Gravitational Waveform: A Tale of Two Formalisms
arxiv(2024)
摘要
We revisit the quantum-amplitude-based derivation of the gravitational
waveform emitted by the scattering of two spinless massive bodies at the third
order in Newton's constant, h ∼ G+G^2+G^3 (one-loop level), and
correspondingly update its comparison with its classically-derived
multipolar-post-Minkowskian counterpart. A spurious-pole-free reorganization of
the one-loop five-point amplitude substantially simplifies the post-Newtonian
expansion. We find complete agreement between the two results up to the fifth
order in the small velocity expansion after taking into account three subtle
aspects of the amplitude derivation: (1) in agreement with [arXiv:2312.07452
[hep-th]], the term quadratic in the amplitude in the observable-based
formalism [JHEP 02, 137 (2019)] generates a frame rotation by half the
classical scattering angle; (2) the dimensional regularization of the infrared
divergences of the amplitude introduces an additional (d-4)/(d-4) finite
term; and (3) zero-frequency gravitons are found to contribute additional terms
both at order h ∼ G^1 and at order h ∼ G^3 when including
disconnected diagrams in the observable-based formalism.
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