Abstract
In this paper we derive for the first time the N3LO gravitational spin-orbit coupling at order G4 in the post-Newtonian (PN) approximation within the effective field theory (EFT) of gravitating spinning objects. This represents the first computation in a spinning sector involving three-loop integration. We provide a comprehensive account of the topologies in the worldline picture for the computation at order G4. Our computation makes use of the publicly-available EFTofPNG code, which is extended using loop-integration techniques from particle amplitudes. We provide the results for each of the Feynman diagrams in this sector. The three-loop graphs in the worldline picture give rise to new features in the spinning sector, including divergent terms and logarithms from dimensional regularization, as well as transcendental numbers, all of which survive in the final result of the topologies at this order. This result enters at the 4.5PN order for maximally-rotating compact objects, and together with previous work in this line, paves the way for the completion of this PN accuracy.
Highlights
In [18], see [19,20,21,22,23,24]
We derive for the first time via the effective field theory (EFT) of spinning gravitating objects the N3LO spin-orbit coupling from interaction at G4, which consists of the highest-loop graphs in this sector at three-loop level
Higher-rank integrals are reduced using the integration by parts (IBP) method [49], which was previously implemented within the EFTofPNG code for rank-two integrals, with the IBP reduction done ‘by hand’
Summary
We first present the formal setup required to carry out the EFT computation of the N3LO spin-orbit sector at order G4. Let us turn to the Feynman rules required for this sector, which go beyond those appearing in the lower-order spinning sectors, presented in [28] The latter can be found for generic d in the public EFTofPNG code [16]. This is in contrast to the action presented in [43,44,45], which does not have generic rotational variables, and does not include the last term in eq (2.14) Note that both the mass and spin couplings play important roles in the spin-orbit interaction. Notice in particular the last term, which involves a time derivative, that enters here at the LO of the vertex; this did not occur in vertices at lower orders These rules are already given in terms of the physical spatial components of the local spin tensor in the canonical gauge [18], so all indices are Euclidean.
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