Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy

Understand

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-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills+\phi^3 theory.
• The construction outlined in this paper holds in general dimension 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.