HEFT kinematic algebra, heavy double copy and classical gravitational scattering
In this talk, I will introduce the kinematic algebra and a new double copy in heavy effective field theory (HEFT). I will also present the application of the novel double copy to classical gravitational scattering. Recently we proposed 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. A new infinite dimensional HEFT kinematic algebra is constructed by introducing the abstract tensors and the binary fusion rules between them. In this set-up, the closed form of the BCJ numerators is obtained from the fusion rules directly. They are manifestly gauge invariance, local and fully crossing symmetric. They also have a simple factorisation behaviour on the heavy mass propagators. We use these HEFT amplitudes to propose a method to compute the scattering angle for classical black hole scattering directly from two massive particle irreducible diagrams in a heavy-mass effective field theory approach to general relativity, without the need of subtracting iteration terms. We use this method to compute the scattering angle up to third post-Minkowskian order in four dimensions, including radiation reaction contributions.