Frequency Shifts Induced by Field Gradients in Muon $g-2$ Experiments

TL;DR

This paper investigates how magnetic field gradients can cause frequency shifts in muon g-2 experiments, potentially affecting precision measurements and systematic error estimates.

Contribution

It analyzes the potential impact of field gradient-induced frequency shifts in muon g-2 experiments, highlighting a possible source of systematic error similar to neutron EDM experiments.

Findings

Field gradients could induce frequency shifts up to 1 ppm in muon g-2 measurements.

Such shifts are comparable to the current experimental error of 0.5 ppm.

The effect warrants consideration in future precision experiments.

Abstract

Two prominent efforts aimed at probing beyond Standard Model physics, searches for a neutron electric dipole moment (EDM) and measurements of the muon $g-2$ anomalous magnetic moment, employ spin precession techniques. In the most recent neutron EDM experiment, frequency shifts induced by magnetic field gradients and $\mathbf{E} \times \mathbf{v}$ motional fields were a significant source of systematic error. We consider the possibility of a similar effect in the most recent muon $g-2$ experiment, and find that such an effect could potentially be as large as $\sim 1$ ppm fractional error, to be compared with the reported $\sim 0.5$ ppm error.