New relations for graviton-matter amplitudes

TL;DR

This paper derives new relations that simplify graviton-matter scattering amplitudes by expressing them in terms of known QCD amplitudes, extending previous Einstein-Yang-Mills relations.

Contribution

It introduces a novel set of relations for graviton-matter amplitudes involving one graviton, generalizing Einstein-Yang-Mills relations using a diagrammatic proof and color basis techniques.

Findings

Reduces graviton-matter amplitudes to QCD partial amplitudes.

Employs a diagrammatic proof with color-kinematic replacements.

Comments on extending relations to multiple gravitons.

Abstract

We present new relations for scattering amplitudes of color ordered gluons, massive quarks and scalars minimally coupled to gravity. Tree-level amplitudes of arbitrary matter and gluon multiplicities involving one graviton are reduced to partial amplitudes in QCD or scalar QCD. The obtained relations are a direct generalization of the recently found Einstein-Yang-Mills relations. The proof of the new relation employs a simple diagrammatic argument trading the graviton-matter couplings to an `upgrade' of a gluon coupling with a color-kinematic replacement rule enforced. The use of the Melia-Johansson-Ochirov color basis is a key element of the reduction. We comment on the generalization to multiple gravitons in the single color trace case.