Classical gravitational scattering from a gauge-invariant double copy

Abstract

We propose a method to compute the scattering angle for classical black hole scattering directly from two massive particle irreducible diagrams in a heavy-mass effective field theory approach to general relativity, without the need of subtracting iteration terms. The amplitudes in this effective theory are constructed using a recently proposed novel colour-kinematic/double copy for tree-level two-scalar, multi-graviton amplitudes, where the BCJ numerators are gauge invariant and local with respect to the massless gravitons. These tree amplitudes, together with graviton tree amplitudes, enter the construction of the required $D$-dimensional loop integrands and allow for a direct extraction of contributions relevant for classical physics. In particular the soft/heavy-mass expansions of full integrands is circumvented, and all iterating contributions can be dropped from the get go. We use this method to compute the scattering angle up to third post-Minkowskian order in four dimensions, including radiation reaction contributions, also providing the expression of the corresponding integrand in $D$ dimensions.

arXiv comment62 pages, 20 figures,reference added, minor revision

References in corpus (104)

• Heavy Quark Symmetry
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Effective one-body approach to general relativistic two-body dynamics
• General relativity as an effective field theory: The leading quantum corrections
• New Relations for Gauge-Theory Amplitudes
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Multiloop integrals in dimensional regularization made simple
• Asymptotic expansion of Feynman integrals near threshold
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Differential Equations for Two-Loop Four-Point Functions
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Algorithm FIRE -- Feynman Integral REduction
• Amplitudes, Observables, and Classical Scattering
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• Quantum Gravitational Corrections to the Nonrelativistic Scattering Potential of Two Masses
• Reparameterisation Invariance Constraints on Heavy Particle Effective Field Theories
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• Post-Newtonian corrections to the motion of spinning bodies in NRGR
• High-energy gravitational scattering and the general relativistic two-body problem
• Dimensional regularization of the gravitational interaction of point masses
• Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems
• Proof of Factorization for Diffractive Hard Scattering
• Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• Classical Space-Times from the S Matrix
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• Classical black hole scattering from a worldline quantum field theory
• Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates
• Eikonal Quantum Gravity and Planckian Scattering
• Quantum Corrections to the Schwarzschild and Kerr Metrics
• Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• The simplest massive S-matrix: from minimal coupling to Black Holes
• Classical and quantum scattering in post-Minkowskian gravity
• On-shell Techniques and Universal Results in Quantum Gravity
• Reducing differential equations for multiloop master integrals
• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• The Eikonal Approach to Gravitational Scattering and Radiation at $\mathcal{O}(G^3)$
• Spinning gravitating objects in the effective field theory in the post-Newtonian scheme
• Integration-by-parts reductions from unitarity cuts and algebraic geometry
• Fourth post-Newtonian effective one-body dynamics
• Sector Decomposition
• Radiative contribution to classical gravitational scattering at the third order in $G$
• Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
• AMBRE - a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Universality of ultra-relativistic gravitational scattering
• Gravitational Bremsstrahlung from Reverse Unitarity
• Revisiting the 2PM eikonal and the dynamics of binary black holes
• Bending of Light in Quantum Gravity
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
• Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation
• Heavy Black Hole Effective Theory
• Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity
• Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
• Effective field theory approach to the gravitational two-body dynamics, at fourth post-Newtonian order and quintic in the Newton constant
• The tail effect in gravitational radiation-reaction: time non-locality and renormalization group evolution
• Geometric approach to asymptotic expansion of Feynman integrals
• New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian
• Binary dynamics at the fifth and fifth-and-a-half post-Newtonian orders
• Classical Physics and Quantum Loops
• Effective field theory calculation of conservative binary dynamics at third post-Newtonian order
• 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
• Light-like Scattering in Quantum Gravity
• Static two-body potential at fifth post-Newtonian order
• Classical Gravitational Scattering at $\mathcal{O}(G^3)$ from Feynman Diagrams
• On an Exponential Representation of the Gravitational S-Matrix
• Classical Gravity from Loop Amplitudes
• The dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant
• Complete Hamiltonian for spinning binary systems at first post-Minkowskian order
• Relationship Between Gravity and Gauge Scattering in the High Energy Limit
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• Quadratic-in-Spin Hamiltonian at $\mathcal{O}(G^2)$ from Scattering Amplitudes
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• Leading order finite size effects with spins for inspiralling compact binaries
• Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses
• Two-Loop Polygon Wilson Loops in N=4 SYM
• Testing binary dynamics in gravity at the sixth post-Newtonian level
• From amplitudes to gravitational radiation with cubic interactions and tidal effects
• On the Apparent Ambiguities in the Post-Newtonian Expansion for Binary Systems
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions
• High Energy Scattering in Perturbative Quantum Gravity at Next to Leading Power
• Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• Towards the 4th post-Newtonian Hamiltonian for two-point-mass systems
• Canonical Formulation of Spin in General Relativity
• A new gauge-invariant double copy for heavy-mass effective theory
• The Non-Abelian Exponentiation theorem for multiple Wilson lines
• Wilson line approach to gravity in the high energy limit
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• On higher-derivative effects on the gravitational potential and particle bending
• Radiation reaction for spinning bodies in effective field theory II: Spin-spin effects
• NNNLO gravitational quadratic-in-spin interactions at the quartic order in G
• The double copy for heavy particles
• The 6th Post-Newtonian Potential Terms at $O(G_N^4)$
• NLO gravitational quartic-in-spin interaction
• On the status of expansion by regions
• Scattering Amplitudes, Black Holes and Leading Singularities in Cubic Theories of Gravity
• The Lamb shift and the gravitational binding energy for binary black holes
• Three-Body Effective Potential in General Relativity at Second Post-Minkowskian Order and Resulting Post-Newtonian Contributions
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• The Amplitude for Classical Gravitational Scattering at Third Post-Minkowskian Order
• Next-to-MHV Yang-Mills kinematic algebra

