with 2% precision can distinguish proton charge radius differences.

The method offers a direct test of lepton universality in proton interactions.

It connects lepton pair photoproduction to fundamental proton structure questions.

Abstract

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 $\gamma p \to l^- l^+ p$ reaction, we show that a measurement of a ratio of $e^-e^+ + \mu^-\mu^+$ 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.