Binding Two-Loop Vacuum-Polarization Corrections to the Bound-Electron G Factor

Ulrich D. Jentschura, Missouri University of Science and Technology

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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 alpha2(Zalpha)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 deltag=7.442(alpha/pi)2(Zalpha)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).