Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity

Abstract

We compute the four-momentum radiated during the scattering of two spinless bodies, at leading order in the Newton's contant $G$ and at all orders in the velocities, using the Effective Field Theory worldline approach. Following \cite{Mougiakakos:2021ckm}, we derive the conserved stress-energy tensor linearly coupled to gravity generated by localized sources, at leading and next-to-leading order in $G$, and from that the classical probability amplitude of graviton emission. The total emitted momentum is obtained by phase-space integration of the graviton momentum weighted by the modulo squared of the radiation amplitude. We recast this as a two-loop integral that we solve using techniques borrowed from particle physics, such as reverse unitarity, reduction to master integrals by integration-by-parts identities and canonical differential equations. The emitted momentum agrees with recent results obtained by other methods. Our approach provides an alternative way of directly computing radiated observables in the post-Minkowskian expansion without going through the classical limit of scattering amplitudes.

arXiv comment41 pages, corrected typos

References in corpus (103)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• 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
• Higgs boson production at hadron colliders in NNLO QCD
• 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
• Transition from inspiral to plunge in binary black hole coalescences
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• An Effective Field Theory of Gravity for Extended Objects
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Amplitudes, Observables, and Classical Scattering
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• The Effective Field Theorist's Approach to Gravitational Dynamics
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• Quantum Gravitational Corrections to the Nonrelativistic Scattering Potential of Two Masses
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• Dimensionally Regulated One-Loop Integrals
• Lectures on differential equations for Feynman integrals
• High-energy gravitational scattering and the general relativistic two-body problem
• General Relativity from Scattering Amplitudes
• Dilepton rapidity distribution in the Drell-Yan process at NNLO in QCD
• Scattering of Spinning Black Holes from Exponentiated Soft Factors
• 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
• Radiation and the classical double copy for color charges
• Classical black hole scattering from a worldline quantum field theory
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• From Boundary Data to Bound States
• Presenting LiteRed: a tool for the Loop InTEgrals REDuction
• Observables and amplitudes for spinning particles and black holes
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• The simplest massive S-matrix: from minimal coupling to Black Holes
• xPert: Computer algebra for metric perturbation theory
• 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
• Gravitational radiative corrections from effective field theory
• The Eikonal Approach to Gravitational Scattering and Radiation at $\mathcal{O}(G^3)$
• Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach
• On Post-Minkowskian Hamiltonians in General Relativity
• Radiative contribution to classical gravitational scattering at the third order in $G$
• On-shell heavy particle effective theories
• From Boundary Data to Bound States II: Scattering Angle to Dynamical Invariants (with Twist)
• Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
• Inelastic Black Hole Scattering from Charged Scalar Amplitudes
• Universality of ultra-relativistic gravitational scattering
• Gravitational Bremsstrahlung from Reverse Unitarity
• Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order
• Radiation Reaction from Soft Theorems
• Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form
• Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
• The tail effect in gravitational radiation-reaction: time non-locality and renormalization group evolution
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Gravitational radiation reaction along general orbits in the effective one-body formalism
• Gravitational Radiation from Color-Kinematics Duality
• Conservative Tidal Effects in Compact Binary Systems to Next-to-Leading Post-Minkowskian Order
• The Duality Between Color and Kinematics and its Applications
• Gravitational Bremsstrahlung in the Post-Minkowskian Effective Field Theory
• Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
• Effective field theory methods to model compact binaries
• SUSY in the Sky with Gravitons
• Iterative structure of finite loop integrals
• Universality in the classical limit of massless gravitational scattering
• Tidal Effects in the Post-Minkowskian Expansion
• Sixth post-Newtonian nonlocal-in-time dynamics of binary systems
• Classical Gravitational Scattering at $\mathcal{O}(G^3)$ from Feynman Diagrams
• Bound states and the classical double copy
• Classical Gravity from Loop Amplitudes
• Radiative contributions to gravitational scattering
• Second-order Post-Minkowskian scattering in arbitrary dimensions
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions
• Scattering Amplitudes For All Masses and Spins
• Soft Expansion of Double-Real-Virtual Corrections to Higgs Production at N${}^3$LO
• Non-conservative effects on Spinning Black Holes from World-Line Effective Field Theory
• Les Houches Lectures on Effective Field Theories and Gravitational Radiation
• NLO Higgs boson rapidity distribution at hadron colliders
• Radiation-reaction force and multipolar waveforms for eccentric, spin-aligned binaries in the effective-one-body formalism
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity
• A tale of two exponentiations in $\mathcal{N}=8$ supergravity at subleading level
• A new gauge-invariant double copy for heavy-mass effective theory
• Tidal effects in quantum field theory
• Mining the Geodesic Equation for Scattering Data
• CFT Unitarity and the AdS Cutkosky Rules
• Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading post-Newtonian order
• Classical Yang-Mills observables from amplitudes
• Classical Double Copy of Worldline Quantum Field Theory
• Horizon radiation reaction forces
• Gravitational self-force in the ultra-relativistic limit: The 'large-N' expansion
• Three-Body Effective Potential in General Relativity at Second Post-Minkowskian Order and Resulting Post-Newtonian Contributions
• Remodeling the Effective One-Body Formalism in Post-Minkowskian Gravity
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• The Amplitude for Classical Gravitational Scattering at Third Post-Minkowskian Order
• Half-solution to the two-body problem in General Relativity
• Analytic Approximations in GR and Gravitational Waves
• Classical gravitational scattering from a gauge-invariant double copy

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• Post-Newtonian Waveforms from Spinning Scattering Amplitudes
• Binary Dynamics from Worldline QFT for Scalar-QED
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