Abstract
We propose a new form of the colour-kinematics/double-copy duality for heavy-mass effective field theories, which we apply to construct compact expressions for tree amplitudes with heavy matter particles in Yang-Mills and in gravity to leading order in the mass. In this set-up, the new BCJ numerators are fixed uniquely and directly written in terms of field strengths, making gauge invariance manifest. Furthermore, they are local and automatically satisfy the Jacobi relations and crossing symmetry. We construct these BCJ numerators explicitly up to six particles. We also discuss relations of the BCJ numerators in the heavy-mass effective theory with those in pure Yang-Mills amplitudes.
Highlights
Considerable effort has been devoted to applying modern amplitude methods to the computation of observable quantities in general relativity
Inspired by recent work on the kinematic algebra of BCJ numerators [62], we will introduce an improved version of the double copy, which will lead to much more compact expressions for the amplitudes
The numerators we have constructed in the heavy-mass effective theory (HEFT) are closely related to the local BCJ numerators for pure Yang-Mills theory by the following equation
Summary
Heavy-quark effective theory [1,2,3,4] plays an important role in hadron physics. One can use these Feynman rules to compute directly HEFT amplitudes, at least for a small number of legs. For higher multiplicities this becomes very involved, and we will introduce more efficient techniques in the two sections.. Note that the gluon-quark amplitude in HEFT does not depend on the soft momentum of the heavy particle. One can check that the leading order term in 1/m of the full five-point gluon-quark amplitude is identical to (2.7)
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