Theory of the two-loop self-energy correction to the g factor in nonperturbative Coulomb fields

B Sikora,V A Yerokhin,N S Oreshkina,C H Keitel,Z Harman,H Cakir

doi:10.1103/physrevresearch.2.012002

Abstract

Two-loop self-energy corrections to the bound-electron $g$ factor are investigated theoretically to all orders in the nuclear binding strength parameter $Z\alpha$. The separation of divergences is performed by dimensional regularization, and the contributing diagrams are regrouped into specific categories to yield finite results. We evaluate numerically the loop-after-loop terms, and the remaining diagrams by treating the Coulomb interaction in the electron propagators up to first order. The results show that such two-loop terms are mandatory to take into account for projected near-future stringent tests of quantum electrodynamics and for the determination of fundamental constants through the $g$ factor.

Highlights

Rapid CommunicationsTheory of the two-loop self-energy correction to the g factor in nonperturbative Coulomb fields
The results show that such two-loop terms are mandatory to take into account for projected near-future stringent tests of quantum electrodynamics and for the determination of fundamental constants through the g factor
In order to assess the relevance of a nonperturbative theory, we evaluate first the F term

Summary

Rapid Communications

Theory of the two-loop self-energy correction to the g factor in nonperturbative Coulomb fields. Two-loop self-energy corrections to the bound-electron g factor are investigated theoretically to all orders in the nuclear binding strength parameter Zα. The diagrams with the magnetic field acting on one of the electron propagators inside the SE loops [Figs. Contribution if the magnetic field acts on the central electron propagator [Figs. I ∈ {N, O} and j ∈ {side, ladder}, |a denotes the 1s reference state, γ 0 is the timelike Dirac matrix, Aμ is the magnetic four-potential with the Lorentz index μ, and the μ ij are the two-loop vertex functions The formulas for the latter are lengthy and will be presented elsewhere. The electron propagator between the magnetic interaction and the SE loops can be represented as a

Published by the American Physical Society

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