A functional approach to the next to eikonal approximation of high energy gravitational scattering

TL;DR

This paper employs functional methods to analyze high-energy gravitational scattering, extending the eikonal approximation to include next-to-eikonal corrections and nonlinear interactions, providing a refined understanding of scattering amplitudes.

Contribution

It introduces a functional approach to derive the next-to-eikonal approximation in high-energy gravitational scattering, including nonlinear effects and impact parameters beyond the Schwarzschild radius.

Findings

Exponentiation of the leading eikonal confirmed.

Next-to-eikonal corrections included.

Interaction at large impact parameters analyzed.

Abstract

The Fradkin-Schwinger functional methods to represent a Green function in an external gravitational field are used to study the eikonal and the next-to-eikonal limit, including the nonlinear gravitational interactions, of the scattering amplitudes of an ultra-relativistic scalar particle on a static super-massive scalar target in the nearly forward limit. The functional approach confirms the exponentiation of the leading eikonal which also applies to the first non-leading power in the energy of the light particle, moreover includes the interaction at impact parameter much larger than the Schwarzschild radius associated with the center of mass energy in the ultra-relativistic limit.