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

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 $Z\to 0$ 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.

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Cited by in corpus (8)

• Stringent test of QED with hydrogenlike tin
• g Factor of Lithiumlike Silicon and Calcium: Resolving the Disagreement between Theory and Experiment
• Testing Standard Model extensions with few-electron ions
• Electron correlation effects on the $g$ factor of lithiumlike ions
• Thermal corrections to the bound-electron $g$-factor
• Improved bound-electron g-factor theory through complete two-loop QED calculations
• QED effects in quadratic Zeeman splitting in highly charged hydrogen-like ions
• Two-loop electron self-energy in bound-electron $g$ factor: diagrams in momentum-coordinate representation