Light-Like Wilson Line in QCD Without Path Ordering

TL;DR

This paper simplifies the mathematical form of light-like Wilson lines in QCD by removing path ordering, and demonstrates their natural emergence in the factorization proof of divergences at high-energy colliders.

Contribution

It introduces a method to eliminate path ordering in light-like Wilson lines in QCD, clarifying their role in factorization proofs.

Findings

Path ordering can be removed in light-like Wilson lines in QCD.

The simplified Wilson line naturally appears in the factorization of divergences.

The approach applies to all orders in coupling constant.

Abstract

Unlike the Wilson line in QED the Wilson line in QCD contains path ordering. In this paper we get rid of the path ordering in the light-like Wilson line in QCD by simplifying all the infinite number of non-commuting terms in the SU(3) pure gauge. We prove that the light-like Wilson line in QCD naturally emerges when path integral formulation of QCD is used to prove factorization of soft and collinear divergences at all order in coupling constant in QCD processes at high energy colliders.