N^3LO Spin-Orbit Interaction via the EFT of Spinning Gravitating Objects

Authors: Jung-Wook Kim, Michèle Levi, Zhewei Yin Preprint number: UUITP-35/22 Abstract: We present the derivation of the next-to-next-to-next-to-leading order (N^3LO) spin-orbit interaction at the state of the art of post-Newtonian (PN) gravity via the Effective Field Theory of spinning objects. The present sector contains the largest and most elaborate collection of Feynman graphs ever tackled to date in spin sectors, and in all PN sectors up to third subleading order. Our computations are carried out via advanced multi-loop methods, and their most demanding aspect is the imperative transition to a generic dimension across the whole derivation, which is common to sectors as of the N^3LO. At this high order of sectors with spin it is also needed to extend the formal procedure for the reduction of higher-order time derivatives of spin variables – beyond linear order – for the first time. The full interaction potentials in Lagrangian and Hamiltonian forms are provided here for the first time. These enable, e.g. the direct derivation of equations of motion for both the position and spin, studies of the related Poincaré algebra, or explorations of various possible effective-one-body models. The consequent gauge-invariant observables are also derived, namely relations among the binding energy, angular momentum, and orbital frequency. Complete agreement is found with the binding energy for circular orbits derived via traditional GR methods. In contrast to the latter derivation, the framework here is free-standing and generic, and provides independent derivations and results, which are critical to carefully establish the state of the art, and keep pushing the present high-order precision frontier.