N^3LO Quadratic-in-Spin Interactions for Generic Compact Binaries

Authors: Jung-Wook Kim, Michèle Levi, Zhewei Yin Preprint number: UUITP-39/22 We derive the third subleading (N^3LO) corrections in the quadratic-in-spin sectors via the EFT of spinning objects in post-Newtonian (PN) gravity. These corrections include contributions from 4 sectors for generic compact objects, entering at the fifth PN order. One of these is a new tidal interaction, first entering in the spinning sectors, which complements the tidal interaction that first enters at the same PN order in the non-spinning sector. The evaluation of Feynman graphs is carried out in a generic dimension via multi-loop methods, and yields dimensional-regularization poles in conjunction with logarithms. At these higher-spin sectors the reduction of generalized Lagrangians entails redefinitions of the position beyond linear order. We provide here for the first time the relevant Lagrangians and Hamiltonians, and their useful simplified versions. We also derive the consequent gauge-invariant binding energy relations to the angular momentum and frequency. We end with a derivation of all scattering angles for aligned spins that correspond to an extension of the Hamiltonians for binary inspirals of the 4 independent sectors, and find complete agreement with the limited available results obtained via traditional GR, EFT and scattering-amplitudes methods.