A reassessment of nuclear effects in muonic deuterium using pionless effective field theory at N3LO

TL;DR

This paper systematically assesses nuclear contributions to the muonic deuterium Lamb shift using pionless EFT at N3LO, refining theoretical models and extracting the deuteron charge radius with quantified uncertainties.

Contribution

It provides a detailed N3LO calculation of nuclear effects in muonic deuterium and improves the understanding of 2γ-exchange contributions, reducing theoretical discrepancies.

Findings

Deuteron charge radius: 2.12763(13)(77) fm

Refined 2γ-exchange contribution estimates

Correlation between deuteron charge and Friar radii

Abstract

We provide a systematic assessment of the order-$\alpha^5$ nuclear contributions to the Lamb shift of muonic deuterium, including the accompanying radiative corrections due to vacuum polarization, up to next-to-next-to-next-to-leading order (N3LO) within the pionless effective field theory (EFT). We also evaluate higher-order corrections due to the single-nucleon structure, which are expected to be the most important corrections beyond N3LO. We find a correlation between the deuteron charge and Friar radii, which can be useful to judge the quality of charge form factor parametrisations. We refine the theoretical description of the $2\gamma$-exchange contribution, especially in the elastic contribution and the radiative corrections, ameliorating the original discrepancy between theory and experiment in the size of $2\gamma$-exchange effects. Based on the experimental Lamb shift of muonic deuterium, we obtain the deuteron charge radius, $r_d(\mu\text{D})=2.12763(13)_\text{exp}(77)_\text{theory}$~fm, which is consistent with (but less precise than) the value obtained by combining the H-D isotope shift with the muonic hydrogen Lamb shift. The theory uncertainty is evaluated using a Bayesian procedure and is dominated by the truncation of the pionless EFT series.