Massive Spin-2 Scattering and Asymptotic Superluminality

TL;DR

The paper derives model-independent infrared constraints on theories with a single massive spin-2 field by enforcing positivity of the eikonal phase in high-energy scattering, tying the absence of asymptotic time advances to the allowed cubic self-interactions. Through a rigorous on-shell amplitude framework, it shows that only a specific linear combination of the Einstein–Hilbert cubic vertex and an h_{μν}^3 term avoids superluminal time advances; otherwise new degrees of freedom or strong coupling must appear at the graviton mass scale. The results apply to both dRGT massive gravity and large-N QCD-like theories, narrowing viable parameter spaces to a one-parameter line in certain models and aligning with shockwave analyses. The work clarifies how S-matrix causality constraints shape low-energy effective theories of massive spin-2 states and lays groundwork for exploring multi-metric extensions and subleading eikonal effects.

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 $h_{μν}^3$ 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.

Figures (1)

• Figure 1: The shockwave geometry and its connection to scattering. The shockwave travels in the $x^{ -}$ direction. It is traversed by a particle traveling in the $x^{ +}$ direction which experiences a time delay $\Delta x^{ -}$ as it crosses the shock.