Lowest-order QED radiative corrections in unpolarized elastic electron-deuteron scattering beyond the ultra-relativistic limit for the proposed deuteron charge radius measurement at Jefferson Laboratory

TL;DR

This paper provides detailed calculations of lowest-order QED radiative corrections for unpolarized elastic electron-deuteron scattering, crucial for the upcoming deuteron charge radius measurement at Jefferson Lab, especially beyond the ultra-relativistic limit.

Contribution

It offers the first comprehensive numerical evaluation of lowest-order radiative corrections in e-d scattering beyond the ultra-relativistic approximation for the DRad experiment.

Findings

Calculated radiative corrections for DRad kinematics.

Estimated systematic uncertainty from higher-order corrections.

Enhanced accuracy in deuteron charge radius extraction.

Abstract

Analogous to the well-known proton charge radius puzzle, a similar puzzle exists for the deuteron charge radius, $r_{d}$. There are discrepancies observed in the results of $r_{d}$, measured from electron-deuteron ($e-d$) scattering experiments, as well as from atomic spectroscopy. In order to help resolve the charge radius puzzle of the deuteron, the PRad collaboration at Jefferson Lab has proposed an experiment for measuring $r_{d}$, named DRad. This experiment is designed to measure the unpolarized elastic $e-d$ scattering cross section in a low-$Q^{2}$ region. To extract the cross section with a high precision, having reliable knowledge of QED radiative corrections is important. In this paper, we present complete numerical calculations of the lowest-order radiative corrections in $e-d$ scattering for the DRad kinematics. The calculations have been performed within a covariant formalism and beyond the ultra-relativistic approximation ($m_{e}^{2} \ll Q^{2}$). Besides, we present a systematic uncertainty on $r_{d}$ arising from higher-order radiative corrections, estimated based on our cross-section results.