The Classical Gravitational Impulse at High Energies

TL;DR

This paper calculates the classical gravitational impulse at high energies for two massive scalars, resumming all large corrections and connecting quantum scattering amplitudes to classical results.

Contribution

It provides a resummation of high-energy gravitational scattering amplitudes to all orders in G_N and predicts the leading behavior of the post-Minkowski expansion.

Findings

Resummed all large G_N s corrections in high-energy gravitational scattering.

Recovered classical high-energy impulse from quantum amplitudes.

Predicted the leading high-energy behavior of the post-Minkowski expansion to eleventh order.

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 $G_N s/m b$ 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.