Planckian Scattering Beyond the Eikonal Approximation in the Quasi-potential Approach

TL;DR

This paper develops a systematic method within quantum field theory to analyze high-energy scattering amplitudes beyond the eikonal approximation, including corrections, using the quasi-potential approach.

Contribution

It introduces a new systematic scheme for calculating leading and correction terms of eikonal scattering amplitudes in the quasi-potential framework.

Findings

First correction to the leading eikonal amplitude is derived.

Connections between quasi-potential and functional approaches are established.

A comprehensive scheme for high-energy scattering amplitude analysis is developed.

Abstract

Asymptotic behavior of the scattering amplitude for two scalar particles by scalar, vector and tensor exchanges at high energy and fixed momentum transfers is reconsidered in quantum field theory. In the framework of the quasi-potential approach and the modified perturbation theory a systematic scheme of finding the leading eikonal scattering amplitudes and its corrections are developed and constructed. The connection between the solutions obtained by quasi-potential and functional approaches is also discussed. The first correction to leading eikonal amplitude is found.