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 $\Delta g=-{\left(\frac{\alpha }{\pi }\right)}^2{\left(Z\alpha \right)}^5\frac{56\pi }{135}\ln Z\alpha$.

Comments: 5 pages, 3 figures