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

Abstract

We present the derivation of the third subleading order (N${}^3$LO) spin-orbit interaction at the state of the art of post-Newtonian (PN) gravity via the EFT of spinning objects. The present sector contains the largest and most elaborate collection of Feynman graphs ever tackled to date in sectors with spin, and in all PN sectors up to third subleading order. Our computations are carried out via advanced multi-loop methods. Their most demanding aspect is the imperative transition to a generic dimension across the whole derivation, due to the emergence of dimensional-regularization poles across all loop orders as of the N${}^3$LO sectors. At this high order of sectors with spin, it is also critical to extend the formal procedure for the reduction of higher-order time derivatives of spin variables beyond linear order for the first time. This gives rise to a new unique contribution at the present sector. The full interaction potential in Lagrangian form and the general Hamiltonian are provided here for the first time. The consequent gravitational-wave (GW) gauge-invariant observables are also derived, including relations among the binding energy, angular momentum, and emitted frequency. Complete agreement is found between our results, and the binding energy of GW sources, and also with the extrapolated scattering angle in the scattering problem, derived via traditional GR. In contrast with the latter derivation, our framework is free-standing and generic, and has provided theory and results, which have been critical to establish the state of the art, and to push the precision frontier for the measurement of GWs.

65 pp, 21 ancillary files, including 386pp pdf of visual graphs

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• Massive twistor worldline in electromagnetic fields
• From the EFT of Spinning Gravitating Objects to Poincaré and Gauge Invariance at the 4.5PN Precision Frontier
• Spin supplementary condition in quantum field theory: covariant SSC and physical state projection
• Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals
• Dynamical Love Numbers for Black Holes and Beyond from Shell Effective Field Theory