Five-dimensional spinor helicity for all masses and spins

TL;DR

This paper introduces a comprehensive five-dimensional spinor helicity formalism capable of describing scattering amplitudes for particles of any mass and spin, providing a new approach that avoids certain low-dimensional isomorphisms.

Contribution

The authors develop an alternative five-dimensional spinor helicity framework that systematically constructs all three-point tree-level scattering amplitudes for arbitrary spins and masses, extending previous methods.

Findings

Systematic construction of five-dimensional three-point amplitudes for all spins and masses.

A prescription for high energy limit computations of scattering amplitudes.

Potential applications to higher spin effective field theories and black hole scattering.

Abstract

We develop a spinor helicity formalism for five-dimensional scattering amplitudes of any mass and spin configuration. While five-dimensional spinor helicity variables have been previously studied in the context of N=2,4 supersymmetric Yang-Mills scattering amplitudes with spin less than two arXiv:2202.08257, we propose an alternative viewpoint that stems from d-dimensional spinor helicity variables avoiding the use of the exceptional low-dimensional isomorphism $SO(4,1) \cong USp(2,2)$ and the decomposition of a massive momentum into the sum of two massless momenta. By enumerating all possible independent little group tensors, we systematically build the full space of five-dimensional three-point tree-level scattering amplitudes for any configuration of spins and masses. Furthermore, we provide a prescription for computing the high energy limit of scattering amplitudes written in our spinor helicity variables. We also expect that our formalism will be applicable to effective field theories with higher spin, in particular, the scattering of highly spinning black holes in five dimensions.