Two-photon exchange corrections in elastic muon-proton scattering

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%.