Binding two-loop vacuum-polarization corrections to the bound-electron g factor

TL;DR

This paper evaluates the one- and two-loop vacuum-polarization corrections to the bound-electron g factor in hydrogenlike systems, providing a specific correction value and a tentative estimate for the complete two-loop correction.

Contribution

It introduces a detailed calculation of two-loop vacuum-polarization corrections with closed fermion loops and offers a tentative estimate for the total two-loop binding correction to the g factor.

Findings

Confirmed the one-loop vacuum-polarization correction.

Calculated a specific two-loop correction of 7.442 (alpha/pi)^2 (Z alpha)^5.

Provided a tentative estimate for the full two-loop correction.

Abstract

We commence the evaluation of the one- and two-loop binding corrections to the $g factor for an electron in a hydrogenlike system of order alpha^2 (Z alpha)^5 and consider diagrams with closed fermion loops. The one-loop vacuum-polarization correction is rederived and confirmed. For the two-loop vacuum-polarization correction, due to a specific gauge-invariant set of diagrams with closed fermion loops, we find a correction delta g = 7.442 (alpha/pi)^2 (Z alpha)^5. Based on the numerical trend of the coefficients inferred from the gauge-invariant subset, we obtain a numerically large tentative estimate for the complete two-loop binding correction to the g factor (sum of self-energy and vacuum polarization).