Abstract
We 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. The amplitudes in this effective theory are constructed using a recently proposed novel colour-kinematic/double copy for tree-level two-scalar, multi-graviton amplitudes, where the BCJ numerators are gauge invariant and local with respect to the massless gravitons. These tree amplitudes, together with graviton tree amplitudes, enter the construction of the required D-dimensional loop integrands and allow for a direct extraction of contributions relevant for classical physics. In particular the soft/heavy-mass expansions of full integrands is circumvented, and all iterating contributions can be dropped from the get go. We use this method to compute the scattering angle up to third post-Minkowskian order in four dimensions, including radiation reaction contributions, also providing the expression of the corresponding integrand in D dimensions.
Highlights
The goal of this paper is to propose an efficient method to compute the scattering angle in a collision of two black holes
We 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
This motivates the use of effective field theory applied to gravity [2], and in particular of a heavy-mass effective field theory (HEFT) [3,4,5,6,7], which is the appropriate tool if one wishes to describe interactions of particles where the exchanged momenta are much smaller than their masses
Summary
The goal of this paper is to propose an efficient method to compute the scattering angle in a collision of two black holes. In [85] we have developed a systematic approach to derive compact, Ddimensional expressions of HEFT amplitudes with two massive scalars and an arbitrary number of massless gravitons at leading order in an inverse mass expansion This is based on a new form of the colour-kinematics/double-copy duality [86, 87] for heavy-mass effective field theories, initially proposed in Yang-Mills and gravity in [88], and further developed in [89]. Two appendices complete the paper: in appendix A we present a study of the asymptotic behaviour of our master integrals and the associated boundary conditions, with explicit examples for our one- and two-loop master integrals; and in appendix B we show explicitly the integrand of the four 2MPI cut diagrams contributing to the two-loop 2MPI HEFT amplitude
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