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

TL;DR

This work addresses the challenge of describing massive higher-spin resonances (spin-2 and spin-3/2) in constant electromagnetic backgrounds when the gyromagnetic ratio deviates from the universal pointlike value $g=2$. By casting the problem as an effective field theory organized in powers of the background field strength $|eF|/M^2$ and residual momentum, the authors introduce specific off-shell operators (notably terms involving $F\Delta$) that restore algebraic consistency while preserving the correct number of physical degrees of freedom. For spin-2, nonminimal couplings induce a controlled non-transverse constraint $J_n=D^m\Phi_{mn}=\mathcal{O}(eF/M^2)$, ensuring constraint-sector closure without new propagating modes. For spin-3/2, a projector-based deformation maintains the $\sigma$-trace constraints and yields a second-order wave operator in which a single gyromagnetic ratio $g$ multiplies both the spinor and vector Zeeman couplings. The paper also provides explicit Landau-level analyses in a constant magnetic field, demonstrating consistent spectra and hyperbolicity within the EFT domain. Overall, the results establish a robust framework for describing composite higher-spin states (e.g., the $\Omega^-$) with generic $g$ factors, with potential extensions to higher orders, gradients, curvature, and a Lagrangian formulation.

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.