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Two-loop electron self-energy in the bound-electron g factor: Diagrams in momentum-coordinate representation

V. A. Yerokhin*, B. Sikora, Z. Harman, and C. H. Keitel

  • *Contact author: vladimir.yerokhin@mpi-hd.mpg.de
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Phys. Rev. A 112, 062806 – Published 2 December, 2025

DOI: https://doi.org/10.1103/yflg-7wz4

Abstract

The two-loop electron self-energy correction is one of the most problematic QED effects and, for a long time, was the dominant source of uncertainty in the theoretical prediction of the bound-electron g factor in hydrogenlike ions. A major breakthrough was recently achieved by B. Sikora et al. [Phys. Rev. Lett. 134, 123001 (2025)], who calculated this effect without any expansion in the nuclear binding strength parameter Zα (where Z is the nuclear charge number and α is the fine-structure constant). In this paper we describe our calculations of one of the most difficult parts of the two-loop self-energy, represented by Feynman diagrams that are treated in the mixed momentum-coordinate representation.

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References (45)

  1. H. Häffner, T. Beier, N. Hermanspahn, H.-J. Kluge, W. Quint, S. Stahl, J. Verdú, and G. Werth, Phys. Rev. Lett. 85, 5308 (2000).
  2. J. Verdú, S. Djekić, S. Stahl, T. Valenzuela, M. Vogel, G. Werth, T. Beier, H.-J. Kluge, and W. Quint, Phys. Rev. Lett. 92, 093002 (2004).
  3. S. Sturm, A. Wagner, B. Schabinger, J. Zatorski, Z. Harman, W. Quint, G. Werth, C. H. Keitel, and K. Blaum, Phys. Rev. Lett. 107, 023002 (2011).
  4. S. Sturm, A. Wagner, M. Kretzschmar, W. Quint, G. Werth, and K. Blaum, Phys. Rev. A 87, 030501(R) (2013).
  5. S. Sturm, F. Köhler, J. Zatorski, A. Wagner, Z. Harman, G. Werth, W. Quint, C. H. Keitel, and K. Blaum, Nature (London) 506, 467 (2014).
  6. T. Sailer, V. Debierre, Z. Harman, F. Heiße, C. König, J. Morgner, B. Tu, A. V. Volotka, C. H. Keitel, K. Blaum et al., Nature (London) 606, 479 (2022).
  7. J. Morgner, B. Tu, C. König, T. Sailer, F. Heiße, H. Bekker, B. Sikora, C. Lyu, V. Yerokhin, Z. Harman et al., Nature (London) 622, 53 (2023).
  8. H. Persson, S. Salomonson, P. Sunnergren, and I. Lindgren, Phys. Rev. A 56, R2499(R) (1997).
  9. T. Beier, Phys. Rep. 339, 79 (2000).
  10. V. M. Shabaev and V. A. Yerokhin, Phys. Rev. Lett. 88, 091801 (2002).
  11. V. A. Yerokhin, P. Indelicato, and V. M. Shabaev, Phys. Rev. Lett. 89, 143001 (2002).
  12. K. Pachucki, U. D. Jentschura, and V. A. Yerokhin, Phys. Rev. Lett. 93, 150401 (2004); 94, 229902 (2005).
  13. K. Pachucki, A. Czarnecki, U. D. Jentschura, and V. A. Yerokhin, Phys. Rev. A 72, 022108 (2005).
  14. A. Czarnecki and R. Szafron, Phys. Rev. A 94, 060501(R) (2016).
  15. A. Czarnecki, M. Dowling, J. Piclum, and R. Szafron, Phys. Rev. Lett. 120, 043203 (2018).
