From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion

We combine tools from effective field theory and generalized unitarity to construct a map between on-shell scattering amplitudes and the classical potential for interacting spinless particles. For general relativity, we obtain analytic expressions for the classical potential of a binary black hole s...

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Bibliographic Details
Published in:Physical review letters 2018-12, Vol.121 (25), p.251101-251101, Article 251101
Main Authors: Cheung, Clifford, Rothstein, Ira Z, Solon, Mikhail P
Format: Article
Language:English
Subjects:
Amplitudes
ASTRONOMY AND ASTROPHYSICS
Effective field theory
Field theory
Gravitational constant
Gravitational waves
Perturbation theory
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Relativity
Scattering
Scattering amplitudes
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Summary:We combine tools from effective field theory and generalized unitarity to construct a map between on-shell scattering amplitudes and the classical potential for interacting spinless particles. For general relativity, we obtain analytic expressions for the classical potential of a binary black hole system at second order in the gravitational constant and all orders in velocity. Our results exactly match all known results up to fourth post-Newtonian order, and offer a simple check of future higher order calculations. By design, these methods should extend to higher orders in perturbation theory.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.121.251101