Exponentiation of the leading eikonal with spin

Abstract

We initiate a study into the eikonal exponentiation of the amplitude in impact-parameter space when spinning particles are involved in the scattering. Considering the gravitational scattering of two spin-1/2 particles, we demonstrate that the leading eikonal exhibits exponentiation up to $\mathcal{O}(G^2)$ in the limit where the spacetime dimension $D\to 4$. We find this to hold for general spin orientations. The exponentiation of the leading eikonal including spin is understood through the unitarity properties at leading order in $\hslash$ of momentum-space amplitudes, allowing the extension of our results to arbitrary-spin scattering.

12 pages + appendices

References in corpus (6)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• A worldsheet for Kerr
• From amplitudes to gravitational radiation with cubic interactions and tidal effects
• Classical observables from coherent-spin amplitudes
• Tidal effects for spinning particles
• Classical gravitational scattering from a gauge-invariant double copy

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