Holomorphic Classical Limit for Spin Effects in Gravitational and Electromagnetic Scattering

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.

37 pages. 4 figures

References in corpus (9)

• Perturbative spacetimes from Yang-Mills theory
• Light-like Scattering in Quantum Gravity
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• Leading order finite size effects with spins for inspiralling compact binaries
• Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order
• Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals
• EFTofPNG: A package for high precision computation with the Effective Field Theory of Post-Newtonian Gravity
• Quantum gravitational corrections for spinning particles
• Amplitudes for Astrophysicists: Known Knowns

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