Searching for Kerr in the 2PM amplitude

• Published in: The journal of high energy physics Vol. 2022; no. 7; pp. 72 - 34
• Main Authors: Aoude, Rafael, Haddad, Kays, Helset, Andreas
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2022; Springer Nature B.V; Springer Nature; SpringerOpen
• Subjects: Amplitudes; Black Holes; Classical and Quantum Gravitation; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Classical Theories of Gravity; Deformation; Effective Field Theories; Elementary Particles; Gravitational waves; Gravity; Helicity; High energy physics; Multipoles; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering; Scattering Amplitudes; Spin structure; String Theory; Variables; Classical Theories of Gravity; Effective Field Theories; Scattering Amplitudes; Black Holes
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP07(2022)072

A bstract 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) 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 supplementary material file 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.