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

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 $Ω^-$ 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.