Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy
Authors: Marco Chiodaroli, Murat Gunaydin, Henrik Johansson and Radu Roiban Preprint number: UUITP-07/17 Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-orderd Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills+\phi^3 theory.
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The construction outlined in this paper holds in general dimension for any number
of external gluons and extends straightforwardly to supergravity theories. For
one, two, and three external gravitons, our expressions give identical or
simpler presentations of amplitudes already constructed through string-theory
considerations or the scattering equations formalism. Our results are based on
color/kinematics duality and gauge invariance, and strongly hint at a recursive
structure underlying the single-trace amplitudes with an arbitrary number of
gravitons. For the single-graviton case, we give amplitudes to any loop order
and obtain, through gauge invariance, new loop-level amplitude relations for
Yang-Mills theory.