Analytical Evaluation of Elastic Lepton-Proton Two-Photon Exchange in Chiral Perturbation Theory

TL;DR

This paper provides an exact analytical evaluation of two-photon exchange contributions in low-energy elastic lepton-proton scattering using chiral perturbation theory, highlighting differences between muon and electron interactions.

Contribution

It introduces a comprehensive next-to-leading order calculation of two-photon exchanges, including all soft and hard contributions, surpassing soft-photon approximation methods.

Findings

Identifies missing contributions in soft-photon approximations.

Analytically evaluates infrared divergent diagrams.

Highlights differences in muon-proton and electron-proton scattering.

Abstract

We present an exact evaluation of the two-photon exchange contribution to the elastic lepton-proton scattering process at low-energies using heavy baryon chiral perturbation theory. The evaluation is performed including next-to-leading order accuracy. This exact analytical evaluation contains all soft and hard two-photon exchanges and we identify the contributions missing in a soft-photon approximation approach. We evaluate the infrared divergent four-point box diagrams analytically using dimensional regularization. We also emphasize the differences between muon-proton and electron-proton scatterings relevant to the MUSE kinematics due to lepton mass differences.