Logarithmically enhanced Euler-Heisenberg Lagrangian contribution to the electron gyromagnetic factor

TL;DR

This paper reveals a previously unknown logarithmic enhancement in two-loop radiative corrections to the electron's g-factor in hydrogen-like ions, using an effective field theory approach with the Euler-Heisenberg Lagrangian.

Contribution

It introduces a novel logarithmic correction to the electron g-factor at two-loop order, derived via an effective field theory framework.

Findings

Logarithmic enhancement in two-loop corrections to g-factor

Quantitative expression for the correction involving ln Zα

Implication for precision tests of QED in bound systems

Abstract

Contrary to what was previously believed, two-loop radiative corrections to the $g$-factor of an electron bound in a hydrogen-like ion at $\mathcal{O}\left(\alpha^2 (Z\alpha)^5\right)$ exhibit logarithmic enhancement. This previously unknown contribution is due to a long-distance light-by-light scattering amplitude. Taking an effective field theory approach, and using the Euler-Heisenberg Lagrangian, we find $\Delta g = -\left( \frac{\alpha}{\pi} \right)^2\left(Z\alpha\right)^5 \frac{56 \pi}{135}\ln Z\alpha$.