Bounds on Amplitudes in Effective Theories with Massive Spinning Particles

TL;DR

This paper develops a method to bound the high-energy growth of scattering amplitudes involving massive spinning particles, identifying limits consistent with fundamental principles and highlighting known theories for spin 2.

Contribution

It introduces a model-independent approach to constrain amplitude growth in effective field theories with massive spins, connecting bounds to known ghost-free theories for spin 2.

Findings

Bounded high-energy growth of amplitudes in effective theories.

Only known ghost-free theories saturate the bounds for spin 2.

Conjecture on amplitude growth for arbitrary integer spins.

Abstract

We consider a procedure for directly constructing general tree-level four-particle scattering amplitudes of massive spinning particles that are consistent with the usual requirements of Lorentz invariance, unitarity, crossing symmetry, and locality. There are infinitely many such amplitudes, but we can isolate interesting theories by bounding the high-energy growth of the tree amplitudes within the effective field theory. This allows us to set model-independent lower bounds on the growth of tree-level amplitudes in any effective field theory with a given particle content and any interaction terms with an arbitrary but finite number of derivatives. In certain common cases this corresponds to finding the highest possible strong coupling scale. When applied to spin 2, we show that the only amplitudes that saturate this bound are generated by the known ghost-free theories of a massive spin-2 particle, namely dRGT massive gravity and the pseudolinear theory. We also make a conjecture for the allowed growth of tree amplitudes in a theory with a single massive particle of any integer spin.