Snowmass White Paper: Gravitational Waves and Scattering Amplitudes

TL;DR

The Snowmass white paper proposes leveraging scattering amplitudes, the double copy, and EFT to build a precision, systematically improvable framework for gravitational-wave predictions in binary black hole and neutron star systems. It surveys the classical-limit foundations (KMOC, eikonal, amplitude-action relations) and reports progress toward state-of-the-art conservative and radiative dynamics, including spins and tides, with integration into EFT-based and NR benchmarks. It also outlines a rich toolkit—EFT matching, advanced loop integration, and generating-function formalisms—that connects quantum amplitudes to classical observables and waveforms, while highlighting theoretical structures that could sharpen predictions and reveal new insights. Looking ahead, the paper identifies major challenges and directions, such as higher-order calculations, nonlocal radiation effects, multi-body dynamics, and tests of GR or new physics, aiming to transform GW modeling and deepen our understanding of gravity through quantum-field-theoretic methods.

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.

Figures (5)

• Figure 1: (left) The binding energy (in units of the reduced mass) versus the orbital frequency of an equal-mass non-spinning binary black hole following an adiabatic quasi-circular orbit towards merger. The horizontal axis is also given as the number of orbits before merger. (right) The scattering angle versus impact parameter of two equal-mass non-spinning black holes following hyperbolic trajectories with initial relative velocity $v=0.4$. These plots are adapted from Khalil:2022, where the authors compared predictions for post-Minkowskian (PM) conservative dynamics obtained using QFT tools (solid lines of increasing accuracy in Newton’s constant $G$, i.e., in the PM approximation) with NR Damour:2014afaOssokine:2017dge and effective-one-body (EOB) results, here at third post-Newtonian (PN) order, which are the benchmarks for building waveform models in the LVK collaboration.
• Figure 2: Map of perturbative corrections to Newton's potential, where $G$ is Newton's constant and $v$ is the relative velocity of the binary constituents. New results through $O(G^4)$ were recently obtained using QFT tools (red box). They are valid to all orders in velocity, and overlap with the state-of-the-art from the PN expansion (dark triangle) and the contributions required by future detectors (light triangle) (see, e.g., Favata:2013rwaSamajdar:2018dcxPurrer:2019jcpHuang:2020pbaGamba:2020wgg).
• Figure 3: (top) Classical binary dynamics is encoded in scattering amplitudes of massive particles (thick lines) interacting through gravitons (wavy lines): (A) four-point scattering encodes higher-order corrections to conservative binary dynamics, (B) five-point scattering encodes radiative effects due to graviton emission, and (C) higher-dimension operators (solid circle) encode tidal deformation of neutron stars. Spinning black holes can be described by higher-spin representations in QFT. (bottom) A sample calculational pipeline using the tools of theoretical high-energy physics: Starting from tree-level gauge theory amplitudes (a), corresponding gravitational amplitudes (b) are obtained using the double-copy. These are then fused into loop amplitudes (c) using generalized unitarity. The integrated amplitude (d) is obtained using advanced multiloop integration methods developed in high-energy physics, in combination with EFT. The amplitude can then be mapped, using a variety of methods, to the EOB Hamiltonian used for producing waveforms (e). The classical limit is applied at every stage, leading to vast simplifications.
• Figure 4: The binding energy (in units of the reduced mass) versus the orbital frequency of an equal-mass non-spinning binary black hole following an adiabatic quasi-circular orbit towards merger. The horizontal axis is also given as the number of orbits before merger. The plot is adapted from Khalil:2022, where the authors compared predictions for post-Minkowskian (PM) conservative dynamics obtained using QFT tools (solid lines of increasing accuracy in Newton’s constant $G$, i.e., in the PM approximation) to NR results Ossokine:2017dge. In contrast to Figure \ref{['fig:binding_and_angle']}, the predictions shown here are obtained by incorporating the QFT results into the EOB formalism, resulting in better agreement with NR towards merger.
• Figure 5: The resummation of these diagrams to all orders in $G$ yields the amplitude for a probe particle in a Schwarzschild background.