Intrinsic Cutoff and Acausality for Massive Spin 2 Fields Coupled to Electromagnetism

TL;DR

This paper uses the Stückelberg formalism to study a massive spin-2 field coupled to electromagnetism in flat space and shows that there is an intrinsic, model-independent UV cutoff that signals the onset of strong coupling and a finite spin-2 size. By diagonalizing the kinetic terms and analyzing the higher-dimension interaction operators, the authors derive a sequence of cutoff scales: a minimal bound $\Lambda_4=(m^4/e)^{1/4}$ and, with a non-minimal dipole term, a higher bound $\Lambda_3=(m^3/e)^{1/3}$, while a naive optimistic bound $\Lambda_2=m/\sqrt{e}$ cannot be achieved without introducing extra heavy states. They demonstrate that the Velo-Zwanziger acausality resides in the Stückelberg sector and that, depending on the non-minimal coupling parameter $\alpha$, the theory can exhibit subluminal or superluminal propagation in external fields, with pathologies arising in strong-field regimes, thereby illustrating the EFT nature of high-spin interactions. The work suggests that intrinsic cutoffs and acausal behavior are general features of interacting high-spin fields and outlines a path toward extending the analysis to arbitrary spin and gravitational couplings.

Abstract

We couple a massive spin 2 particle to electromagnetism. By introducing new, redundant degrees of freedom using the Stueckelberg formalism, we extract an intrinsic, model independent UV cutoff of the effective field theory describing this system. The cutoff signals both the onset of a strongly interacting dynamical regime and a finite size for the spin 2 particle. We show that the existence of a cutoff is strictly connected to other pathologies of interacting high-spin fields, such as the Velo-Zwanziger acausality. We also briefly comment on implications of this result for the detection of high spin states and on its possible generalization to arbitrary spin.