  16. A. Czarnecki, J. Piclum, and R. Szafron, Phys. Rev. A 102, 050801(R) (2020).
  17. V. A. Yerokhin and Z. Harman, Phys. Rev. A 88, 042502 (2013).
  18. V. Debierre, B. Sikora, H. Cakir, N. S. Oreshkina, V. A. Yerokhin, C. H. Keitel, and Z. Harman, Phys. Rev. A 103, L030802 (2021).
  19. V. A. Yerokhin, P. Indelicato, and V. M. Shabaev, Phys. Rev. Lett. 91, 073001 (2003).
  20. V. A. Yerokhin, P. Indelicato, and V. M. Shabaev, Phys. Rev. A 71, 040101(R) (2005).
  21. V. A. Yerokhin, P. Indelicato, and V. M. Shabaev, Phys. Rev. Lett. 97, 253004 (2006).
  22. V. A. Yerokhin, Phys. Rev. A 80, 040501(R) (2009).
  23. V. A. Yerokhin, Phys. Rev. A 97, 052509 (2018).
  24. V. A. Yerokhin, Z. Harman, and C. H. Keitel, Phys. Rev. Lett. 133, 251803 (2024).
  25. V. A. Yerokhin, Z. Harman, and C. H. Keitel, Phys. Rev. A 111, 042820 (2025).
  26. B. Sikora, Ph.D. thesis, Ruperto-Carola-University of Heidelberg, 2018, https://archiv.ub.uni-heidelberg.de/volltextserver/24575/1/DoktorarbeitSikora.pdf.
  27. B. Sikora, V. A. Yerokhin, N. S. Oreshkina, H. Cakir, C. H. Keitel, and Z. Harman, Phys. Rev. Res. 2, 012002(R) (2020).
  28. B. Sikora, V. A. Yerokhin, C. H. Keitel, and Z. Harman, Phys. Rev. Lett. 134, 123001 (2025).
  29. V. A. Yerokhin and V. M. Shabaev, Phys. Rev. A 64, 062507 (2001).
  30. V. A. Yerokhin, P. Indelicato, and V. M. Shabaev, Eur. Phys. J. D 25, 203 (2003).
  31. V. A. Yerokhin, Eur. Phys. J. D 58, 57 (2010).
  32. V. A. Yerokhin and U. D. Jentschura, Phys. Rev. A 81, 012502 (2010).
  33. S. Mallampalli and J. Sapirstein, Phys. Rev. A 57, 1548 (1998).
  34. V. A. Yerokhin and V. M. Shabaev, Phys. Rev. A 60, 800 (1999).
  35. V. A. Yerokhin and A. V. Maiorova, Symmetry 12, 800 (2020).
  36. V. A. Yerokhin, P. Indelicato, and V. M. Shabaev, Phys. Rev. A 69, 052503 (2004).
  37. S. A. Blundell, K. T. Cheng, and J. Sapirstein, Phys. Rev. A 55, 1857 (1997).
  38. V. A. Yerokhin, A. N. Artemyev, T. Beier, G. Plunien, V. M. Shabaev, and G. Soff, Phys. Rev. A 60, 3522 (1999).
  39. V. A. Yerokhin, K. Pachucki, and V. M. Shabaev, Phys. Rev. A 72, 042502 (2005).
  40. I. Angeli and K. Marinova, At. Data Nucl. Data Tables 99, 69 (2013).
  41. B. Ohayon, At. Data Nucl. Data Tables 165, 101732 (2025).
  42. S. Sturm, I. Arapoglou, A. Egl, M. Höcker, S. Kraemer, T. Sailer, B. Tu, A. Weigel, R. Wolf, J. C. López-Urrutia et al., Eur. Phys. J.: Spec. Top. 227, 1425 (2019).
  43. J. Sapirstein and K. T. Cheng, Phys. Rev. A 108, 042804 (2023).
  44. V. A. Yerokhin, Z. Harman, and C. H. Keitel, Phys. Rev. A 111, 012802 (2025).
  45. V. A. Yerokhin, K. Pachucki, M. Puchalski, C. H. Keitel, and Z. Harman, Phys. Rev. A 102, 022815 (2020).

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Phys. Rev. A 112, 062806– Published 2 December, 2025
  • Received 29 September 2025
  • Accepted 10 November 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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