Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian

Abstract

We complete the derivation of the conservative dynamics of binary systems to fourth Post-Newtonian (4PN) order in the effective field theory (EFT) approach. We present a self-contained (ambiguity-free) computation of the renormalized Lagrangian, entirely within the confines of the PN expansion. While we confirm the final results reported in the literature, we clarify several issues regarding intermediate infrared (IR) and ultraviolet (UV) divergences, as well as the renormalization procedure. First, we properly identify the IR and UV singularities using (only) dimensional regularization and the method of regions, which are the pillars of the EFT formalism. This requires a careful study of scaleless integrals in the potential region, as well as conservative contributions from radiation modes due to tail effects. As expected by consistency, the UV divergences in the near region (due to the point-particle limit) can be absorbed into two counter-terms in the worldline effective theory. The counter-terms can then be removed by field redefinitions, such that the renormalization scheme-dependence has no physical effect to 4PN order. The remaining IR poles, which are spurious in nature, are unambiguously removed by implementing the zero-bin subtraction in the EFT approach. The procedure transforms the IR singularities into UV counter-parts. As anticipated, the left-over UV poles explicitly cancel out against UV divergences in conservative terms from radiation-reaction, uniquely determining the gravitational potential. Similar artificial IR/UV poles, which are intimately linked to the split into regions, are manifest at lower orders. Starting at 4PN, both local- and nonlocal-in-time contributions from the radiation region enter in the conservative dynamics. Neither additional regulators nor ambiguity-parameters are introduced at any stage of the computations.

40 pages. 8 figures. v2: Published version

References in corpus (23)

• Relativistic theory of tidal Love numbers
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• The Zero-Bin and Mode Factorization in Quantum Field Theory
• Scattering of Spinning Black Holes from Exponentiated Soft Factors
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order
• Gravitational spin Hamiltonians from the S matrix
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian
• The Tune of Love and the Nature(ness) of Spacetime
• 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 dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant
• Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses
• Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order
• TASI Lectures on Effective Field Theories
• Les Houches Lectures on Effective Field Theories and Gravitational Radiation
• Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order
• Spin Effects in Long Range Gravitational Scattering
• Soft gravitational radiation from ultra-relativistic collisions at sub- and sub-sub-leading order
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• The principle of stationary nonconservative action for classical mechanics and field theories

Cited by in corpus (93)

• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• New Horizons for Fundamental Physics with LISA
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• 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
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Kerr Black Holes as Elementary Particles
• Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach
• From Boundary Data to Bound States II: Scattering Angle to Dynamical Invariants (with Twist)
• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
• Radiation Reaction and Gravitational Waves at Fourth Post-Minkowskian Order
• Novel approach to binary dynamics: application to the fifth post-Newtonian level
• Second-order self-force calculation of the gravitational binding energy in compact binaries
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian
• Conservative Tidal Effects in Compact Binary Systems to Next-to-Leading Post-Minkowskian Order
• Binary dynamics at the fifth and fifth-and-a-half post-Newtonian orders
• Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
• 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
• Radiative contributions to gravitational scattering
• Interpreting Binary Neutron Star Mergers: Describing the Binary Neutron Star Dynamics, Modelling Gravitational Waveforms, and Analyzing Detections
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
• The Science of the Einstein Telescope
• From amplitudes to gravitational radiation with cubic interactions and tidal effects
• Gravitational-Wave Phasing of Quasi-Circular Compact Binary Systems to the Fourth-and-a-Half post-Newtonian Order
• Gravitational radiation from inspiralling compact objects: Spin effects to fourth Post-Newtonian order
• Gravitational Wave Flux and Quadrupole Modes from Quasi-Circular Non-Spinning Compact Binaries to the Fourth Post-Newtonian Order
• Gravitational waves at the first post-Newtonian order with the Weyssenhoff fluid in Einstein-Cartan theory
• Mining the Geodesic Equation for Scattering Data
• Resummed spinning waveforms from five-point amplitudes
• Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO
• Gravitational spin-orbit coupling through third-subleading post-Newtonian order: from first-order self-force to arbitrary mass ratios
• Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading post-Newtonian order
• Hereditary Terms at Next-To-Leading Order in Two-Body Gravitational Dynamics
• From Boundary Data to Bound States III: Radiative Effects
• Gravitational spin-orbit and aligned spin${}_1$-spin${}_2$ couplings through third-subleading post-Newtonian orders
• Quasi-circular inspirals and plunges from non-spinning effective-one-body Hamiltonians with gravitational self-force information
• Generalized quasi-Keplerian solution for eccentric, non-spinning compact binaries at 4PN order and the associated IMR waveform
• Logarithmic tail contributions to the energy function of circular compact binaries
• The mass quadrupole moment of compact binary systems at the fourth post-Newtonian order
• Scalar QED as a toy model for higher-order effects in classical gravitational scattering
• Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework
• Tail contributions to gravitational conservative dynamics
• Second post-Newtonian order radiative dynamics of inspiralling compact binaries in the Effective Field Theory approach
• Worldline effective field theory of inspiralling black hole binaries in presence of dark photon and axionic dark matter
• Gravitational-wave tails of memory
• Gravitational Quadratic-in-Spin Hamiltonian at NNNLO in the post-Newtonian framework
• The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: II. Dimensional Regularization and Renormalization
• Post-Minkowskian Theory Meets the Spinning Effective-One-Body Approach for Two-Body Scattering
• Renormalizing Love: tidal effects at the third post-Newtonian order
• Gravitational Scattering and Beyond from Extreme Mass Ratio Effective Field Theory
• Three-Body Effective Potential in General Relativity at Second Post-Minkowskian Order and Resulting Post-Newtonian Contributions
• Prospects of detecting deviations to Kerr geometry with radiation reaction effects in EMRIs
• Near and far zone in two-body dynamics: an effective field theory perspective
• Classical Gravitational Self-Energy from Double Copy
• The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: I. Non-Locality in Time and Infra-Red Divergencies
• Self-force effects on the marginally bound zoom-whirl orbit in Schwarzschild spacetime
• Efficient resummation of high post-Newtonian contributions to the binding energy
• Binary Dynamics from Worldline QFT for Scalar-QED
• Gravitational radiation contributions to the two-body scattering angle
• Radiation Reaction for Non-Spinning Bodies at 4.5PN in the Effective Field Theory Approach
• Gravitational Multipole Renormalization
• Scattering Amplitudes and N-Body Post-Minkowskian Hamiltonians in General Relativity and Beyond
• Multipole expansion at the level of the action in $d$-dimensions
• Next-to-leading order spin-orbit effects in the equations of motion, energy loss and phase evolution of binaries of compact bodies in the effective field theory approach
• Conservative (failed)-tail effects at the fifth post-Newtonian order
• Binary systems in massive scalar-tensor theories: Next-to-leading order gravitational wave phase from effective field theory
• Gravitational radiation from inspiralling compact binaries to N${}^3$LO in the Effective Field Theory approach
• Detweiler's redshift invariant for extended bodies orbiting a Schwarzschild black hole
• Radiating Love: adiabatic tidal fluxes and modes up to next-to-next-to-leading post-Newtonian order
• Schott term in the binding energy for compact binaries on circular orbits at fourth post-Newtonian order
• Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order
• Waveforms from Amplitudes
• Half-solution to the two-body problem in General Relativity
• Analytic Solutions to Compact Binary Inspirals With Leading Order Spin-Orbit Contribution Using The Dynamical Renormalization Group
• Binary dynamics to second post-Newtonian order in scalar-tensor and Einstein-scalar-Gauss-Bonnet gravity from effective field theory
• Post-Newtonian Dynamics of Spinning Black Hole Binaries in Einstein-Scalar-Gauss-Bonnet Gravity
• Machine Learning Post-Minkowskian Integrals
• Post-Newtonian Lagrangian of an N-body System with Arbitrary Mass and Spin Multipoles
• Tidal Love Numbers of Neutron Stars in Horndeski Theories
• Classical gravitational scattering from a gauge-invariant double copy
• Tests of general relativity at the fourth post-Newtonian order
• Quantum gravity phenomenology from the perspective of quantum general relativity and quadratic gravity
• Comparison of 4.5PN and 2SF gravitational energy fluxes from quasicircular compact binaries
• Compact binary system dynamics at the second post-Newtonian order: analytical formula of the coordinate time for eccentric and circular orbits
• Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order in harmonic coordinates