Two-photon exchange correction to muon-proton elastic scattering at low momentum transfer

TL;DR

This paper calculates the two-photon exchange correction to low-momentum transfer muon-proton elastic scattering, showing elastic contributions dominate and inelastic effects are within experimental uncertainties.

Contribution

It provides an exact calculation of elastic TPE and an approximate method for inelastic TPE using proton structure functions and Regge fits, relevant for upcoming experiments.

Findings

Elastic TPE dominates at low momentum transfer.

Inelastic TPE contributions are within expected experimental errors.

The approach uses unpolarized structure functions and a Regge-based subtraction function.

Abstract

We evaluate the two-photon exchange (TPE) correction to the muon-proton elastic scattering at small momentum transfer. Besides the elastic (nucleon) intermediate state contribution, which is calculated exactly, we account for the inelastic intermediate states by expressing the TPE process approximately through the forward doubly virtual Compton scattering. The input in our evaluation is given by the unpolarized proton structure functions and by one subtraction function. For the latter, we provide an explicit evaluation based on a Regge fit of high-energy proton structure function data. It is found that, for the kinematics of the forthcoming muon-proton elastic scattering data of the MUSE experiment, the elastic TPE contribution dominates, and the size of the inelastic TPE contributions is within the anticipated error of the forthcoming data.