On tree amplitudes with gluons coupled to gravitons

Abstract

In this paper, we study the tree amplitudes with gluons coupled to gravitons. We first study the relations among the mixed amplitudes. With BCFW on-shell recursion relation, we will show the color-order reversed relation, $U(1)$-decoupling relation and KK relation hold for tree amplitudes with gluons coupled to gravitons. We then study the disk relation which expresses mixed amplitudes by pure gluon amplitudes. More specifically we will prove the disk relation for mixed amplitudes with gluons coupled to one graviton. Using the disk relation and the properties of pure gluon amplitudes, the color-order reversed relation, $U(1)$-decoupling relation and KK relation for mixed amplitudes can also be proved. Finally, we give some brief discussions on BCJ-like relation for mixed amplitudes.

33pages,no figure

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• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Algebras for Amplitudes
• Type D Spacetimes and the Weyl Double Copy
• Expansion of Einstein-Yang-Mills Amplitude
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Manifesting Color-Kinematics Duality in the Scattering Equation Formalism
• BCJ Relation of Color Scalar Theory and KLT Relation of Gauge Theory
• An Introduction to On-shell Recursion Relations
• Graviton as a Pair of Collinear Gauge Bosons
• On Primary Relations at Tree-level in String Theory and Field Theory
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• One-loop SYM-supergravity relation for five-point amplitudes
• Constructing EYM amplitudes by inverse soft limit
• Note on Cyclic Sum and Combination Sum of Color-ordered Gluon Amplitudes