Improved Bound-Electron g -Factor Theory through Complete Two-Loop QED Calculations

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 Zα. Here, Z is the nuclear charge number and α 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 Zα. We apply our theory to the recently measured g factor of the hydrogenlike Sn11849+ ion [J. Morgner , ] 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. Published by the American Physical Society 2025