Abstract
Following a recent proposal to describe inelastic eikonal scattering processes in terms of gravitationally dressed elastic eikonal amplitudes, we motivate a collinear double graviton dressing and investigate its properties. This is derived from a generalized Wilson line operator in the worldline formalism by integrating over fluctuations of the eikonal trajectories of external particles in gravitationally interacting theories. The dressing can be expressed as a product of exponential terms — a coherent piece with contributions to all odd orders in the gravitational coupling constant and a term quadratic in graviton modes, with the former providing classical gravitational wave observables. In particular, the coherent dressing involves \( \mathcal{O}\left({\kappa}^3\right) \) subleading double graviton corrections to the Weinberg soft factor. We use this dressing to derive expressions for the waveform, radiative momentum spectrum and angular momentum. In a limiting case of the waveform, we derive the nonlinear memory effect resulting from the emission of nearly soft gravitons from a scattering process.
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References
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].
W.D. Goldberger and A.K. Ridgway, Radiation and the classical double copy for color charges, Phys. Rev. D 95 (2017) 125010 [arXiv:1611.03493] [INSPIRE].
T. Damour, Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory, Phys. Rev. D 94 (2016) 104015 [arXiv:1609.00354] [INSPIRE].
A. Luna et al., The double copy: Bremsstrahlung and accelerating black holes, JHEP 06 (2016) 023 [arXiv:1603.05737] [INSPIRE].
A. Luna, I. Nicholson, D. O’Connell and C.D. White, Inelastic Black Hole Scattering from Charged Scalar Amplitudes, JHEP 03 (2018) 044 [arXiv:1711.03901] [INSPIRE].
N.E.J. Bjerrum-Bohr et al., General Relativity from Scattering Amplitudes, Phys. Rev. Lett. 121 (2018) 171601 [arXiv:1806.04920] [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].
D.A. Kosower, B. Maybee and D. O’Connell, Amplitudes, Observables, and Classical Scattering, JHEP 02 (2019) 137 [arXiv:1811.10950] [INSPIRE].
A. Cristofoli, N.E.J. Bjerrum-Bohr, P.H. Damgaard and P. Vanhove, Post-Minkowskian Hamiltonians in general relativity, Phys. Rev. D 100 (2019) 084040 [arXiv:1906.01579] [INSPIRE].
N.E.J. Bjerrum-Bohr, A. Cristofoli and P.H. Damgaard, Post-Minkowskian Scattering Angle in Einstein Gravity, JHEP 08 (2020) 038 [arXiv:1910.09366] [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].
P.H. Damgaard, L. Plante and P. Vanhove, On an exponential representation of the gravitational S-matrix, JHEP 11 (2021) 213 [arXiv:2107.12891] [INSPIRE].
S. Caron-Huot, M. Giroux, H.S. Hannesdottir and S. Mizera, What can be measured asymptotically?, JHEP 01 (2024) 139 [arXiv:2308.02125] [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].
T. Damour, Classical and quantum scattering in post-Minkowskian gravity, Phys. Rev. D 102 (2020) 024060 [arXiv:1912.02139] [INSPIRE].
Z. Bern, H. Ita, J. Parra-Martinez and M.S. Ruf, Universality in the classical limit of massless gravitational scattering, Phys. Rev. Lett. 125 (2020) 031601 [arXiv:2002.02459] [INSPIRE].
G. Kälin, Z. Liu and R.A. Porto, Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach, Phys. Rev. Lett. 125 (2020) 261103 [arXiv:2007.04977] [INSPIRE].
J. Parra-Martinez, M.S. Ruf and M. Zeng, Extremal black hole scattering at \( \mathcal{O}\left({G}^3\right) \): graviton dominance, eikonal exponentiation, and differential equations, JHEP 11 (2020) 023 [arXiv:2005.04236] [INSPIRE].
T. Damour, Radiative contribution to classical gravitational scattering at the third order in G, Phys. Rev. D 102 (2020) 124008 [arXiv:2010.01641] [INSPIRE].
E. Herrmann, J. Parra-Martinez, M.S. Ruf and M. Zeng, Gravitational Bremsstrahlung from Reverse Unitarity, Phys. Rev. Lett. 126 (2021) 201602 [arXiv:2101.07255] [INSPIRE].
S. Mougiakakos, M.M. Riva and F. Vernizzi, Gravitational Bremsstrahlung in the post-Minkowskian effective field theory, Phys. Rev. D 104 (2021) 024041 [arXiv:2102.08339] [INSPIRE].
