Exponentiation of the leading eikonal with spin

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 $\mathrm{\hslash }$ of momentum-space amplitudes, allowing the extension of our results to arbitrary-spin scattering.