Effective Equations of Motion for Massive Higher Spins with Generic Gyromagnetic Ratio

TL;DR

This paper develops effective equations of motion for massive higher-spin particles with arbitrary gyromagnetic ratios in electromagnetic backgrounds, ensuring consistency and avoiding pathologies through an EFT approach.

Contribution

It introduces a method to incorporate non-minimal couplings for higher-spin particles with arbitrary g-factors using an effective field theory framework.

Findings

Consistent equations of motion for spin 2 and 3/2 particles with arbitrary g.

Restoration of algebraic consistency via specific operators in EFT.

Avoidance of superluminal propagation and degree-of-freedom loss.

Abstract

We construct consistent effective equations of motion for massive charged particles of spin 2 and spin $3/2$ interacting with constant electromagnetic backgrounds. While tree-level unitarity restricts point-like particles to a universal gyromagnetic ratio $g=2$, long-lived composite states such as the $\Omega^-$ baryon generically deviate from this value. We propose describing such non-minimal couplings without triggering pathologies such as superluminal propagation or the loss of degrees of freedom by treating the system as an Effective Field Theory expanded in powers of the background field strength. By introducing specific operators, we show that algebraic consistency can be restored perturbatively for arbitrary $g$-factors.