Path integral approach to eikonal and next-to-eikonal exponentiation

TL;DR

This paper presents a path integral framework for understanding the exponentiation of soft gauge boson corrections in scattering amplitudes, providing new insights into eikonal and next-to-eikonal effects in both abelian and non-abelian theories.

Contribution

It introduces a novel path integral approach to exponentiation, clarifies the structure of next-to-eikonal corrections, and offers a new perspective on webs and color factors in non-abelian gauge theories.

Findings

Exponentiation in abelian theories derived from path-integral combinatorics.

New formulation of non-abelian exponentiation using webs and color factors.

Clarification of next-to-eikonal correction structures.

Abstract

We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed coordinate-momentum space representation, a charged particle interacting with a soft gauge field is represented as a Wilson line for a semi-infinite line segment, together with calculable fluctuations. Combining such line segments, we show that exponentiation in an abelian field theory follows immediately from standard path-integral combinatorics. In the non-abelian case, we consider color singlet hard interactions with two outgoing external lines, and obtain a new viewpoint for exponentiation in terms of ``webs'', with a closed form solution for their corresponding color factors. We investigate and clarify the structure of next-to-eikonal corrections.