Eikonal Scattering and Asymptotic Superluminality of Massless Higher Spin Fields

TL;DR

This paper investigates constraints on massless higher-spin particle interactions in four dimensions using eikonal scattering, showing that certain cubic couplings lead to superluminal signals and are thus forbidden unless new physics appears.

Contribution

It provides new bounds on cubic couplings of massless higher spins from eikonal positivity and four-particle amplitude consistency, refining the understanding of higher-spin interactions.

Findings

Abelian higher-spin couplings cause asymptotic time advances.

Some non-abelian cubic couplings are consistent with eikonal positivity.

Constraints rule out trivial cubic curvature couplings without new physics.

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.