[Paper Review] Snowmass White Paper: Gravitational Waves and Scattering Amplitudes

Alessandra Buonanno, Mohammed Khalil+4 more|arXiv (Cornell University)|Apr 11, 2022

Pulsars and Gravitational Waves Research17 citations

TL;DR

This white paper proposes integrating advanced theoretical high-energy physics tools—such as scattering amplitudes, effective field theory (EFT), and the double copy—into gravitational-wave physics to develop systematically improvable, high-precision waveform models for binary black hole and neutron star systems. The key contribution is a framework that unifies quantum field theory techniques with classical general relativity, enabling analytic progress in the post-Minkowskian and post-Newtonian regimes and paving the way for next-generation detector sensitivity.

ABSTRACT

We review recent progress and future prospects for harnessing powerful tools from theoretical high-energy physics, such as scattering amplitudes and effective field theory, to develop a precise and systematically improvable framework for calculating gravitational-wave signals from binary systems composed of black holes and/or neutron stars. This effort aims to provide state-of-the-art predictions that will enable high-precision measurements at future gravitational-wave detectors. In turn, applying the tools of quantum field theory in this new arena will uncover theoretical structures that can transform our understanding of basic phenomena and lead to new tools that will further the cycle of innovation. While still in a nascent stage, this research direction has already derived new analytic results in general relativity, and promises to advance the development of highly accurate waveform models for ever more sensitive detectors.

Motivation & Objective

• Develop a systematically improvable theoretical framework for gravitational-wave waveforms using tools from high-energy physics.
• Address the challenge of nonlinear, multi-scale dynamics in binary coalescences through analytic methods rooted in quantum field theory.
• Enable high-precision predictions for upcoming LIGO-Virgo-KAGRA runs and future space-based (LISA) and ground-based (Cosmic Explorer, Einstein Telescope) detectors.
• Explore deep theoretical structures in the classical limit of scattering amplitudes to uncover new mathematical and physical insights.
• Bridge the gap between quantum field theory and general relativity by applying on-shell methods and EFT to classical gravitational systems.

Proposed method

• Apply on-shell scattering amplitude techniques, including the double copy, to classical gravitational systems in the post-Minkowskian approximation.
• Use effective field theory (EFT) to systematically organize and compute gravitational interactions at different orders in the post-Newtonian expansion.
• Implement advanced multiloop integration and renormalization techniques adapted to classical gravity to compute conservative dynamics.
• Combine analytic results with numerical relativity (NR) and effective-one-body (EOB) models to validate and extend waveform predictions.
• Generalize amplitude methods to curved spacetime to study the ringdown phase and final-state observables such as tidal deformability.
• Utilize the KMOC formalism and classical limit of scattering amplitudes to explore initial-to-final state correlations in binary mergers.

Experimental results

Research questions

• RQ1 How can on-shell methods and the double copy be systematically applied to compute classical gravitational dynamics in the post-Minkowskian regime?
• RQ2 What is the role of effective field theory in organizing and improving the precision of gravitational-wave waveforms for binary systems with spins and tidal effects?
• RQ3 How do theoretical structures in scattering amplitudes—such as UV finiteness and hidden symmetries—manifest in the classical limit of gravity?
• RQ4 Can the classical limit of scattering amplitudes provide new analytic insights into the ringdown phase and remnant properties of binary mergers?
• RQ5 How can amplitude-theoretic tools help distinguish between classical extensions of general relativity and quantum gravity effects in gravitational-wave observations?

Key findings

• The application of scattering amplitude techniques to classical gravity has already yielded new analytic results in the two-body problem, particularly in the post-Minkowskian approximation.
• High-accuracy predictions for binding energy and scattering angle in binary systems now match numerical relativity and effective-one-body benchmarks up to third post-Newtonian order.
• The double copy and EFT frameworks have enabled systematic computation of conservative dynamics, with results valid to higher orders in Newton's constant G.
• Generalizations of the amplitudes program to curved spacetime show promise for analyzing the ringdown phase and final-state properties like tidal deformability.
• Model-independent classification of higher-dimension operators in EFT has been advanced, enabling systematic study of physics beyond general relativity in gravitational-wave signals.
• The synergy between amplitude theory, EFT, and numerical relativity is already producing waveform models that are competitive with existing state-of-the-art approaches.