Abstract
We establish and develop a novel methodology to treat higher-order non-linear effects of gravitational radiation that is scattered from binary inspirals, which employs modern scattering-amplitudes methods on the effective picture of the binary as a composite particle. We spell out our procedure to study such effects: assembling tree amplitudes via generalized-unitarity methods and employing the closed-time-path formalism to derive the causal effective actions, which encompass the full conservative and dissipative dynamics. We push through to a new state of the art for these higher-order effects, up to the third subleading tail effect, at order \( {G}_N^5 \) and the 5-loop level, which corresponds to the 8.5PN order. We formulate the consequent dissipated energy for these higher-order corrections, and carry out a renormalization analysis, where we uncover new subleading RG flow of the quadrupole coupling. For all higher-order tail effects we find perfect agreement with partial observable results in PN and self-force theories, where available.
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LIGO Scientific and Virgo collaborations, Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116 (2016) 061102 [arXiv:1602.03837] [INSPIRE].
LIGO Scientific and Virgo collaborations, GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence, Phys. Rev. Lett. 116 (2016) 241103 [arXiv:1606.04855] [INSPIRE].
LIGO Scientific and Virgo collaborations, GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral, Phys. Rev. Lett. 119 (2017) 161101 [arXiv:1710.05832] [INSPIRE].
LIGO Scientific and VIRGO collaborations, GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2, Phys. Rev. Lett. 118 (2017) 221101 [Erratum ibid. 121 (2018) 129901] [arXiv:1706.01812] [INSPIRE].
LIGO Scientific and Virgo collaborations, GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence, Phys. Rev. Lett. 119 (2017) 141101 [arXiv:1709.09660] [INSPIRE].
LIGO Scientific and Virgo collaborations, GW170608: Observation of a 19-solar-mass Binary Black Hole Coalescence, Astrophys. J. Lett. 851 (2017) L35 [arXiv:1711.05578] [INSPIRE].
LIGO Scientific collaboration, Advanced LIGO, Class. Quant. Grav. 32 (2015) 074001 [arXiv:1411.4547] [INSPIRE].
VIRGO collaboration, Advanced Virgo: a second-generation interferometric gravitational wave detector, Class. Quant. Grav. 32 (2015) 024001 [arXiv:1408.3978] [INSPIRE].
KAGRA collaboration, Overview of KAGRA: Detector design and construction history, PTEP 2021 (2021) 05A101 [arXiv:2005.05574] [INSPIRE].
LISA collaboration, Laser Interferometer Space Antenna, arXiv:1702.00786 [INSPIRE].
D. Reitze et al., Cosmic Explorer: The U.S. Contribution to Gravitational-Wave Astronomy beyond LIGO, Bull. Am. Astron. Soc. 51 (2019) 035 [arXiv:1907.04833] [INSPIRE].
M. Maggiore et al., Science Case for the Einstein Telescope, JCAP 03 (2020) 050 [arXiv:1912.02622] [INSPIRE].
L. Blanchet, Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries, Living Rev. Rel. 17 (2014) 2 [arXiv:1310.1528] [INSPIRE].
D. Bini, T. Damour and A. Geralico, Novel approach to binary dynamics: application to the fifth post-Newtonian level, Phys. Rev. Lett. 123 (2019) 231104 [arXiv:1909.02375] [INSPIRE].
D. Bini, T. Damour and A. Geralico, Binary dynamics at the fifth and fifth-and-a-half post-Newtonian orders, Phys. Rev. D 102 (2020) 024062 [arXiv:2003.11891] [INSPIRE].
D. Bini et al., Gravitational dynamics at O(G6): perturbative gravitational scattering meets experimental mathematics, arXiv:2008.09389 [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, An effective field theory of gravity for extended objects, Phys. Rev. D 73 (2006) 104029 [hep-th/0409156] [INSPIRE].
J. Blümlein, A. Maier and P. Marquard, Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses, Phys. Lett. B 800 (2020) 135100 [arXiv:1902.11180] [INSPIRE].
J. Blümlein, A. Maier, P. Marquard and G. Schäfer, The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach, Nucl. Phys. B 983 (2022) 115900 [Erratum ibid. 985 (2022) 115991] [arXiv:2110.13822] [INSPIRE].
J. Blümlein, A. Maier, P. Marquard and G. Schäfer, Gravity in binary systems at the fifth and sixth post-Newtonian order, PoS LL2022 (2022) 012 [arXiv:2208.04552] [INSPIRE].
