Scattering Amplitudes for Binary Systems beyond GR

TL;DR

This paper extends amplitude methods for Post-Minkowskian calculations beyond General Relativity, applying them to conformally coupled matter and deriving new insights into binary system potentials and scattering angles.

Contribution

It introduces a novel extension of amplitude techniques to conformally coupled matter, providing new calculations for binary system dynamics beyond standard GR.

Findings

Reproduces known field profiles in the probe limit

Calculates conservative potential and scattering angle for conformally coupled particles

Discovers a complex dependence on coupling strengths and particle energy

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.