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

Abstract

We derive the third subleading (N${}^3$LO) corrections of the quadratic-in-spin sectors via the EFT of spinning objects in post-Newtonian (PN) gravity. These corrections consist of contributions from $4$ sectors for generic compact binaries, that enter at the fifth PN order. One of these contributions is due to a new tidal interaction, that is unique to the sectors with spin, and complements the first tidal interaction that also enters at this PN order in the simple point-mass sector. The evaluation of Feynman graphs is carried out in a generic dimension via advanced multi-loop methods, and gives rise to 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 the most general Lagrangians and Hamiltonians. We then specify the latter to simplified configurations, and derive the consequent gauge-invariant relations among the binding energy, angular momentum, and frequency. We end with a derivation of all the scattering angles that correspond to an extension of our Hamiltonians to the scattering problem in the simplified aligned-spins configuration, as a guide to scattering-amplitudes studies.

arXiv comment57 pp, 1 figure; 25 ancillary files, including pdf of ~1000 visual graphs

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• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• Completing the Fifth PN Precision Frontier via the EFT of Spinning Gravitating Objects
• N${}^3$LO Spin-Orbit Interaction via the EFT of Spinning Gravitating Objects
• Gravitational Quadratic-in-Spin Hamiltonian at NNNLO in the post-Newtonian framework
• Large Gauge Effects and the Structure of Amplitudes
• 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
• Charged test-particle scattering and effective one-body metrics with spin
• 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