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.
Highlights
At the Lagrangian level Einstein’s theory of gravity and Yang-Mills (YM) gauge theory look quite different
We present new relations for scattering amplitudes of color ordered gluons, massive quarks and scalars minimally coupled to gravity
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
Summary
At the Lagrangian level Einstein’s theory of gravity and Yang-Mills (YM) gauge theory look quite different. In a perturbative quantization on a flat space-time background intimate relations between their S-matrices exist, allowing one to express pure graviton scattering amplitudes through pure gluon scattering data. The first such connection are the Kawai-Lewellen-Tye relations [1] derived from string theory. The double copy technique may be used to generate loop-level integrands of gravitational theories from the simpler gaugetheory ones, this being the state-of-the-art method for higher loop computations in (super)-gravity. In this letter we report on an extension of these results to generic massive non-Abelian matter fields, i.e., QCD and scalar QCD with Nf flavors minimally coupled to Einstein’s gravity. We comment on generalizations to higher graviton multiplicity in the discussion
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