A new approach to piecewise linear Wilson lines

TL;DR

This paper introduces an algorithm to efficiently compute piecewise linear Wilson lines in QCD, simplifying calculations and enabling easy comparison of different path topologies for gauge invariance and universality studies.

Contribution

It develops a novel algorithm to express piecewise linear Wilson lines in terms of their segments, reducing computational complexity and facilitating comparison of different path structures.

Findings

Reduces the number of diagrams needed for calculations.

Provides a method to relate different linear path topologies.

Enables easier testing of universality properties.

Abstract

Wilson lines are key objects in many QCD calculations. They are parallel transporters of the gauge field that can be used to render non-local operator products gauge invariant, which is especially useful for calculations concerning validation of factorization schemes and in calculations for constructing or modelling parton density functions. We develop an algorithm to express Wilson lines that are defined on piecewise linear paths in function of their Wilson segments, reducing the number of diagrams needed to be calculated. We show how different linear path topologies can be related using their color structure. This framework allows one to easily switch results between different Wilson line structures, which is helpful when testing different structures against each other, e.g. when checking universality properties of non-perturbative objects.