Improved bound-electron g-factor theory through complete two-loop QED calculations

TL;DR

This paper presents an exact all-order calculation of the two-loop self-energy correction to the bound-electron g-factor in hydrogenlike ions, significantly reducing theoretical uncertainties and enabling more precise tests of quantum electrodynamics.

Contribution

The authors provide the first complete Zα-all-order calculation of the two-loop self-energy correction to the bound-electron g-factor, surpassing previous expansion-based methods.

Findings

Achieved the last missing parts of the two-loop self-energy correction in Zα.

Improved the theoretical accuracy of the g-factor for hydrogenlike $^{118}$Sn$^{49+}$ by a factor of 8.

Enabled more precise tests of QED and potential new physics in strong electromagnetic fields.

Abstract

The two-loop self-energy correction to the bound-electron $g$-factor in hydrogenlike ions is investigated, taking into account the electron-nucleus interaction exactly. This all-order calculation is required to improve the total theoretical uncertainty of the $g$-factor, which is limited by the fact that two-loop self-energy corrections have only been calculated so far in the form of an expansion in $Z\alpha$. Here, $Z$ is the nuclear charge number and $\alpha$ is the fine-structure constant. In this work, we report calculations of the last missing parts of the total two-loop self-energy correction, exactly in $Z\alpha$. We apply our theory to the recently measured $g$-factor of the hydrogenlike $^{118}$Sn$^{49+}$ ion [J. Morgner et al., Nature 622, 53 (2023)] and, with a factor of 8, improve the accuracy of its state-of-the-art theoretical value by almost one order of magnitude, enabling more detailed tests of quantum electrodynamics and new physics in strong fields.