Two-photon exchange corrections in elastic electron-proton scattering

TL;DR

This paper refines predictions for two-photon exchange corrections in elastic electron-proton scattering using a dispersion relation approach, and extends the formalism to muon-proton scattering relevant for upcoming experiments.

Contribution

It introduces a subtracted dispersion relation formalism for TPE corrections and applies it to both electron and muon scattering, including the impact of the VVCS subtraction function.

Findings

TPE corrections are negligible in electron-proton scattering.

The corrections are smaller than MUSE experiment uncertainties.

The formalism is extended to muon-proton scattering at low momentum transfer.

Abstract

We apply a subtracted dispersion relation (DR) formalism with the aim to improve predictions for the two-photon exchange (TPE) corrections to elastic electron-proton scattering observables at small momentum transfers. We study the formalism on the elastic TPE contribution in comparison with existing data for unpolarized cross sections. We extend the general formalism of TPE to elastic scattering with massive lepton and perform a numerical estimate of the muon-proton scattering at low momentum transfer in view of the upcoming muon-proton scattering experiment (MUSE). We study the influence of the double-virtual Compton scattering (VVCS) subtraction function on the unpolarized lepton-proton scattering cross-section. We show that the resulting TPE correction is negligible in the electron-proton scattering and smaller than planned uncertainties of the MUSE experiment for the subtraction functions evaluated in chiral perturbation theory.