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arXiv · 0904.0835

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

U. D. Jentschura
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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).

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U. D. Jentschura. 2009-04-06. Binding two-loop vacuum-polarization corrections to the bound-electron g factor. https://doi.org/10.1103/physreva.79.044501

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