E. Herrmann, J. Parra-Martinez, M.S. Ruf and M. Zeng, Radiative classical gravitational observables at \( \mathcal{O}\left({G}^3\right) \) from scattering amplitudes, JHEP 10 (2021) 148 [arXiv:2104.03957] [INSPIRE].
P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, The eikonal approach to gravitational scattering and radiation at \( \mathcal{O}\left({G}^3\right) \), JHEP 07 (2021) 169 [arXiv:2104.03256] [INSPIRE].
D. Bini, T. Damour and A. Geralico, Radiative contributions to gravitational scattering, Phys. Rev. D 104 (2021) 084031 [arXiv:2107.08896] [INSPIRE].
P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, The eikonal operator at arbitrary velocities I: the soft-radiation limit, JHEP 07 (2022) 039 [arXiv:2204.02378] [INSPIRE].
G. Kälin, J. Neef and R.A. Porto, Radiation-reaction in the Effective Field Theory approach to Post-Minkowskian dynamics, JHEP 01 (2023) 140 [arXiv:2207.00580] [INSPIRE].
A.V. Manohar, A.K. Ridgway and C.-H. Shen, Radiated Angular Momentum and Dissipative Effects in Classical Scattering, Phys. Rev. Lett. 129 (2022) 121601 [arXiv:2203.04283] [INSPIRE].
P. Di Vecchia, C. Heissenberg and R. Russo, Angular momentum of zero-frequency gravitons, JHEP 08 (2022) 172 [arXiv:2203.11915] [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].
Z. Bern et al., Scattering Amplitudes and Conservative Binary Dynamics at \( \mathcal{O}\left({G}^4\right) \), Phys. Rev. Lett. 126 (2021) 171601 [arXiv:2101.07254] [INSPIRE].
C. Dlapa, G. Kälin, Z. Liu and R.A. Porto, Dynamics of binary systems to fourth Post-Minkowskian order from the effective field theory approach, Phys. Lett. B 831 (2022) 137203 [arXiv:2106.08276] [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].
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].
C. Dlapa, G. Kälin, Z. Liu and R.A. Porto, Bootstrapping the relativistic two-body problem, JHEP 08 (2023) 109 [arXiv:2304.01275] [INSPIRE].
P.H. Damgaard, E.R. Hansen, L. Planté and P. Vanhove, Classical observables from the exponential representation of the gravitational S-matrix, JHEP 09 (2023) 183 [arXiv:2307.04746] [INSPIRE].
Z. Bern et al., Spinning black hole binary dynamics, scattering amplitudes, and effective field theory, Phys. Rev. D 104 (2021) 065014 [arXiv:2005.03071] [INSPIRE].
D. Kosmopoulos and A. Luna, Quadratic-in-spin Hamiltonian at \( \mathcal{O}\left({G}^2\right) \) from scattering amplitudes, JHEP 07 (2021) 037 [arXiv:2102.10137] [INSPIRE].
Z. Liu, R.A. Porto and Z. Yang, Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics, JHEP 06 (2021) 012 [arXiv:2102.10059] [INSPIRE].
R. Aoude and A. Ochirov, Classical observables from coherent-spin amplitudes, JHEP 10 (2021) 008 [arXiv:2108.01649] [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].
K. Haddad, Exponentiation of the leading eikonal phase with spin, Phys. Rev. D 105 (2022) 026004 [arXiv:2109.04427] [INSPIRE].
R. Aoude, K. Haddad and A. Helset, Searching for Kerr in the 2PM amplitude, JHEP 07 (2022) 072 [arXiv:2203.06197] [INSPIRE].
F. Febres Cordero et al., Conservative Binary Dynamics with a Spinning Black Hole at O(G3) from Scattering Amplitudes, Phys. Rev. Lett. 130 (2023) 021601 [arXiv:2205.07357] [INSPIRE].
M.M. Riva, F. Vernizzi and L.K. Wong, Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion, Phys. Rev. D 106 (2022) 044013 [arXiv:2205.15295] [INSPIRE].
C. Heissenberg, Angular momentum loss due to spin-orbit effects in the post-Minkowskian expansion, Phys. Rev. D 108 (2023) 106003 [arXiv:2308.11470] [INSPIRE].
Z. Bern et al., Quantum field theory, worldline theory, and spin magnitude change in orbital evolution, Phys. Rev. D 109 (2024) 045011 [arXiv:2308.14176] [INSPIRE].
A. Luna, N. Moynihan, D. O’Connell and A. Ross, Observables from the Spinning Eikonal, arXiv:2312.09960 [INSPIRE].
Z. Bern et al., Leading Nonlinear Tidal Effects and Scattering Amplitudes, JHEP 05 (2021) 188 [arXiv:2010.08559] [INSPIRE].
