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 arguments to arbitrary-spin scattering.

• Received 1 October 2021
• Accepted 13 December 2021

DOI:https://doi.org/10.1103/PhysRevD.105.026004

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Published by the American Physical Society