Eikonal Scattering and Asymptotic Superluminality of Massless Higher Spin Fields

TL;DR

This work analyzes the constraints on interactions of massless higher-spin fields in four-dimensional flat space by imposing positivity of the eikonal phase to avoid asymptotic superluminality. The authors classify cubic vertices into lower-derivative non-abelian and higher-derivative abelian (curvature-based) types and show that abelian curvature couplings generically produce time advances unless new physics enters at the derivative suppression scale $\Lambda$. They demonstrate that many cubic curvature interactions are forbidden, and even certain non-abelian couplings are incompatible with either eikonal positivity or four-particle factorization, thereby strongly constraining the space of consistent higher-spin theories in 4D. The results complement older no-go theorems and collectively suggest that, for a finite set of massless higher spins, cubic interactions are essentially ruled out in flat space unless new states appear at or below $\Lambda$, with possible exceptions only in more elaborate setups (infinite towers or higher dimensions).

Abstract

We consider scattering of massless higher-spin particles in the eikonal regime in four dimensions. By demanding the absence of asymptotic superluminality, corresponding to positivity of the eikonal phase, we place constraints on the possible cubic couplings which can appear in the theory. The cubic couplings come in two types: lower-derivative non-abelian vertices, and higher-derivative abelian vertices made out of gauge-invariant curvature tensors. We find that the abelian couplings between massless higher spins lead to an asymptotic time advance for certain choices of polarizations, indicating that these couplings should be absent unless new states come in at the scale suppressing the derivatives in these couplings. A subset of non-abelian cubic couplings are consistent with eikonal positivity, but are ruled out by consistency of the four-particle amplitude away from the eikonal limit. The eikonal constraints are therefore complementary to the four-particle test, ruling out even trivial cubic curvature couplings in any theory with a finite number of massless higher spins and no new physics at the scale suppressing derivatives in these vertices.