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Holomorphic classical limit for spin effects in gravitational and electromagnetic scattering

  • Alfredo GuevaraEmail author
Open Access
Regular Article - Theoretical Physics
  • 28 Downloads

Abstract

We provide universal expressions for the classical piece of the amplitude given by the graviton/photon exchange between massive particles of arbitrary spin, at both tree and one loop level. In the gravitational case this leads to higher order terms in the post-Newtonian expansion, which have been previously used in the binary inspiral problem. The expressions are obtained in terms of a contour integral that computes the Leading Singularity, which was recently shown to encode the relevant information up to one loop. The classical limit is performed along a holomorphic trajectory in the space of kinematics, such that the leading order is enough to extract arbitrarily high multipole corrections. These multipole interactions are given in terms of a recently proposed representation for massive particles of any spin by Arkani-Hamed et al. This explicitly shows universality of the multipole interactions in the effective potential with respect to the spin of the scattered particles. We perform the explicit match to standard EFT operators for S = \( \frac{1}{2} \) and S = 1. As a natural byproduct we obtain the classical pieces up to one loop for the bending of light.

Keywords

Scattering Amplitudes Black Holes Effective Field Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  2. 2.Department of Physics & AstronomyUniversity of WaterlooWaterlooCanada
  3. 3.CECs Valdivia & Departamento de FísicaUniversidad de ConcepciónConcepciónChile

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