Abstract
We compute the N3LO gravitational quadratic-in-spin interactions at G4 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.
Highlights
Framework of the effective field theory (EFT) of gravitating spinning objects [16]
This work derives for the first time the complete N3LO gravitational interactions which are quadratic in the spins from a diagrammatic expansion at order G4
We start by reviewing the framework of the EFT of gravitating spinning objects, which enables our derivation of the N3LO quadratic-in-spin sectors from a diagrammatic expansion at order G4
Summary
We start by reviewing the framework of the EFT of gravitating spinning objects, which enables our derivation of the N3LO quadratic-in-spin sectors from a diagrammatic expansion at order G4. Finite-size effects that involve the spin-induced quadrupole of each of the rotating objects Due to the latter interaction, the effective action should be considered beyond minimal coupling, which is sufficient for the spin-orbit sector, and for interactions that are dependent on the linear spin couplings as in the spin1-spin and spin1-spin interactions. Where LNMC denotes the non-minimal coupling part of the action induced by the spin of the object This part is initially formulated in terms of the definite-parity pseudovector Sμ, as defined in [16, 19, 24]. (2.8) while there is a new Feynman rule for the four-graviton coupling to the worldline spin-induced quadrupole, given by CES2 d2 12m (d − 2) dt dSiSj 3φ2 ∂iφ ∂jφ + φ3 ∂i ∂jφ. We remind the reader that these rules are already given in terms of the physical spatial components of the local Euclidean spin vector in the canonical gauge [16], and that all of the indices are Euclidean
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