Two-loop vacuum polarization in a Coulomb field
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917085299343360 |
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| author | Volkov, S. A. Yerokhin, V. A. Harman, Z. Keitel, C. H. |
| author_facet | Volkov, S. A. Yerokhin, V. A. Harman, Z. Keitel, C. H. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_03284 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-loop vacuum polarization in a Coulomb field Volkov, S. A. Yerokhin, V. A. Harman, Z. Keitel, C. H. Atomic Physics High Energy Physics - Phenomenology 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. |
| title | Two-loop vacuum polarization in a Coulomb field |
| topic | Atomic Physics High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2509.03284 |