A. Einstein, Über Gravitationswellen, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys. ) 1918 (1918) 154 [INSPIRE].
W.L. Burke, GRAVITATIONAL RADIATION DAMPING OF SLOWLY MOVING SYSTEMS CALCULATED USING MATCHED ASYMPTOTIC EXPANSIONS, J. Math. Phys. 12 (1971) 401 [INSPIRE].
K.S. Thorne, Nonradial Pulsation of General-Relativistic Stellar Models.IV. The Weakfield Limit, Astrophys. J. 158 (1969) 997 [INSPIRE].
L. Blanchet and T. Damour, Tail Transported Temporal Correlations in the Dynamics of a Gravitating System, Phys. Rev. D 37 (1988) 1410 [INSPIRE].
L. Blanchet and T. Damour, Hereditary effects in gravitational radiation, Phys. Rev. D 46 (1992) 4304 [INSPIRE].
W.D. Goldberger and A. Ross, Gravitational radiative corrections from effective field theory, Phys. Rev. D 81 (2010) 124015 [arXiv:0912.4254] [INSPIRE].
C.R. Galley, A.K. Leibovich, R.A. Porto and A. Ross, Tail effect in gravitational radiation reaction: Time nonlocality and renormalization group evolution, Phys. Rev. D 93 (2016) 124010 [arXiv:1511.07379] [INSPIRE].
S. Foffa and R. Sturani, Tail terms in gravitational radiation reaction via effective field theory, Phys. Rev. D 87 (2013) 044056 [arXiv:1111.5488] [INSPIRE].
S. Foffa and R. Sturani, Hereditary terms at next-to-leading order in two-body gravitational dynamics, Phys. Rev. D 101 (2020) 064033 [Erratum ibid. 103 (2021) 089901] [arXiv:1907.02869] [INSPIRE].
L. Blanchet, Gravitational wave tails of tails, Class. Quant. Grav. 15 (1998) 113 [Erratum ibid. 22 (2005) 3381] [gr-qc/9710038] [INSPIRE].
T. Marchand, L. Blanchet and G. Faye, Gravitational-wave tail effects to quartic non-linear order, Class. Quant. Grav. 33 (2016) 244003 [arXiv:1607.07601] [INSPIRE].
C. Cheung, I.Z. Rothstein and M.P. Solon, From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion, Phys. Rev. Lett. 121 (2018) 251101 [arXiv:1808.02489] [INSPIRE].
Z. Bern et al., Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order, Phys. Rev. Lett. 122 (2019) 201603 [arXiv:1901.04424] [INSPIRE].
Z. Bern et al., Black Hole Binary Dynamics from the Double Copy and Effective Theory, JHEP 10 (2019) 206 [arXiv:1908.01493] [INSPIRE].
Z. Bern et al., Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at O(G4), Phys. Rev. Lett. 128 (2022) 161103 [arXiv:2112.10750] [INSPIRE].
G. Mogull, J. Plefka and J. Steinhoff, Classical black hole scattering from a worldline quantum field theory, JHEP 02 (2021) 048 [arXiv:2010.02865] [INSPIRE].
G.U. Jakobsen, G. Mogull, J. Plefka and J. Steinhoff, SUSY in the sky with gravitons, JHEP 01 (2022) 027 [arXiv:2109.04465] [INSPIRE].
G.U. Jakobsen, G. Mogull, J. Plefka and B. Sauer, All things retarded: radiation-reaction in worldline quantum field theory, JHEP 10 (2022) 128 [arXiv:2207.00569] [INSPIRE].
C. Dlapa, G. Kälin, Z. Liu and R.A. Porto, Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-Eccentricity Expansion, Phys. Rev. Lett. 128 (2022) 161104 [arXiv:2112.11296] [INSPIRE].
C. Dlapa et al., Radiation Reaction and Gravitational Waves at Fourth Post-Minkowskian Order, Phys. Rev. Lett. 130 (2023) 101401 [arXiv:2210.05541] [INSPIRE].
G. Kälin and R.A. Porto, From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist), JHEP 02 (2020) 120 [arXiv:1911.09130] [INSPIRE].
G. Kälin and R.A. Porto, From Boundary Data to Bound States, JHEP 01 (2020) 072 [arXiv:1910.03008] [INSPIRE].
G. Cho, G. Kälin and R.A. Porto, From boundary data to bound states. Part III. Radiative effects, JHEP 04 (2022) 154 [Erratum ibid. 07 (2022) 002] [arXiv:2112.03976] [INSPIRE].
