High Energy Scattering in Perturbative Quantum Gravity at Next to Leading Power

TL;DR

This paper analyzes high-energy scattering of unequal-mass scalar particles via graviton exchange, extending the eikonal approximation to include next-to-leading power gravitational corrections and exploring impact parameter modifications.

Contribution

It provides a detailed calculation of next-to-leading power corrections in gravitational scattering, demonstrating their effects on the impact parameter and phase exponentiation.

Findings

Gravitational corrections dominate the phase in impact parameter space.

Next-to-leading power effects modify the impact parameter saddle point.

Corrections are independent of the light particle's energy at leading order.

Abstract

We consider the relativistic scattering of unequal-mass scalar particles through graviton exchange in the small-angle high-energy regime. We show the self-consistency of expansion around the eikonal limit and compute the scattering amplitude up to the next-to-leading power correction of the light particle energy, including gravitational effects of the same order. The first power correction is suppressed by a single power of the ratio of momentum transfer to the energy of the light particle in the rest frame of the heavy particle, independent of the heavy particle mass. We find that only gravitational corrections contribute to the exponentiated phase in impact parameter space in four dimensions. For large enough heavy-particle mass, the saddle point for the impact parameter is modified compared to the leading order by a multiple of the Schwarzschild radius determined by the mass of the heavy particle, independent of the energy of the light particle.