Conservative Black Hole Scattering at Fifth Post-Minkowskian and First Self-Force Order

We compute the fifth post-Minkowskian (5PM) order contributions to the scattering angle and impulse of classical black hole scattering in the conservative sector at first self-force order using the worldline quantum field theory formalism. This challenging four-loop computation required the use of advanced integration-by-parts and differential equation technology implemented on high-performance computing systems. Use of partial fraction identities allowed us to render the complete integrand in a fully planar form. The resulting function space is simpler than expected: In the scattering angle, we see only multiple polylogarithms up to weight three and a total absence of the elliptic integrals that appeared at 4PM order. All checks on our result, both internal—cancellation of dimensional regularization poles and preservation of the on-shell condition—and external—matching the slow-velocity limit with the post-Newtonian (PN) literature up to 5PN order and matching the tail terms to the 4PM loss of energy—are passed.Received 26 March 2024Accepted 13 May 2024DOI:https://doi.org/10.1103/PhysRevLett.132.241402Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEffective field theoryFeynman diagramsGravitational wavesQuantum field theoryScattering amplitudesGravitation, Cosmology & AstrophysicsParticles & Fields