Thomas-BMT equation generalized to electric dipole moments and field gradients

TL;DR

This paper generalizes the Thomas-BMT equation to include electric dipole moments and field gradients, providing improved models for particle dynamics in precision experiments.

Contribution

It introduces a relativistic equation of motion with field gradients and electric dipole moments, extending the classical Thomas-BMT equation using electromagnetic duality.

Findings

Derived a generalized Thomas-BMT equation with gradient terms

Calculated corrections for particle dynamics in storage rings

Discussed applications to precision $(g-2)$ and electric dipole moment measurements

Abstract

An expression is presented for the relativistic equations of motion, including field gradients, of a particle and its spin with electric and magnetic dipole moments aligned along the spin axis. An electromagnetic duality transformation is used to generalize a Thomas-BMT equation with gradient terms. Corrections to particle dynamics in storage rings for precision $(g-2)$ and electric dipole moment measurements are calculated, and applications to precision particle tracking programs are considered.