QED at a cusp: vacuum fluctuations as function of magnetic moment

Precision QED experiments (muon g-2 and muonic protium Lamb shift) motivate closer examination of QED for the case that gyromagnetic ratio is larger than the Dirac value, g>2. We evaluate the nonperturbative one-loop effective potential in a quasi-constant external field as a function of g. Extending the result to g>2 requires a projection onto the physical states of the spectrum that leads to the effective potential being periodic in g. From the effective potential, we extract the beta-function and low-energy light-light scattering coefficients and show that periodicity as a function of g implies cusps at the Dirac value g=2 and at periodic points, g=2+4N for N integer. Consequently, the beta-function and light-light scattering differ from their perturbative values for g>2. As an application of these results, we show how top quark g \neq 2 enhances the rate of Higgs two-photon decay.