Cited by in corpus (50)

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• SUSY in the Sky with Gravitons
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
• Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory
• Binary Dynamics Through the Fifth Power of Spin at $\mathcal{O}(G^2)$
• Radiated Angular Momentum and Dissipative Effects in Classical Scattering
• Classical gravitational spinning-spinless scattering at $\mathcal{O}(G^2{S}^{\infty })$
• The 2PM Hamiltonian for binary Kerr to quartic in spin
• Conservative Binary Dynamics with a Spinning Black Hole at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• A new gauge-invariant double copy for heavy-mass effective theory
• Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
• Kinematic Hopf Algebra for BCJ Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory
• Linear Response, Hamiltonian and Radiative Spinning Two-Body Dynamics
• Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion
• Post-Minkowskian Radial Action from Soft Limits and Velocity Cuts
• Sources in the Weyl double copy
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Angular momentum of zero-frequency gravitons
• Self-force effects in post-Minkowskian scattering
• Exponentiation of the leading eikonal with spin
• Scattering Angles in Kerr Metrics
• Eikonal amplitudes from curved backgrounds
• Scalar QED as a toy model for higher-order effects in classical gravitational scattering
• Angular momentum loss in gravitational scattering, radiation reaction, and the Bondi gauge ambiguity
• Classical vs Quantum Eikonal Scattering and its Causal Structure
• Gravitational Faraday effect from on-shell amplitudes
• Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework
• Light bending from eikonal in worldline quantum field theory
• Amplitudes, Hopf algebras and the colour-kinematics duality
• Amplitude bases in generic EFTs
• Graviton particle statistics and coherent states from classical scattering amplitudes
• Bethe-Salpeter equation for classical gravitational bound states
• Angular Momentum Loss Due to Tidal Effects in the Post-Minkowskian Expansion
• All order gravitational waveforms from scattering amplitudes
• Remodeling the Effective One-Body Formalism in Post-Minkowskian Gravity
• Post-Newtonian Waveforms from Spinning Scattering Amplitudes
• Classical Double Copy of Spinning Worldline Quantum Field Theory
• Kinematic Hopf algebra for amplitudes and form factors
• A Supertranslation-Invariant Formula for the Angular Momentum Flux in Gravitational Scattering
• Binary Dynamics from Worldline QFT for Scalar-QED
• Large Gauge Effects and the Structure of Amplitudes
• Color-kinematics duality, double copy and the unitarity method for higher-derivative QCD and quadratic gravity
• Scattering Amplitudes and N-Body Post-Minkowskian Hamiltonians in General Relativity and Beyond
• Quantization Conditions and the Double Copy
• Covariant color-kinematics duality, Hopf algebras and permutohedra
• Machine Learning Post-Minkowskian Integrals
• The Radial Action from Probe Amplitudes to All Orders
• Effective-one-body formalism for leading-order radiative effects in the post-linear framework
• Energetics and scattering of gravitational two-body systems at fourth post-Minkowskian order