Abstract
Amplitude methods have proven to be a promising technique to perform Post-Minkowskian calculations used as inputs to construct gravitational waveforms. In this paper, we show how these methods can be extended beyond the standard calculations in General Relativity with a minimal coupling to matter. As proof of principle, we consider spinless particles conformally coupled to a gravitational helicity-0 mode. We clarify the subtleties in the matching procedure that lead to the potential for conformally coupled matter. We show that in the probe particle limit, we can reproduce well known results for the field profile. With the scattering amplitudes at hand, we compute the conservative potential and scattering angle for the binary system. We find that the result is a non trivial expansion that involves not only the coupling strengths, but also a non trivial dependence on the energy/momentum of the scattered particles.
Highlights
One-body (EOB) formalism [3, 4] supplemented by numerical relativity [5,6,7] and selfforce [8, 9] computations in the strong field regime and analytic computations during the inspiral phase
We show how these methods can be extended beyond the standard calculations in General Relativity with a minimal coupling to matter
The connection between quantum scattering amplitudes and classical observables has been investigated in detail, and extensive progress has been made in the past few years [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51]
Summary
We analyze classical scatterings of spinless particles. We will first review the kinematics of these scatterings and afterwards we will explain how to extract classical physics from quantum scattering amplitudes. We explain the regions of momenta that can contribute to the classical scatterings and how to perform the loop integration in these regimes
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