Logarithmically enhanced Euler-Heisenberg Lagrangian contribution to the electron gyromagnetic factor

Abstract

Contrary to what was previously believed, two-loop radiative corrections to the $g$-factor of an electron bound in a hydrogen-like ion at $\mathcal{O}\left({\alpha }^2(Z\alpha {)}^5\right)$ exhibit logarithmic enhancement. This previously unknown contribution is due to a long-distance light-by-light scattering amplitude. Taking an effective field theory approach, and using the Euler-Heisenberg Lagrangian, we find $\Delta g=-{\left(\frac{\alpha }{\pi }\right)}^2{\left(Z\alpha \right)}^5\frac{56\pi }{135}\ln Z\alpha$.

5 pages, 3 figures

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• The QED four-photon amplitudes off-shell: part 2
• Testing Standard Model extensions with few-electron ions
• Two-photon exchange corrections to the $g$ factor of Li-like ions
• Electron correlation effects on the $g$ factor of lithiumlike ions
• Testing inter-electronic interaction in lithium-like tin
• Thermal corrections to the bound-electron $g$-factor
• An analysis of Bayesian estimates for missing higher orders in perturbative calculations
• $g$ factor of the $2p_j$ excited states in lithium-like ions
• Two-loop electron self-energy in bound-electron $g$ factor: diagrams in momentum-coordinate representation