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


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
Article number161103
Pages (from-to)1-7
Number of pages7
JournalPhysical Review Letters
Issue number16
Publication statusPublished - 22 Apr 2022


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