P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, Classical gravitational observables from the Eikonal operator, Phys. Lett. B 843 (2023) 138049 [arXiv:2210.12118] [INSPIRE].
P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, The eikonal approach to gravitational scattering and radiation at 𝒪(G3), JHEP 07 (2021) 169 [arXiv:2104.03256] [INSPIRE].
A. Buonanno et al., Snowmass White Paper: Gravitational Waves and Scattering Amplitudes, in the proceedings of the Snowmass 2021, Seattle, U.S.A., July 17–26 (2022) [arXiv:2204.05194] [INSPIRE].
A. Edison and M. Levi, A tale of tails through generalized unitarity, Phys. Lett. B 837 (2023) 137634 [arXiv:2202.04674] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B 435 (1995) 59 [hep-ph/9409265] [INSPIRE].
R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills, Nucl. Phys. B 725 (2005) 275 [hep-th/0412103] [INSPIRE].
C. Anastasiou et al., D-dimensional unitarity cut method, Phys. Lett. B 645 (2007) 213 [hep-ph/0609191] [INSPIRE].
W.D. Goldberger, A. Ross and I.Z. Rothstein, Black hole mass dynamics and renormalization group evolution, Phys. Rev. D 89 (2014) 124033 [arXiv:1211.6095] [INSPIRE].
C.R. Galley, Classical Mechanics of Nonconservative Systems, Phys. Rev. Lett. 110 (2013) 174301 [arXiv:1210.2745] [INSPIRE].
C.R. Galley, D. Tsang and L.C. Stein, The principle of stationary nonconservative action for classical mechanics and field theories, arXiv:1412.3082 [INSPIRE].
R. Fujita, Gravitational radiation for extreme mass ratio inspirals to the 14th post-Newtonian order, Prog. Theor. Phys. 127 (2012) 583 [arXiv:1104.5615] [INSPIRE].
R. Fujita, Gravitational Waves from a Particle in Circular Orbits around a Schwarzschild Black Hole to the 22nd Post-Newtonian Order, Prog. Theor. Phys. 128 (2012) 971 [arXiv:1211.5535] [INSPIRE].
R.A. Porto, The effective field theorist’s approach to gravitational dynamics, Phys. Rept. 633 (2016) 1 [arXiv:1601.04914] [INSPIRE].
M. Levi, Effective Field Theories of Post-Newtonian Gravity: A comprehensive review, Rept. Prog. Phys. 83 (2020) 075901 [arXiv:1807.01699] [INSPIRE].
R.A. Porto, Post-Newtonian corrections to the motion of spinning bodies in NRGR, Phys. Rev. D 73 (2006) 104031 [gr-qc/0511061] [INSPIRE].
R.A. Porto and I.Z. Rothstein, Spin(1)Spin(2) Effects in the Motion of Inspiralling Compact Binaries at Third Order in the Post-Newtonian Expansion, Phys. Rev. D 78 (2008) 044012 [Erratum ibid. 81 (2010) 029904] [arXiv:0802.0720] [INSPIRE].
R.A. Porto and I.Z. Rothstein, Next to Leading Order Spin(1)Spin(1) Effects in the Motion of Inspiralling Compact Binaries, Phys. Rev. D 78 (2008) 044013 [Erratum ibid. 81 (2010) 029905] [arXiv:0804.0260] [INSPIRE].
R.A. Porto, Absorption effects due to spin in the worldline approach to black hole dynamics, Phys. Rev. D 77 (2008) 064026 [arXiv:0710.5150] [INSPIRE].
M. Levi, Next to Leading Order gravitational Spin-Orbit coupling in an Effective Field Theory approach, Phys. Rev. D 82 (2010) 104004 [arXiv:1006.4139] [INSPIRE].
M. Levi, Next to Leading Order gravitational Spin1-Spin2 coupling with Kaluza-Klein reduction, Phys. Rev. D 82 (2010) 064029 [arXiv:0802.1508] [INSPIRE].
B. Kol, M. Levi and M. Smolkin, Comparing space+time decompositions in the post-Newtonian limit, Class. Quant. Grav. 28 (2011) 145021 [arXiv:1011.6024] [INSPIRE].
