Theory of the Lamb shift in hydrogen and light hydrogen-like ions

TL;DR

This paper reviews the current theoretical understanding of the Lamb shift in hydrogen and light hydrogen-like ions, emphasizing recent progress and remaining uncertainties in high-precision QED calculations crucial for fundamental constant determinations.

Contribution

It provides a comprehensive review of the latest theoretical calculations of the Lamb shift, highlighting the impact of recent proton radius measurements and the need for improved multi-loop QED computations.

Findings

Proton radius measurement significantly reduced Lamb shift uncertainty.

Two- and three-loop QED effects are now the dominant theoretical uncertainties.

Critical assessment of various effects' contributions to the Lamb shift.

Abstract

Theoretical calculations of the Lamb shift provide the basis required for the determination of the Rydberg constant from spectroscopic measurements in hydrogen. The recent high-precision determination of the proton charge radius drastically reduced the uncertainty in the hydrogen Lamb shift originating from the proton size. As a result, the dominant theoretical uncertainty now comes from the two- and three-loop QED effects, which calls for further advances in their calculations. We review the present status of theoretical calculations of the Lamb shift in hydrogen and light hydrogen-like ions with the nuclear charge number up to $Z = 5$. Theoretical errors due to various effects are critically examined and estimated.