Dispersion relation formalism for the two-photon exchange correction to elastic muon-proton scattering: elastic intermediate state

TL;DR

This paper develops a dispersion relation formalism to accurately calculate the two-photon exchange correction in elastic muon-proton scattering, incorporating the muon mass and polarization effects, and provides predictions across different beam energies.

Contribution

It introduces a novel dispersion relation approach with a subtraction function fixed by a model estimate, enabling precise predictions of two-photon exchange effects in muon-proton scattering.

Findings

The subtraction function is fixed using a model estimate at one energy.

Predictions are made for two additional beam energies.

Polarization observables are calculated considering the muon mass.

Abstract

We evaluate the two-photon exchange correction to the unpolarized cross section in the elastic muon-proton scattering within dispersion relations. One of the six independent invariant amplitudes requires a subtraction. We fix the subtraction function to the model estimate of the full two-photon exchange at one of three MUSE beam energies and make a prediction for the two other energies. Additionally, we present single and double polarization observables accounting for the lepton mass.