Magnetic correction to the Anomalous Magnetic Moment of Electron

TL;DR

This paper calculates the leading order magnetic correction to the electron's anomalous magnetic moment in weak magnetic fields, showing it is negative and field-dependent, with negligible effects at laboratory field strengths but significant at stronger fields.

Contribution

It provides the first detailed analysis of magnetic corrections to the electron's AMM, highlighting their dependence on magnetic field strength and potential implications for QCD matter studies.

Findings

Magnetic correction is negative and depends on magnetic field strength.

At laboratory fields (~Tesla), correction is negligible (~10^{-34}).

At stronger fields, correction becomes significant.

Abstract

We investigate the leading order correction of anomalous magnetic moment (AMM) to the electron in weak magnetic field and find that the magnetic correction is negative and magnetic field dependent, indicating a magnetic catalysis effect for the electron gas. In the laboratory to measure the $g-2$, the magnitude of the magnetic field $B$ is several $\mathrm{T}$, correspondingly the magnetic correction to the AMM of electron/muon is around $10^{-34}$/$10^{-42}$, therefore the magnetic correction can be safely neglected in current measurement. However, when the magnitude of the magnetic field strength is comparable with the electron mass, the magnetic correction of electron's AMM will become considerable. This general magnetic correction to charged fermion's AMM can be extended to study QCD matter under strong magnetic field.