Non-Perturbative Relativistic Calculation of the Muonic Hydrogen Spectrum

TL;DR

This paper performs a precise, non-perturbative numerical calculation of the muonic hydrogen spectrum, confirming earlier perturbative results and addressing discrepancies related to the proton charge radius.

Contribution

It introduces a non-perturbative Dirac equation approach including finite-size effects, validating perturbative methods used in muonic hydrogen spectroscopy.

Findings

No significant discrepancy between perturbative and non-perturbative calculations.

Results support the validity of perturbative methods in muonic hydrogen.

Confirms the need to reconsider proton charge radius measurements.

Abstract

We investigate the muonic hydrogen 2P^{F=2}_{3/2} to 2S^{F=1}_{1/2} transition through a precise, non-perturbative numerical solution of the Dirac equation including the finite-size Coulomb force and finite size vacuum polarization. The results are compared with earlier perturbative calculations of (primarily) Borie, Martynenko, and Pachucki; and experimental results recently presented by Pohl et al., in which this very comparison is interpreted as requiring a modification of the proton charge radius from that obtained in electron scattering and electronic hydrogen analyses. We find no significant discrepancy between the perturbative and non-perturbative calculations, and present our results as confirmation of the perturbative methods.