Massive Spin-2 Scattering and Asymptotic Superluminality

TL;DR

This paper derives model-independent constraints on massive spin-2 theories by analyzing the phase shift in high-energy scattering, revealing conditions for avoiding superluminal signals and implications for gravity and QCD models.

Contribution

It establishes new constraints on cubic vertices in massive spin-2 theories based on positivity of phase shifts, extending previous results and applying to gravity and QCD.

Findings

No time advance implies specific cubic vertex combinations.

Constraints are consistent with known massive gravity models.

Large-N QCD spectra with a massive spin-2 must have particular cubic couplings.

Abstract

We place model-independent constraints on theories of massive spin-2 particles by considering the positivity of the phase shift in eikonal scattering. The phase shift is an asymptotic $S$-matrix observable, related to the time delay/advance experienced by a particle during scattering. Demanding the absence of a time advance leads to constraints on the cubic vertices present in the theory. We find that, in theories with massive spin-2 particles, requiring no time advance means that either: (i) the cubic vertices must appear as a particular linear combination of the Einstein-Hilbert cubic vertex and an $h_{\mu\nu}^3$ potential term or (ii) new degrees of freedom or strong coupling must enter at parametrically the mass of the massive spin-2 field. These conclusions have implications for a variety of situations. Applied to theories of large-$N$ QCD, this indicates that any spectrum with an isolated massive spin-2 at the bottom must have these particular cubic self-couplings. Applied to de Rham-Gabadadze-Tolley massive gravity, the constraint is in accord with and generalizes previous results obtained from a shockwave calculation: of the two free dimensionless parameters in the theory there is a one parameter line consistent with a subluminal phase shift.