The Classical Gravitational Impulse at High Energies

Abstract

We compute the gravitational impulse for two classical massive scalars in the ultrarelativistic limit to all orders in Newton's constant $G_N$ at fixed $G_{N}s/mb$ to $O(m^4/s^2)$. By computing the 4 and 5-point scattering amplitudes in the small-mass regime of $-t\sim m^2$, we are able to resum all large $G_{N}s$ corrections. Applying the KMOC formula for the impulse and taking the large mass limit, we recover the classical result at high energies. This resummation is in complete agreement with known results in the post-Minkowski expansion, and in the massless limit we recover previous results for the radiated energy. We use this resummed amplitude to predict the leading high-energy behavior of the PM expansion to eleventh post-Minkowski order.

11 page, 3 figures