Scattering of conformal higher spin fields

TL;DR

This paper develops a formalism for tree-level scattering amplitudes in 4d conformal higher spin theory, identifying admissible states for finite amplitudes and providing compact expressions for 3-point amplitudes, including in conformal gravity.

Contribution

It introduces a new formalism for scattering amplitudes in conformal higher spin theory, characterizing admissible states and extending spinor helicity methods with twistor-spinors.

Findings

Finite tree amplitudes depend on a broader set of states than standard massless higher spins.

Explicit compact formulas for all finite 3-point amplitudes in conformal higher spin theory.

Some 3-point amplitudes vanish, while others are non-zero, including in conformal gravity.

Abstract

We develop a formalism for describing the most general notion of tree-level scattering amplitudes in 4d conformal higher spin theory. As conformal higher spin fields obey higher-derivative equations of motion, there are many distinct on-shell external states which may contribute to their scattering, some of which grow polynomially with time, leading to ill-defined amplitudes. We characterize the set of admissible scattering states which produce finite tree amplitudes, noting that there are more such states than just standard massless higher spins obeying two-derivative equations of motion. We use conformal gravity as a prime example, where the set of scattering states includes the usual Einstein graviton and a `ghost' massless spin 1 particle. An extension of the usual spinor helicity formalism allows us to encode these scattering states efficiently in terms of `twistor-spinors'. This leads to compact momentum space expressions for all finite tree-level 3-point amplitudes of conformal higher spin theory. While some of these 3-point amplitudes vanish (including all those with only standard two-derivative higher spin external states), there are many others which are non-vanishing. We also comment on the generalization to scattering of conformal higher spins in AdS$_4$.