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

Zvi Bern, Julio Parra-Martinez, Radu Roiban, Michael S. Ruf, Chia Hsien Shen, Mikhail P. Solon, Mao Zeng

Research output: Contribution to journalArticlepeer-review

81 Scopus citations


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.

Original languageEnglish (US)
Article number161103
JournalPhysical review letters
Issue number16
StatePublished - Apr 22 2022

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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