Two-photon exchange corrections in elastic muon-proton scattering

TL;DR

This paper extends the two-photon exchange formalism to include lepton mass effects and estimates its impact on low-momentum transfer muon-proton scattering, relevant for the upcoming MUSE experiment.

Contribution

It introduces a comprehensive formalism accounting for lepton mass in two-photon exchange and provides numerical estimates for muon-proton scattering corrections at low momentum transfer.

Findings

Two-photon exchange correction is about 0.5% in the MUSE kinematic region.

Proton intermediate state dominates the two-photon exchange contribution.

Formalism can be used for precise interpretation of muon-proton scattering data.

Abstract

We extend the general formalism of two-photon exchange to elastic lepton-nucleon scattering by accounting for all lepton mass terms. We then perform a numerical estimate of the muon-proton scattering at low momentum transfer in view of the future MUSE experiment. For this purpose, we estimate the two-photon exchange corrections to muon-proton scattering observables by considering the contribution of the proton intermediate state, which is expected to dominate at very low momentum transfers. We find that the two-photon exchange effect to the unpolarized muon- proton scattering cross section in the MUSE kinematical region is of the order of 0.5%.