K. Haddad and A. Helset, Tidal effects in quantum field theory, JHEP 12 (2020) 024 [arXiv:2008.04920] [INSPIRE].
R. Aoude, K. Haddad and A. Helset, Tidal effects for spinning particles, JHEP 03 (2021) 097 [arXiv:2012.05256] [INSPIRE].
M. Accettulli Huber, A. Brandhuber, S. De Angelis and G. Travaglini, From amplitudes to gravitational radiation with cubic interactions and tidal effects, Phys. Rev. D 103 (2021) 045015 [arXiv:2012.06548] [INSPIRE].
S. Mougiakakos, M.M. Riva and F. Vernizzi, Gravitational Bremsstrahlung with Tidal Effects in the Post-Minkowskian Expansion, Phys. Rev. Lett. 129 (2022) 121101 [arXiv:2204.06556] [INSPIRE].
C. Heissenberg, Angular Momentum Loss due to Tidal Effects in the Post-Minkowskian Expansion, Phys. Rev. Lett. 131 (2023) 011603 [arXiv:2210.15689] [INSPIRE].
C.R.T. Jones and M.S. Ruf, Absorptive effects and classical black hole scattering, JHEP 03 (2024) 015 [arXiv:2310.00069] [INSPIRE].
G.U. Jakobsen, G. Mogull, J. Plefka and B. Sauer, Tidal effects and renormalization at fourth post-Minkowskian order, Phys. Rev. D 109 (2024) L041504 [arXiv:2312.00719] [INSPIRE].
M.M. Riva, L. Santoni, N. Savić and F. Vernizzi, Vanishing of Nonlinear Tidal Love Numbers of Schwarzschild Black Holes, arXiv:2312.05065 [INSPIRE].
L. Barack and O. Long, Self-force correction to the deflection angle in black-hole scattering: A scalar charge toy model, Phys. Rev. D 106 (2022) 104031 [arXiv:2209.03740] [INSPIRE].
L. Barack et al., Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model, Phys. Rev. D 108 (2023) 024025 [arXiv:2304.09200] [INSPIRE].
T. Adamo, A. Cristofoli, A. Ilderton and S. Klisch, Scattering amplitudes for self-force, Class. Quant. Grav. 41 (2024) 065006 [arXiv:2307.00431] [INSPIRE].
D. Kosmopoulos and M.P. Solon, Gravitational self force from scattering amplitudes in curved space, JHEP 03 (2024) 125 [arXiv:2308.15304] [INSPIRE].
C. Cheung et al., Effective Field Theory for Extreme Mass Ratio Binaries, Phys. Rev. Lett. 132 (2024) 091402 [arXiv:2308.14832] [INSPIRE].
G.U. Jakobsen, G. Mogull, J. Plefka and J. Steinhoff, Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory, Phys. Rev. Lett. 126 (2021) 201103 [arXiv:2101.12688] [INSPIRE].
A. Cristofoli, R. Gonzo, D.A. Kosower and D. O’Connell, Waveforms from amplitudes, Phys. Rev. D 106 (2022) 056007 [arXiv:2107.10193] [INSPIRE].
G.U. Jakobsen, G. Mogull, J. Plefka and J. Steinhoff, Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies, Phys. Rev. Lett. 128 (2022) 011101 [arXiv:2106.10256] [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].
T. Adamo, A. Cristofoli, A. Ilderton and S. Klisch, All Order Gravitational Waveforms from Scattering Amplitudes, Phys. Rev. Lett. 131 (2023) 011601 [arXiv:2210.04696] [INSPIRE].
A. Elkhidir, D. O’Connell, M. Sergola and I.A. Vazquez-Holm, Radiation and Reaction at One Loop, arXiv:2303.06211 [INSPIRE].
A. Brandhuber et al., One-loop gravitational bremsstrahlung and waveforms from a heavy-mass effective field theory, JHEP 06 (2023) 048 [arXiv:2303.06111] [INSPIRE].
A. Herderschee, R. Roiban and F. Teng, The sub-leading scattering waveform from amplitudes, JHEP 06 (2023) 004 [arXiv:2303.06112] [INSPIRE].
A. Georgoudis, C. Heissenberg and I. Vazquez-Holm, Inelastic exponentiation and classical gravitational scattering at one loop, JHEP 06 (2023) 126 [arXiv:2303.07006] [INSPIRE].
