Conservative Binary Dynamics with a Spinning Black Hole at O(G3) from Scattering Amplitudes

Fernando Febres Cordero*, Manfred Kraus, Guanda Lin, Michael S. Ruf, Mao Zeng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We compute the conservative two-body Hamiltonian of a compact binary system with a spinning black hole through O(G3) to all orders in velocity, including linear and quadratic spin terms. To obtain our results we calculate the classical limit of the two-loop amplitude for the scattering of a massive scalar particle with a massive spin-1 particle minimally coupled to gravity. We employ modern scattering amplitude and loop integration techniques, in particular numerical unitarity, integration-by-parts identities, and the method of regions. The conservative potential in terms of rest-frame spin vectors is extracted by matching to a nonrelativistic effective field theory. We also apply the Kosower-Maybee-O’Connell (KMOC) formalism to calculate the impulse in the covariant spin formalism directly from the amplitude. We work systematically in conventional dimensional regularization and explicitly evaluate all divergent integrals that appear in full- and effective-theory amplitudes, as well as in the phase-space integrals that arise in the KMOC formalism.
Original languageEnglish
Article number021601
Pages (from-to)1-11
Number of pages11
JournalPhysical Review Letters
Issue number2
Early online date12 Jan 2023
Publication statusPublished - 13 Jan 2023

Keywords / Materials (for Non-textual outputs)

  • hep-th
  • hep-ph


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