Soft-photon radiative corrections to the $e^- p \to e^- p l^- l^+$ process

TL;DR

This paper computes leading-order QED radiative corrections in the soft-photon approximation for the $e^- p o e^- p l^- l^+$ process across different energy regimes, highlighting their importance for nucleon structure studies.

Contribution

It provides the first detailed analysis of soft-photon radiative corrections for this process in both low- and high-energy regimes, crucial for accurate nucleon structure extraction.

Findings

Radiative corrections significantly impact cross sections.

Forward-backward asymmetry is minimally affected by corrections.

Beam-spin asymmetry remains unaffected in the soft-photon approximation.

Abstract

We calculate the leading-order QED radiative corrections to the process $e^- p\rightarrow e^- p l^- l^+ $ in the soft-photon approximation, in two different energy regimes which are of relevance to extract nucleon structure information. In the low-energy region, this process is studied to better constrain the hadronic corrections to precision muonic Hydrogen spectroscopy. In the high-energy region, the beam-spin asymmetry for double virtual Compton scattering allows to directly access the Generalized Parton Distributions. We find that the soft-photon radiative corrections have a large impact on the cross sections and are therefore of paramount importance to extract the nucleon structure information from this process. For the forward-backward asymmetry the radiative corrections are found to affect the asymmetry only around or below the 1\% level, whereas the beam-spin asymmetry is not affected at all in the soft-photon approximation, which makes them gold-plated observables to extract nucleon structure information in both the low- and high-energy regimes.