M. Levi, Binary dynamics from spin1-spin2 coupling at fourth post-Newtonian order, Phys. Rev. D 85 (2012) 064043 [arXiv:1107.4322] [INSPIRE].
M. Levi and J. Steinhoff, Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals, JCAP 12 (2014) 003 [arXiv:1408.5762] [INSPIRE].
M. Levi and J. Steinhoff, Spinning gravitating objects in the effective field theory in the post-Newtonian scheme, JHEP 09 (2015) 219 [arXiv:1501.04956] [INSPIRE].
M. Levi and J. Steinhoff, Leading order finite size effects with spins for inspiralling compact binaries, JHEP 06 (2015) 059 [arXiv:1410.2601] [INSPIRE].
M. Levi and J. Steinhoff, Complete conservative dynamics for inspiralling compact binaries with spins at the fourth post-Newtonian order, JCAP 09 (2021) 029 [arXiv:1607.04252] [INSPIRE].
M. Levi and J. Steinhoff, Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme, JCAP 01 (2016) 011 [arXiv:1506.05056] [INSPIRE].
M. Levi and J. Steinhoff, Next-to-next-to-leading order gravitational spin-squared potential via the effective field theory for spinning objects in the post-Newtonian scheme, JCAP 01 (2016) 008 [arXiv:1506.05794] [INSPIRE].
M. Levi and J. Steinhoff, EFTofPNG: A package for high precision computation with the Effective Field Theory of Post-Newtonian Gravity, Class. Quant. Grav. 34 (2017) 244001 [arXiv:1705.06309] [INSPIRE].
N.T. Maia, C.R. Galley, A.K. Leibovich and R.A. Porto, Radiation reaction for spinning bodies in effective field theory I: Spin-orbit effects, Phys. Rev. D 96 (2017) 084064 [arXiv:1705.07934] [INSPIRE].
N.T. Maia, C.R. Galley, A.K. Leibovich and R.A. Porto, Radiation reaction for spinning bodies in effective field theory II: Spin-spin effects, Phys. Rev. D 96 (2017) 084065 [arXiv:1705.07938] [INSPIRE].
M. Levi, S. Mougiakakos and M. Vieira, Gravitational cubic-in-spin interaction at the next-to-leading post-Newtonian order, JHEP 01 (2021) 036 [arXiv:1912.06276] [INSPIRE].
M. Levi and F. Teng, NLO gravitational quartic-in-spin interaction, JHEP 01 (2021) 066 [arXiv:2008.12280] [INSPIRE].
M. Levi, A.J. Mcleod and M. Von Hippel, N3LO gravitational spin-orbit coupling at order G4, JHEP 07 (2021) 115 [arXiv:2003.02827] [INSPIRE].
M. Levi, A.J. Mcleod and M. Von Hippel, N3LO gravitational quadratic-in-spin interactions at G4, JHEP 07 (2021) 116 [arXiv:2003.07890] [INSPIRE].
J.-W. Kim, M. Levi and Z. Yin, Quadratic-in-spin interactions at fifth post-Newtonian order probe new physics, Phys. Lett. B 834 (2022) 137410 [arXiv:2112.01509] [INSPIRE].
J.-W. Kim, M. Levi and Z. Yin, N3LO spin-orbit interaction via the EFT of spinning gravitating objects, JHEP 05 (2023) 184 [arXiv:2208.14949] [INSPIRE].
J.-W. Kim, M. Levi and Z. Yin, N3LO quadratic-in-spin interactions for generic compact binaries, JHEP 03 (2023) 098 [arXiv:2209.09235] [INSPIRE].
M. Levi, R. Morales and Z. Yin, From the EFT of spinning gravitating objects to Poincaré and gauge invariance at the 4.5PN precision frontier, JHEP 09 (2023) 090 [arXiv:2210.17538] [INSPIRE].
M. Levi and Z. Yin, Completing the fifth PN precision frontier via the EFT of spinning gravitating objects, JHEP 04 (2023) 079 [arXiv:2211.14018] [INSPIRE].
A. Ross, Multipole expansion at the level of the action, Phys. Rev. D 85 (2012) 125033 [arXiv:1202.4750] [INSPIRE].
P. Jaranowski and G. Schafer, Towards the 4th post-Newtonian Hamiltonian for two-point-mass systems, Phys. Rev. D 86 (2012) 061503 [arXiv:1207.5448] [INSPIRE].
