Resumming Scattering Amplitudes for Waveforms

TL;DR

This paper introduces a novel formalism to compute non-perturbative gravitational waveforms from two-body scattering amplitudes, extending effective field theory methods to include radiative effects for arbitrary trajectories.

Contribution

It develops a new approach combining Feshbach's projector formalism and the KMOC framework to derive gravitational waveforms from on-shell scattering amplitudes non-perturbatively.

Findings

Computed gravitational waveforms for generic two-body trajectories.

Established a link between scattering amplitudes and radiative phenomena in gravity.

Abstract

We develop a formalism to compute non-perturbative 5-point scattering amplitudes and apply it to gravitational waveforms in the two-body problem for arbitrary trajectories. Drawing inspiration from Feshbach's projector formalism in nuclear physics, we introduce effective potentials governing graviton emission and relate them to perturbative scattering amplitudes at arbitrary order in the gravitational coupling and mass ratio. Once these potentials are determined, the corresponding non-perturbative amplitudes in the classical limit are obtained by iterative insertions and subsequently translated into gravitational waveforms using the KMOC formalism. As an application, we compute the gravitational waveform emitted by a conservative two-body dynamics moving along a generic, potentially highly bent, trajectory. Our formalism extends effective field theory matching of the gravitational two-body potential to radiative phenomena, enabling the extraction of gravitational-wave source terms directly from perturbative on-shell amplitudes.