Non-relativistic contributions in order $\alpha^5m_\mu c^2$ to the Lamb shift in muonic hydrogen, deuterium and helium ion

TL;DR

This paper calculates specific non-relativistic quantum electrodynamics corrections of order α^5m_μ to the Lamb shift in muonic hydrogen, deuterium, and helium ion, refining previous partial results.

Contribution

It provides a complete calculation of the α^5m_μ contributions to the Lamb shift, including effects from vacuum polarization and light-by-light scattering, for multiple muonic atoms.

Findings

Calculated full α^5m_μ contributions to the Lamb shift in muonic hydrogen.

Adjusted results for muonic deuterium and helium ion.

Refined theoretical predictions for energy level shifts in light muonic atoms.

Abstract

Contributions to the energy levels in light muonic atoms and, in particular, to the Lamb shift fall into a few well-distinguished classes. The related diagrams are calculated using different approaches. In particular, there is a specific kind of non-relativistic contributions. Here we consider such corrections to the Lamb shift in order $\alpha^5m_\mu$. These contributions are due to free vacuum polarization loops as well as to various effects of light-by-light scattering. The closed loop in the related diagrams is an electronic one, which allows a non-relativistic consideration of the muon. Both kinds of contributions have been known for a while, however, the results obtained up to date are only partial ones. We complete a calculation of the $\alpha^5m_\mu$ contributions for muonic hydrogen. The results are also adjusted for muonic deuterium and muonic helium ion.