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 $D\rightarrow4$. 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 $\hbar$ of momentum-space amplitudes, allowing the extension of our results to arbitrary-spin scattering.