Evolution of cusped light-like Wilson loops and geometry of the loop space

TL;DR

This paper explores the geometric and renormalization properties of cusped light-like Wilson loops, proposing a quantum dynamical approach to understand their energy evolution and implications for parton distribution functions.

Contribution

It introduces a novel perspective on the renormalization of light-cone cusped Wilson loops using the Schwinger approach and discusses their relation to the Makeenko-Migdal equations.

Findings

Ultraviolet and rapidity divergences affect Wilson loop renormalization.

Proposes a quantum dynamical framework for Wilson loop analysis.

Links Wilson loop evolution to phenomenologically relevant quantities.

Abstract

We discuss the possible relation between certain geometrical properties of the loop space and energy evolution of the cusped Wilson exponentials defined on the light-cone. Analysis of the area differential equations for this special class of the Wilson loops calls for careful treatment of the ultraviolet and rapidity divergences which make those loops non-multiplicatively-renormalizable. We propose to consider the renormalization properties of the light-cone cusped Wilson loops from the point of view of the universal quantum dynamical approach introduced by Schwinger. We conjecture and discuss the relevance of the Makeenko-Migdal loop equations supplied with the modified Schwinger principle to the energy evolution of some phenomenologically significant objects, such as transverse-momentum dependent distribution functions, collinear parton densities at large-$x$, etc.