Two-loop electron self-energy in bound-electron $g$ factor: diagrams in momentum-coordinate representation

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 hydrogen-like ions. A major breakthrough was recently achieved in [B. Sikora et al. Phys. Rev. Lett. 134, 123001 (2025)], where this effect was calculated without any expansion in the nuclear binding strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ 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.

References in corpus (30)

• High-precision measurement of the atomic mass of the electron
• Complete two-loop correction to the bound-electron g factor
• Recoil correction to the bound-electron g factor in H-like atoms to all orders in $\alpha Z$
• Self-energy correction to the bound-electron g factor in H-like ions
• Two-loop self-energy correction in high-Z hydrogen-like ions
• Evaluation of the self-energy correction to the g-factor of S states in H-like ions
• Non-perturbative calculation of the two-loop Lamb shift in Li-like ions
• Nonrelativistic QED approach to the bound-electron g factor
• Two-loop self-energy correction in H-like ions
• Direct Bound-Electron $g$ factor Difference Measurement with Coupled Ions
• Stringent test of QED with hydrogenlike tin
• Two-loop self-energy contribution to the Lamb shift in H-like ions
• Self-energy correction to the hyperfine splitting and the electron g factor in hydrogen-like ions
• Light-by-light scattering in the Lamb shift and the bound electron g factor
• Two-loop binding corrections to the electron gyromagnetic factor
• Two-loop QED corrections with closed fermion loops for the bound-electron g factor
• The two-loop self-energy for the ground state of medium-Z hydrogen-like ions
• Two-loop self-energy in the Lamb shift of the ground and excited states of hydrogen-like ions
• One-loop self-energy correction in a strong binding field
• Theory of the two-loop self-energy correction to the $\mathbf{g}$ factor in non-perturbative Coulomb fields
• The two-loop self-energy: diagrams in the coordinate-momentum representation
• Calculations of QED effects with the Dirac Green function
• Logarithmically enhanced Euler-Heisenberg Lagrangian contribution to the electron gyromagnetic factor
• Self-energy screening effects in the $g$ factor of Li-like ions
• Two-loop electron self-energy for low nuclear charges
• Critical evaluation of reference charge radii and applications in mirror nuclei
• Two-loop virtual light-by-light scattering corrections to the bound-electron $g$ factor
• Two-loop electron self-energy with accelerated partial-wave expansion
• One-loop electron self-energy with accelerated partial-wave expansion in Coulomb gauge
• Improved bound-electron g-factor theory through complete two-loop QED calculations