Muonic hydrogen and the proton size

TL;DR

This paper refines the theoretical understanding of muonic hydrogen's energy levels using a comprehensive QED-based potential, leading to a more precise determination of the proton's size that supports the smaller radius suggested by muonic measurements.

Contribution

It introduces a detailed two-body potential including all relevant corrections to accurately analyze muonic hydrogen spectra and extract the proton radius.

Findings

Proton radius from muonic hydrogen is smaller than from electron scattering.

Theoretical calculations align with other muonic hydrogen studies.

The approach incorporates relativistic, recoil, and one-loop QED corrections.

Abstract

We reexamine the structure of the $n=2$ levels of muonic hydrogen using a two-body potential that includes all relativistic, recoil and one loop corrections. The potential was originally derived from QED to describe the muonium atom and accounts for all contributions to order $\alpha^5$. Since one loop corrections are included, the anomalous magnetic moment contributions of the muon can be identified and replaced by the proton anomalous magnetic moment to describe muonic hydrogen with a point-like proton. This serves as a convenient starting point to include the dominant electron vacuum polarization corrections to the spectrum and extract the proton's mean squared radius $r_p=\sqrt{\langle r^2\rangle}$. Our results are consistent with other theoretical calculations that find that the muonic hydrogen value for $r_p$ is smaller than the result obtained from electron scattering.