Contribution of \sigma-meson exchange to elastic lepton-proton scattering

TL;DR

This paper estimates the contribution of -meson exchange in elastic lepton-proton scattering, highlighting its significance for muons in the MUSE experiment and its negligible effect for electrons.

Contribution

It provides the first estimate of -meson exchange effects in lepton-proton scattering, emphasizing the impact of lepton mass differences in the MUSE kinematic region.

Findings

-meson exchange contributes up to 0.1% for muons at MUSE energies.

The effect is about 1000 times larger for muons than for electrons.

Lepton mass effects are crucial in elastic scattering analyses.

Abstract

Lepton mass effects play a decisive role in description of elastic lepton-proton scattering when the beam's energy is comparable to the mass of the lepton. The future MUSE experiment, which is devised to solve the "Proton Radius Puzzle", is going to cover the corresponding kinematic region for a scattering of muons by a proton target. We anticipate that helicity-flip meson exchanges will make a difference in comparison of elastic electron-proton versus muon-proton scattering in MUSE. In this article, we estimate the $\sigma$ meson exchange contribution in the $t$-channel. This contribution, mediated by two-photon coupling of $\sigma$, is calculated to be at most $\sim 0.1 \%$ for muons in the kinematics of MUSE and it is about 3 orders in magnitude larger than for electrons because of the lepton-mass difference.