The effects of magnetic fields on magnetic dipole moments

TL;DR

This paper investigates how magnetic fields influence the magnetic dipole moments of leptons, revealing subtle effects on muon experiments and discussing theoretical form factors under magnetic influence.

Contribution

It provides a detailed calculation of magnetic field effects on lepton dipole moments up to quadratic order, including QCD contributions, and explores implications for muon g-2 experiments.

Findings

Linear refraction of electrons from muons in magnetic fields affects muon g-2 measurements.

Quadratic magnetic field effects on dipole moments are calculated including QCD contributions.

Potential measurable impact on experimental uncertainties in muon anomaly experiments.

Abstract

We calculate the effect of magnetic fields on the magnetic dipole moment of leptons up to the quadratic order in the magnetic field, including the QCD contributions. Since the leading contribution, which is linear in the magnetic field, depends on the spin, its effect is not measurable directly in the Penning trap experiment for the electron dipole moment. In the muon anomaly, however, we find that the electrons decayed from muons are refracted linearly in the magnetic field. This effect, though quite small, changes the distribution of the detected electrons in the muon $g-2$ experiment and could be measurable, improving the experimental uncertainties. We also discuss the general field-dependent form factors and the Ward-Takahashi identity under the external magnetic fields.