Theory of the two-loop self-energy correction to the $\boldsymbol g$ factor in non-perturbative Coulomb fields

TL;DR

This paper provides a comprehensive theoretical analysis of two-loop self-energy corrections to the bound-electron g factor in strong Coulomb fields, crucial for high-precision tests of QED and fundamental constants.

Contribution

It develops a non-perturbative approach to calculate two-loop self-energy corrections to the g factor in Coulomb fields, including divergence separation and numerical evaluation.

Findings

Two-loop corrections are essential for precise QED tests.

Numerical results for loop-after-loop terms are provided.

First-order treatment of Coulomb interaction in remaining diagrams.

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.