Two-loop virtual light-by-light scattering corrections to the bound-electron <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>g</mml:mi></mml:math> factor

Abstract

A critical set of two-loop quantum electrodynamics corrections to the $g$ factor of hydrogenlike ions is calculated in the Furry picture. These corrections are due to the polarization of the external magnetic field by the quantum vacuum, which is dressed by the binding field. The result obtained for the self-energy--magnetic-loop diagrams is compared with the current state-of-the-art result, derived through a perturbative expansion in the binding strength parameter $Z\ensuremath{\alpha}$, with $Z$ the atomic number and $\ensuremath{\alpha}$ the fine-structure constant. Agreement is found in the $Z\ensuremath{\rightarrow}0$ limit. However, even for very light ions, the perturbative result fails to approximate the magnitude of the corresponding correction to the $g$ factor. The total correction to the $g$ factor coming from all diagrams considered in this work is found to be highly relevant for upcoming experimental tests of fundamental physics with highly charged ions.