Emergence of periodic in magnetic moment effective QED action

TL;DR

This paper investigates the imaginary part of the effective QED action for particles with magnetic moments, revealing periodic behavior in the gyromagnetic ratio and implications for asymptotic freedom.

Contribution

It introduces a novel method to evaluate the effective action for particles with arbitrary magnetic moments, showing periodicity and cusp behavior at specific g-values.

Findings

Effective action is convergent for all g-values.

The periodicity in g relates to the QED beta-function.

Asymptotic freedom conditions are confirmed for a wider g-range.

Abstract

We evaluate for the inhomogeneous static electric Sauter step potential the imaginary part of the emerging homogeneous in electric field effective Euler-Heisenberg-Schwinger action sourced by vacuum fluctuations of a charged particle with magnetic moment of arbitrary strength. The result is convergent for all values of gyromagnetic ratio $g$, periodic in $g$, with a cusp at $g=2$. We consider the relation to the QED beta-function which is also found to be periodic in $g$. We confirm presence of asymptotic freedom conditions using this novel method and document a wider range of $g$-values for which asymptotic freedom is present.