Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations

TL;DR

This paper introduces new formulas for tree-level scattering amplitudes involving mixed spins in various dimensions, using integrals over scattering equations, and applies them to Einstein-Yang-Mills theory and related models.

Contribution

It provides a unified framework for computing tree-level S-matrix elements for theories with different spins using scattering equations, including Einstein-Yang-Mills and extensions with scalars, B-fields, and dilatons.

Findings

Derived formulas for n-particle scattering amplitudes in various theories.

Obtained all single-trace amplitudes in Einstein-Yang-Mills theory.

Presented double-trace gluon amplitudes in extended Einstein-Yang-Mills models.

Abstract

We present the building blocks that can be combined to produce tree-level S-matrix elements of a variety of theories with various spins mixed in arbitrary dimensions. The new formulas for the scattering of $n$ massless particles are given by integrals over the positions of $n$ points on a sphere restricted to satisfy the scattering equations. As applications, we obtain all single-trace amplitudes in Einstein--Yang--Mills (EYM) theory, and generalizations to include scalars. Also in EYM but extended by a B-field and a dilaton, we present all double-trace gluon amplitudes. The building blocks are made of Pfaffians and Parke--Taylor-like factors of subsets of particle labels.