Exponentiation of the leading eikonal phase 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 $D\ensuremath{\rightarrow}4$. 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 $\ensuremath{\hbar}$ of momentum-space amplitudes, allowing the extension of our arguments to arbitrary-spin scattering.

Topics & Concepts