N3LO gravitational quadratic-in-spin interactions at G 4

• Main Authors: Michèle Levi, Andrew J. McLeod, Matthew von Hippel
• Format: Article
• Language: English
• Published: SpringerOpen 2021-07-01
• Series: Journal of High Energy Physics
• Subjects: Classical Theories of Gravity; Effective Field Theories; Renormalization Regularization and Renormalons; Scattering Amplitudes
• Online Access: https://doi.org/10.1007/JHEP07(2021)116

Abstract We compute the N3LO gravitational quadratic-in-spin interactions at G 4 in the post-Newtonian (PN) expansion via the effective field theory (EFT) of gravitating spinning objects for the first time. This result contributes at the 5PN order for maximally-spinning compact objects, adding the spinning case to the static sector at this PN accuracy. This sector requires extending the EFT of a spinning particle beyond linear order in the curvature to include higher-order operators quadratic in the curvature that are relevant at this PN order. We make use of a diagrammatic expansion in the worldline picture, and rely on our recent upgrade of the EFTofPNG code, which we further extend to handle this sector. Similar to the spin-orbit sector, we find that the contributing three-loop graphs give rise to divergences, logarithms, and transcendental numbers. However, in this sector all of these features conspire to cancel out from the final result, which contains only finite rational terms.