Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations

TL;DR

The paper extends the CHY scattering-equation framework by introducing subset-based building blocks to construct tree-level S-matrices for theories mixing spins in arbitrary dimensions. It presents a compact single-trace Einstein–Yang–Mills amplitude formula and a double-trace gluon generalization within EYM, plus Yang–Mills–Scalar and EYMS generalizations, all expressed as integrals localized on scattering equations using C_S and E blocks. The authors validate these constructs through gauge invariance, soft theorems, and comparisons with known results including disk relations and 4D MHV/NMHV amplitudes, and show how EYMS arises via KLT from YMS and gluon amplitudes. They further analyze factorization properties, discuss KLT orthogonality, and outline future directions such as multi-trace extensions, fermions, supersymmetry, and connections to ambitwistor-string formulations. Overall, the work provides a flexible, unifying framework for mixed-spin tree amplitudes in arbitrary dimensions with compact, analytically tractable building blocks.

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.