D. Bini and A. Geralico, Higher-order tail contributions to the energy and angular momentum fluxes in a two-body scattering process, Phys. Rev. D 104 (2021) 104020 [arXiv:2108.05445] [INSPIRE].
C.R. Galley and M. Tiglio, Radiation reaction and gravitational waves in the effective field theory approach, Phys. Rev. D 79 (2009) 124027 [arXiv:0903.1122] [INSPIRE].
C.R. Galley and A.K. Leibovich, Radiation reaction at 3.5 post-Newtonian order in effective field theory, Phys. Rev. D 86 (2012) 044029 [arXiv:1205.3842] [INSPIRE].
L. Blanchet, S. Foffa, F. Larrouturou and R. Sturani, Logarithmic tail contributions to the energy function of circular compact binaries, Phys. Rev. D 101 (2020) 084045 [arXiv:1912.12359] [INSPIRE].
G.L. Almeida, S. Foffa and R. Sturani, Tail contributions to gravitational conservative dynamics, Phys. Rev. D 104 (2021) 124075 [arXiv:2110.14146] [INSPIRE].
L. Kadanoff and G. Baym, Quantum Statistical Mechanics: Green’s Function Methods in Equilibrium and Nonequilibrium Problems, Frontiers in Physics. A Lecture Note and Reprint Series. W.A. Benjamin (1962).
L.V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [INSPIRE].
H. Elvang and Y.-T. Huang, Scattering Amplitudes, arXiv:1308.1697 [INSPIRE].
H. Elvang and Y.-T. Huang, Scattering Amplitudes in Gauge Theory and Gravity, Cambridge University Press, Cambridge, U.K. (2015).
L.J. Dixon, A brief introduction to modern amplitude methods, in the proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics: Particle Physics: The Higgs Boson and Beyond, La Pommeraye, France, June 06–19 (2012) [https://doi.org/10.5170/CERN-2014-008.31] [arXiv:1310.5353] [INSPIRE].
J.J.M. Carrasco, Gauge and Gravity Amplitude Relations, in the proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics: Journeys Through the Precision Frontier: Amplitudes for Colliders, Boulder, U.S.A., June 02–27 (2014) [https://doi.org/10.1142/9789814678766_0011] [arXiv:1506.00974] [INSPIRE].
Z. Bern, S. Davies and J. Nohle, Double-Copy Constructions and Unitarity Cuts, Phys. Rev. D 93 (2016) 105015 [arXiv:1510.03448] [INSPIRE].
J.L. Bourjaily, E. Herrmann and J. Trnka, Prescriptive Unitarity, JHEP 06 (2017) 059 [arXiv:1704.05460] [INSPIRE].
J.J.M. Carrasco and H. Johansson, Generic multiloop methods and application to N = 4 super-Yang-Mills, J. Phys. A 44 (2011) 454004 [arXiv:1103.3298] [INSPIRE].
J.J.M. Carrasco and H. Johansson, Five-point amplitudes in \( \mathcal{N} \) = 4 super-Yang-Mills theory and \( \mathcal{N} \) = 8 supergravity, Phys. Rev. D 85 (2012) 025006 [arXiv:1106.4711] [INSPIRE].
Z. Bern et al., Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes, Phys. Rev. D 85 (2012) 105014 [arXiv:1201.5366] [INSPIRE].
Z. Bern et al., The duality between color and kinematics and its applications, J. Phys. A 57 (2024) 333002 [arXiv:1909.01358] [INSPIRE].
A. Edison et al., Perfecting one-loop BCJ numerators in SYM and supergravity, JHEP 02 (2023) 164 [arXiv:2211.00638] [INSPIRE].
A. Edison and M. Tegevi, Color-kinematics dual representations of one-loop matrix elements in the open-superstring effective action, JHEP 10 (2023) 022 [arXiv:2210.14865] [INSPIRE].
J.J.M. Carrasco and N.H. Pavao, Even-point multi-loop unitarity and its applications: exponentiation, anomalies and evanescence, JHEP 01 (2024) 019 [arXiv:2307.16812] [INSPIRE].
N. Arkani-Hamed and J. Trnka, The Amplituhedron, JHEP 10 (2014) 030 [arXiv:1312.2007] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
Z. Bern, T. Dennen, Y.-T. Huang and M. Kiermaier, Gravity as the Square of Gauge Theory, Phys. Rev. D 82 (2010) 065003 [arXiv:1004.0693] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476] [INSPIRE].
