Two-loop virtual light-by-light scattering corrections to the bound-electron $g$ factor

TL;DR

This paper calculates two-loop quantum electrodynamics corrections to the bound-electron g factor in hydrogenlike ions without relying on small binding field approximations, revealing significant effects for experimental tests.

Contribution

It provides a non-perturbative calculation of two-loop light-by-light scattering corrections to the bound-electron g factor, extending beyond previous perturbative methods.

Findings

Agreement with perturbative results as Z→0

Perturbative approach fails for light ions

Corrections are significant for experimental tests

Abstract

A critical set of two-loop QED corrections to the $g$ factor of hydrogenlike ions is calculated without expansion in the nuclear binding field. 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 $Z\alpha$, with $Z$ the atomic number and $\alpha$ the fine-structure constant. Agreement is found in the $Z\rightarrow0$ 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.