Theory of the two-loop self-energy correction to the $\mathbf{g}$ factor in non-perturbative Coulomb fields

Abstract

Two-loop self-energy corrections to the bound-electron $g$ factor are investigated theoretically to all orders in the nuclear binding strength parameter $Z\alpha$. The separation of divergences is performed by dimensional regularization, and the contributing diagrams are regrouped into specific categories to yield finite results. We evaluate numerically the loop-after-loop terms, and the remaining diagrams by treating the Coulomb interaction in the electron propagators up to first order. The results show that such two-loop terms are mandatory to take into account for projected near-future stringent tests of quantum electrodynamics and for the determination of fundamental constants through the $g$ factor.

References in corpus (21)

• High-precision measurement of the atomic mass of the electron
• Dual kinetic balance approach to basis set expansions for the Dirac equation
• Two-time Green function method in quantum electrodynamics of high-Z few-electron atoms
• 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
• Nonrelativistic QED approach to the bound-electron g factor
• Non-perturbative calculation of the two-loop Lamb shift in Li-like ions
• The $g$-factor of light ions for an improved determination of the fine-structure constant
• Virtual light-by-light scattering and the g factor of a bound electron
• $g$-factor of Boronlike Argon ${}^{40}{\text{Ar}}^{13+}$
• Light-by-light scattering in the Lamb shift and the bound electron g factor
• QED theory of the nuclear magnetic shielding in hydrogen-like ions
• Two-loop binding corrections to the electron gyromagnetic factor
• Two-loop QED corrections with closed fermion loops for the bound-electron g factor
• One-loop electron self-energy for the bound-electron $g$ factor
• Two-loop self-energy in the Lamb shift of the ground and excited states of hydrogen-like ions
• The two-loop self-energy: diagrams in the coordinate-momentum representation
• One-loop binding corrections to the electron $g$ factor

Cited by in corpus (16)

• Stringent test of QED with hydrogenlike tin
• QED corrections to the $g$ factor of Li- and B-like ions
• g Factor of Lithiumlike Silicon and Calcium: Resolving the Disagreement between Theory and Experiment
• Logarithmically enhanced Euler-Heisenberg Lagrangian contribution to the electron gyromagnetic factor
• Testing Standard Model extensions with few-electron ions
• Self-energy screening effects in the $g$ factor of Li-like ions
• Two-loop electron self-energy for low nuclear charges
• Electron correlation effects on the $g$ factor of lithiumlike ions
• Two-loop virtual light-by-light scattering corrections to the bound-electron $g$ factor
• Testing inter-electronic interaction in lithium-like tin
• Improved bound-electron g-factor theory through complete two-loop QED calculations
• Hadronic vacuum polarization correction to the bound-electron $g$ factor
• Electron EM-mass melting in strong fields
• A relativistic QFT description for the interaction of a spin with a magnetic field
• Flat Bundles on Function Manifolds and Evolution Equations in Quantum Field Theories
• Two-loop electron self-energy in bound-electron $g$ factor: diagrams in momentum-coordinate representation