R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [INSPIRE].
R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [INSPIRE].
N. Arkani-Hamed, J. Bourjaily, F. Cachazo and J. Trnka, Local Spacetime Physics from the Grassmannian, JHEP 01 (2011) 108 [arXiv:0912.3249] [INSPIRE].
N. Arkani-Hamed et al., Grassmannian Geometry of Scattering Amplitudes, Cambridge University Press (2016) [https://doi.org/10.1017/CBO9781316091548] [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, Scattering amplitudes for all masses and spins, JHEP 11 (2021) 070 [arXiv:1709.04891] [INSPIRE].
M.-Z. Chung, Y.-T. Huang, J.-W. Kim and S. Lee, The simplest massive S-matrix: from minimal coupling to Black Holes, JHEP 04 (2019) 156 [arXiv:1812.08752] [INSPIRE].
P.H. Damgaard, K. Haddad and A. Helset, Heavy Black Hole Effective Theory, JHEP 11 (2019) 070 [arXiv:1908.10308] [INSPIRE].
R. Aoude, K. Haddad and A. Helset, On-shell heavy particle effective theories, JHEP 05 (2020) 051 [arXiv:2001.09164] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles: Scalars, Gluons and Gravitons, JHEP 07 (2014) 033 [arXiv:1309.0885] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles in Arbitrary Dimensions, Phys. Rev. Lett. 113 (2014) 171601 [arXiv:1307.2199] [INSPIRE].
A. Edison and F. Teng, Efficient Calculation of Crossing Symmetric BCJ Tree Numerators, JHEP 12 (2020) 138 [arXiv:2005.03638] [INSPIRE].
G. Passarino and M.J.G. Veltman, One Loop Corrections for e+e− Annihilation Into μ+μ− in the Weinberg Model, Nucl. Phys. B 160 (1979) 151 [INSPIRE].
S. Laporta and E. Remiddi, The analytical value of the electron (g – 2) at order α3 in QED, Phys. Lett. B 379 (1996) 283 [hep-ph/9602417] [INSPIRE].
V.A. Smirnov, Feynman integral calculus, Springer, Berlin, Heidelberg, (2006).
V.A. Smirnov, Analytic tools for Feynman integrals, Springer (2012) [https://doi.org/10.1007/978-3-642-34886-0] [INSPIRE].
W.L. van Neerven and J.A.M. Vermaseren, Large loop integrals, Phys. Lett. B 137 (1984) 241 [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, Dimensionally regulated one loop integrals, Phys. Lett. B 302 (1993) 299 [Erratum ibid. 318 (1993) 649] [hep-ph/9212308] [INSPIRE].
Z. Bern, L.J. Dixon and D.A. Kosower, Dimensionally regulated pentagon integrals, Nucl. Phys. B 412 (1994) 751 [hep-ph/9306240] [INSPIRE].
L.M. Brown and R.P. Feynman, Radiative corrections to Compton scattering, Phys. Rev. 85 (1952) 231 [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Scalar One Loop Integrals, Nucl. Phys. B 153 (1979) 365 [INSPIRE].
R. Britto and B. Feng, Integral coefficients for one-loop amplitudes, JHEP 02 (2008) 095 [arXiv:0711.4284] [INSPIRE].
G. Ossola, C.G. Papadopoulos and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level, Nucl. Phys. B 763 (2007) 147 [hep-ph/0609007] [INSPIRE].
D. Forde, Direct extraction of one-loop integral coefficients, Phys. Rev. D 75 (2007) 125019 [arXiv:0704.1835] [INSPIRE].
D. Kosmopoulos, Simplifying D-dimensional physical-state sums in gauge theory and gravity, Phys. Rev. D 105 (2022) 056025 [arXiv:2009.00141] [INSPIRE].
E. Gardi et al., The diagrammatic coaction, PoS LL2022 (2022) 015 [arXiv:2207.07843] [INSPIRE].
H. Frellesvig et al., Decomposition of Feynman Integrals by Multivariate Intersection Numbers, JHEP 03 (2021) 027 [arXiv:2008.04823] [INSPIRE].
D.A. Kosower, B. Maybee and D. O’Connell, Amplitudes, Observables, and Classical Scattering, JHEP 02 (2019) 137 [arXiv:1811.10950] [INSPIRE].