S. De Angelis, R. Gonzo and P.P. Novichkov, Spinning waveforms from KMOC at leading order, arXiv:2309.17429 [INSPIRE].
D. Bini, T. Damour and A. Geralico, Comparing one-loop gravitational bremsstrahlung amplitudes to the multipolar-post-Minkowskian waveform, Phys. Rev. D 108 (2023) 124052 [arXiv:2309.14925] [INSPIRE].
A. Brandhuber et al., Resummed spinning waveforms from five-point amplitudes, JHEP 02 (2024) 026 [arXiv:2310.04405] [INSPIRE].
R. Aoude, K. Haddad, C. Heissenberg and A. Helset, Leading-order gravitational radiation to all spin orders, Phys. Rev. D 109 (2024) 036007 [arXiv:2310.05832] [INSPIRE].
A. Georgoudis, C. Heissenberg and R. Russo, An eikonal-inspired approach to the gravitational scattering waveform, JHEP 03 (2024) 089 [arXiv:2312.07452] [INSPIRE].
A. Georgoudis, C. Heissenberg and I. Vazquez-Holm, Addendum to: Inelastic exponentiation and classical gravitational scattering at one loop, JHEP 02 (2024) 161 [arXiv:2312.14710] [INSPIRE].
L. Bohnenblust, H. Ita, M. Kraus and J. Schlenk, Gravitational Bremsstrahlung in Black-Hole Scattering at \( \mathcal{O}\left({G}^3\right) \): Linear-in-Spin Effects, arXiv:2312.14859 [INSPIRE].
D. Bini et al., Gravitational Waveform: A Tale of Two Formalisms, arXiv:2402.06604 [INSPIRE].
P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, Radiation Reaction from Soft Theorems, Phys. Lett. B 818 (2021) 136379 [arXiv:2101.05772] [INSPIRE].
P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, The gravitational eikonal: from particle, string and brane collisions to black-hole encounters, arXiv:2306.16488 [INSPIRE].
A. Cristofoli et al., The Uncertainty Principle and Classical Amplitudes, arXiv:2112.07556 [INSPIRE].
R. Britto, R. Gonzo and G.R. Jehu, Graviton particle statistics and coherent states from classical scattering amplitudes, JHEP 03 (2022) 214 [arXiv:2112.07036] [INSPIRE].
C. Heissenberg, Infrared divergences and the eikonal exponentiation, Phys. Rev. D 104 (2021) 046016 [arXiv:2105.04594] [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [INSPIRE].
F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [INSPIRE].
C.D. White, Factorization Properties of Soft Graviton Amplitudes, JHEP 05 (2011) 060 [arXiv:1103.2981] [INSPIRE].
D. Bonocore, A. Kulesza and J. Pirsch, Classical and quantum gravitational scattering with Generalized Wilson Lines, JHEP 03 (2022) 147 [arXiv:2112.02009] [INSPIRE].
C. Gerry and P. Knight, Introductory Quantum Optics, Cambridge University Press (2004).
A. Luna, S. Melville, S.G. Naculich and C.D. White, Next-to-soft corrections to high energy scattering in QCD and gravity, JHEP 01 (2017) 052 [arXiv:1611.02172] [INSPIRE].
E. Laenen, G. Stavenga and C.D. White, Path integral approach to eikonal and next-to-eikonal exponentiation, JHEP 03 (2009) 054 [arXiv:0811.2067] [INSPIRE].
F. Bloch and A. Nordsieck, Note on the Radiation Field of the electron, Phys. Rev. 52 (1937) 54 [INSPIRE].
S. Chakrabarti et al., Subleading Soft Theorem for Multiple Soft Gravitons, JHEP 12 (2017) 150 [arXiv:1707.06803] [INSPIRE].
S. Chakrabarti et al., Testing Subleading Multiple Soft Graviton Theorem for CHY Prescription, JHEP 01 (2018) 090 [arXiv:1709.07883] [INSPIRE].
J. Distler, R. Flauger and B. Horn, Double-soft graviton amplitudes and the extended BMS charge algebra, JHEP 08 (2019) 021 [arXiv:1808.09965] [INSPIRE].
R. Marotta and M. Mojaza, Double-soft behavior of massless closed strings interacting with any number of closed string tachyons, JHEP 08 (2020) 083 [arXiv:2005.05877] [INSPIRE].
G. Veneziano and G.A. Vilkovisky, Angular momentum loss in gravitational scattering, radiation reaction, and the Bondi gauge ambiguity, Phys. Lett. B 834 (2022) 137419 [arXiv:2201.11607] [INSPIRE].
