N3LO gravitational quadratic-in-spin interactions at G 4
Michèle Levi (Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen, 2100, Denmark, Institut de Physique Théorique, CEA & CNRS, Université Paris-Saclay, Gif-sur-Yvette, 91191, France); Andrew McLeod (Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen, 2100, Denmark); Matthew Hippel (Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen, 2100, Denmark)
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.