A. Herderschee, R. Roiban and F. Teng, The sub-leading scattering waveform from amplitudes, JHEP 06 (2023) 004 [arXiv:2303.06112] [INSPIRE].
B.R. Holstein and A. Ross, Spin Effects in Long Range Gravitational Scattering, arXiv:0802.0716 [INSPIRE].
V. Vaidya, Gravitational spin Hamiltonians from the S matrix, Phys. Rev. D 91 (2015) 024017 [arXiv:1410.5348] [INSPIRE].
G.L. Almeida, A. Müller, S. Foffa and R. Sturani, Conservative binary dynamics from gravitational tail emission processes, Phys. Rev. D 108 (2023) 124010 [arXiv:2307.05327] [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, Dissipative effects in the worldline approach to black hole dynamics, Phys. Rev. D 73 (2006) 104030 [hep-th/0511133] [INSPIRE].
A. Brandhuber, G. Chen, G. Travaglini and C. Wen, A new gauge-invariant double copy for heavy-mass effective theory, JHEP 07 (2021) 047 [arXiv:2104.11206] [INSPIRE].
C. Galley, Radiation reaction and self-force in curved spacetime in a field theory approach, Ph.D. thesis, Maryland University, U.S.A. (2007) [INSPIRE].
A.V. Smirnov and F.S. Chuharev, FIRE6: Feynman Integral REduction with Modular Arithmetic, Comput. Phys. Commun. 247 (2020) 106877 [arXiv:1901.07808] [INSPIRE].
L. Blanchet, Time asymmetric structure of gravitational radiation, Phys. Rev. D 47 (1993) 4392 [INSPIRE].
Z. Bern, H.-H. Chi, L. Dixon and A. Edison, Two-Loop Renormalization of Quantum Gravity Simplified, Phys. Rev. D 95 (2017) 046013 [arXiv:1701.02422] [INSPIRE].
L. Blanchet, Quadrupole-quadrupole gravitational waves, Class. Quant. Grav. 15 (1998) 89 [gr-qc/9710037] [INSPIRE].
L. Blanchet, B.R. Iyer and B. Joguet, Gravitational waves from inspiralling compact binaries: Energy flux to third postNewtonian order, Phys. Rev. D 65 (2002) 064005 [Erratum ibid. 71 (2005) 129903] [gr-qc/0105098] [INSPIRE].
Q. Henry and F. Larrouturou, Conservative tail and failed-tail effects at the fifth post-Newtonian order, Phys. Rev. D 108 (2023) 084048 [arXiv:2307.05860] [INSPIRE].
D. Gerosa and M. Vallisneri, filltex: Automatic queries to ADS and INSPIRE databases to fill LaTex bibliography, J. Open Source Softw. 2 (2017) 222 [INSPIRE].
X. Liu and Y.-Q. Ma, AMFlow: A Mathematica package for Feynman integrals computation via auxiliary mass flow, Comput. Phys. Commun. 283 (2023) 108565 [arXiv:2201.11669] [INSPIRE].
J. Klappert, F. Lange, P. Maierhöfer and J. Usovitsch, Integral reduction with Kira 2.0 and finite field methods, Comput. Phys. Commun. 266 (2021) 108024 [arXiv:2008.06494] [INSPIRE].
D.H. Bailey and D.J. Broadhurst, Parallel integer relation detection: Techniques and applications, Math. Comput. 70 (2001) 1719 [math/9905048] [INSPIRE].
A. Smirnov, https://gitlab.com/feynmanintegrals/pslq.
Acknowledgments
We thank John Joseph Carrasco, Sasank Chava, and Radu Roiban for feedback on the manuscript. AE is supported by the USDOE under contract DE-SC0015910 and by Northwestern University via the Amplitudes and Insight Group, Department of Physics and Astronomy, and Weinberg College of Arts and Sciences. ML has been supported by the Science and Technology Facilities Council (STFC) Rutherford Grant ST/V003895 “Harnessing QFT for Gravity”, and by the Mathematical Institute University of Oxford.
This research was supported in part through the computational resources and staff contributions provided for the Quest high performance computing facility at Northwestern University which is jointly supported by the Office of the Provost, the Office for Research, and Northwestern University Information Technology.
fillTEXwas used as part of writing the bibliography [151].
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Edison, A., Levi, M. Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals. J. High Energ. Phys. 2024, 161 (2024). https://doi.org/10.1007/JHEP08(2024)161
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DOI: https://doi.org/10.1007/JHEP08(2024)161