TY - JOUR

T1 - Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at O(G4)

AU - Bern, Zvi

AU - Parra-Martinez, Julio

AU - Roiban, Radu

AU - Ruf, Michael S.

AU - Shen, Chia-Hsien

AU - Solon, Mikhail P.

AU - Zeng, Mao

N1 - Funding Information:
We thank Johannes Blümlein, Martin Bojowald, Alessandra Buonanno, Clifford Cheung, Thibault Damour, Enrico Herrmann, Mohammed Khalil, David Kosower, Andrés Luna, Andreas Maier, Philipp Maierhöfer, Aneesh Manohar, Peter Marquard, Rafael Porto, Ira Rothstein, Jan Steinhoff, Johann Usovitsch, and Justin Vines for helpful discussions. Z. B. is supported by the U.S. Department of Energy (DOE) under Grant No. DE-SC0009937. J. P.-M. is supported by the DOE under Grant No. DE-SC0011632. R. R. is supported by the DOE under Grant No. DE-SC00019066. C.-H. S. is supported by the DOE under Grant No. DE-SC0009919. M. Z.’s work is supported by the U.K. Royal Society through Grant No. URF\R1\20109. We also are grateful to the Mani L. Bhaumik Institute for Theoretical Physics for support.
Publisher Copyright:
© 2022 authors. Published by the American Physical Society.

PY - 2022/4/22

Y1 - 2022/4/22

N2 - We complete the calculation of conservative two-body scattering dynamics at fourth post-Minkowskian order, i.e., O(G4) and all orders in velocity, including radiative contributions corresponding to the tail effect in general relativity. As in previous calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves complete elliptic integrals, and polylogarithms with up to transcendental weight 2. Using the amplitude-action relation, we obtain the radial action directly from the amplitude, and match the known overlapping terms in the post-Newtonian expansion.

AB - We complete the calculation of conservative two-body scattering dynamics at fourth post-Minkowskian order, i.e., O(G4) and all orders in velocity, including radiative contributions corresponding to the tail effect in general relativity. As in previous calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves complete elliptic integrals, and polylogarithms with up to transcendental weight 2. Using the amplitude-action relation, we obtain the radial action directly from the amplitude, and match the known overlapping terms in the post-Newtonian expansion.

U2 - 10.1103/PhysRevLett.128.161103

DO - 10.1103/PhysRevLett.128.161103

M3 - Article

VL - 128

SP - 1

EP - 7

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 16

M1 - 161103

ER -