Scattering of Massless Particles in Arbitrary Dimension

TL;DR

This paper introduces a compact, dimension-independent formula for the complete tree-level scattering matrix of massless particles in Yang-Mills and gravity theories, applicable in any spacetime dimension.

Contribution

It provides a novel integral formula involving Pfaffians and determinants for calculating scattering amplitudes in arbitrary dimensions, unifying Yang-Mills and gravity cases.

Findings

Explicit formula for n-particle scattering in arbitrary dimensions

Manifest gauge invariance of the scattering amplitudes

Simplified expressions using Pfaffians and determinants

Abstract

We present a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimension. The new formula for the scattering of n particles is given by an integral over the position of n points on a sphere restricted to satisfy a dimension-independent set of equations. The integrand is constructed using the reduced Pfaffian of a 2n by 2n matrix that depends on momenta and polarization vectors. In its simplest form, the gravity integrand is a reduced determinant which is the square of the Pfaffian in the Yang-Mills integrand. Gauge invariance is completely manifest as it follows from a simple property of the Pfaffian.