Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$

Abstract

We complete the calculation of conservative two-body scattering dynamics at fourth post-Minkowskian order, i.e. $O(G^4)$ and all orders in velocity, including radiative contributions corresponding to the tail effect in general relativity. As in previous calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves complete elliptic integrals, and polylogarithms with up to transcendental weight two. Using the amplitude-action relation, we obtain the radial action directly from the amplitude, and match the known overlapping terms in the post-Newtonian expansion.

8 pages; 2 figures

References in corpus (24)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Laser Interferometer Space Antenna
• New Relations for Gauge-Theory Amplitudes
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Algorithm FIRE -- Feynman Integral REduction
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Effective field theory calculation of second post-Newtonian binary dynamics
• Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order
• Static two-body potential at fifth post-Newtonian order
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• The dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant
• Non-Relativistic Gravitation: From Newton to Einstein and Back
• Four-loop beta function and mass anomalous dimension in Dimensional Reduction
• Classical Effective Field Theory and Caged Black Holes
• Gravitational scattering of two black holes at the fourth post-Newtonian approximation
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions
• Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order
• Scattering of tidally interacting bodies in post-Minkowskian gravity
• The 6th Post-Newtonian Potential Terms at $O(G_N^4)$
• Dimensional Reduction applied to QCD at three loops