Searching for Kerr in the 2PM amplitude

TL;DR

This paper derives all-spin Compton amplitudes in the classical limit for QED, QCD, and gravity, enabling higher-order spin calculations in 2PM scattering and fixing some higher-spin contributions through spin structure relations.

Contribution

It introduces spurious-pole-free, all-spin Compton amplitudes in the classical limit and extends the calculation of spinning 2PM scattering to eighth order in spin vectors.

Findings

Derived all-spin Compton amplitudes for QED, QCD, and gravity.

Extended spinning 2PM scattering calculations to eighth order in spin vectors.

Fixed some higher-spin contributions by imposing relations between spin structures.

Abstract

The classical scattering of spinning objects is well described by the spinor-helicity formalism for heavy particles. Using these variables, we derive spurious-pole-free, all-spin opposite-helicity Compton amplitudes (factorizing on physical poles to the minimal, all-spin three-point amplitudes of ref. \cite{Arkani-Hamed:2017jhn}) in the classical limit for QED, QCD, and gravity. The cured amplitudes are subject to deformations by contact terms, the vast majority of whose contributions we can fix by imposing a relation between spin structures -- motivated by lower spin multipoles of black hole scattering -- at the second post-Minkowskian (2PM) order. For QED and gravity, this leaves a modest number of unfixed coefficients parametrizing contact-term deformations, while the QCD amplitude is uniquely determined. Our gravitational Compton amplitude allows us to push the state-of-the-art of spinning-2PM scattering to any order in the spin vectors of both objects; we present results here and in the auxiliary file \texttt{2PMSpin8Aux.nb} up to eighth order in the spin vectors. Interestingly, despite leftover coefficients in the Compton amplitude, imposing the aforementioned relation between spin structures uniquely fixes some higher-spin parts of the 2PM amplitude.