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arXiv · 2509.03284

Two-loop vacuum polarization in a Coulomb field

S. A. Volkov·V. A. Yerokhin·Z. Harman·C. H. Keitel
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Abstract

The leading-order two-loop vacuum-polarization potential, linear in the Coulomb field of a nucleus, was first derived in the seminal 1955 work of Källén-Sabry. The higher-order two-loop vacuum-polarization corrections, however, have remained unknown until now. In this work, we compute Coulomb corrections to the Källén-Sabry potential, specifically those involving three, five, and seven Coulomb interactions inside the vacuum-polarization loop. The potentials are evaluated in momentum space and subsequently used to calculate one-electron energy shifts. Our results drastically reduce the theoretical uncertainty of the two-loop vacuum-polarization contribution to transition energies, which is required for next-generation tests of bound-state QED in heavy one and few-electron ions as well as for the determination of nuclear charge radii.

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S. A. Volkov, V. A. Yerokhin, Z. Harman, C. H. Keitel. 2025-11-17. Two-loop vacuum polarization in a Coulomb field. https://arxiv.org/abs/2509.03284

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