S.J. Kovacs and K.S. Thorne, The Generation of Gravitational Waves. 3. Derivation of Bremsstrahlung Formulas, Astrophys. J. 217 (1977) 252 [INSPIRE].
B. Sahoo and A. Sen, Classical soft graviton theorem rewritten, JHEP 01 (2022) 077 [arXiv:2105.08739] [INSPIRE].
D. Ghosh and B. Sahoo, Spin-dependent gravitational tail memory in D = 4, Phys. Rev. D 105 (2022) 025024 [arXiv:2106.10741] [INSPIRE].
D. Christodoulou, Nonlinear nature of gravitation and gravitational wave experiments, Phys. Rev. Lett. 67 (1991) 1486 [INSPIRE].
A.G. Wiseman and C.M. Will, Christodoulou’s nonlinear gravitational wave memory: Evaluation in the quadrupole approximation, Phys. Rev. D 44 (1991) R2945 [INSPIRE].
K.S. Thorne, Gravitational-wave bursts with memory: The Christodoulou effect, Phys. Rev. D 45 (1992) 520 [INSPIRE].
M. Favata, The gravitational-wave memory effect, Class. Quant. Grav. 27 (2010) 084036 [arXiv:1003.3486] [INSPIRE].
R. Gonzo and A. Ilderton, Wave scattering event shapes at high energies, JHEP 10 (2023) 108 [arXiv:2305.17166] [INSPIRE].
P.-N. Chen, M.-T. Wang, Y.-K. Wang and S.-T. Yau, Supertranslation invariance of angular momentum, Adv. Theor. Math. Phys. 25 (2021) 777 [arXiv:2102.03235] [INSPIRE].
D. Bini and T. Damour, Radiation-reaction and angular momentum loss at the second post-Minkowskian order, Phys. Rev. D 106 (2022) 124049 [arXiv:2211.06340] [INSPIRE].
R. Aoude et al., Silence of Binary Kerr Black Holes, Phys. Rev. Lett. 125 (2020) 181602 [arXiv:2007.09486] [INSPIRE].
A. Bose et al., Relative entropy in scattering and the S-matrix bootstrap, SciPost Phys. 9 (2020) 081 [arXiv:2006.12213] [INSPIRE].
A. Sinha and A. Zahed, Bell inequalities in 2-2 scattering, Phys. Rev. D 108 (2023) 025015 [arXiv:2212.10213] [INSPIRE].
C. Cheung, T. He and A. Sivaramakrishnan, Entropy growth in perturbative scattering, Phys. Rev. D 108 (2023) 045013 [arXiv:2304.13052] [INSPIRE].
R. Aoude, G. Elor, G.N. Remmen and O. Sumensari, Positivity in Amplitudes from Quantum Entanglement, arXiv:2402.16956 [INSPIRE].
D. Carney, L. Chaurette, D. Neuenfeld and G.W. Semenoff, Dressed infrared quantum information, Phys. Rev. D 97 (2018) 025007 [arXiv:1710.02531] [INSPIRE].
D. Carney, L. Chaurette, D. Neuenfeld and G. Semenoff, On the need for soft dressing, JHEP 09 (2018) 121 [arXiv:1803.02370] [INSPIRE].
G.W. Semenoff, Entanglement and the Infrared, Springer Proc. Math. Stat. 335 (2019) 151 [arXiv:1912.03187] [INSPIRE].
S. Blanes and F. Casas, On the convergence and optimization of the Baker-Campbell-Hausdorff formula, Linear Algebra Appl. 378 (2004) 135.
Acknowledgments
We would like to thank Paolo Di Vecchia, Carlo Heissenberg, Filippo Vernizzi, Chia-Hsien Shen, Yu-tin Huang and Fei Teng for their valuable feedback and comments on our results. FLL thanks the hospitality of the organizers of the workshop “Gravitational waves meet effective field theories” held at Benasque, Spain on Aug 20-26 of 2023, during which he presented an earlier version of this work. The work of KF is supported by Taiwan’s NSTC with grant numbers 111-2811-M-003-005 and 112-2811-M-003 -003-MY3. The work of FLL is supported by Taiwan’s NSTC with grant numbers 109-2112-M-003-007-MY3 and 112-2112-M-003-006-MY3. We also like to thank the support of iCAG funding by NTNU.
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Fernandes, K., Lin, FL. Next-to-eikonal corrected double graviton dressing and gravitational wave observables at \( \mathcal{O}\left({G}^2\right) \). J. High Energ. Phys. 2024, 15 (2024). https://doi.org/10.1007/JHEP06(2024)015
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DOI: https://doi.org/10.1007/JHEP06(2024)015