Abstract
Here we discuss color-kinematics duality for higher-derivative QCD-like amplitudes. We explicitly show that the duality still holds in this case and it can be instrumental in constructing the associated quadratic-gravity amplitudes by using the double-copy prescription. This allows one to drastically simplify calculations. We also evaluate some tree-level Compton scattering amplitudes in higher-derivative Yang-Mills and quadratic gravity coupled with matter. Furthermore, we illustrate the application of generalized unitarity method for both cases by studying a specific one-loop amplitude.
Highlights
We evaluate some tree-level Compton scattering amplitudes in higher-derivative Yang-Mills and quadratic gravity coupled with matter
In the low energy limit, such results implied that tree-level graviton amplitudes can be written in terms of sums of products of color-ordered tree-level Yang-Mills amplitudes multiplied by kinematic factors
It is important to understand in detail some features of tree-level amplitudes involving Merlins since in principle these can display undesirable behavior in some situations — and if a pathology arises already at tree level, we must definitely worry about the associated loop amplitudes
Summary
Gravitational scattering amplitudes has a double-copy structure expressed in a suitable factorization in terms of gauge-theory amplitudes. The fact that the numerators are related to each other via a Jacobi-like relation, together with their known gauge-dependent property, implies that we can obtain a gauge-invariant homogeneous relation between color-ordered partial amplitudes [2] Such BCJ amplitude relations are a direct consequence of the duality between color and kinematics. One can use the color-kinematics relation and the BCJ relations in order to rewrite gravity amplitudes as products of partial Yang-Mills amplitudes In this way, it is possible to obtain a set of relations, called Kawai-Lewellen-Tye (KLT) relations, between gravity and gauge-theory amplitudes as the upshot of color-kinematics duality and gauge-invariance constraints. The KLT relations furnishes a framework for obtaining gravity tree amplitudes in terms of gauge-theory partial amplitudes In the more general context of modern on-shell methods for effective field theories, see refs. [95–97]
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