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

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.

6 pages, 3 eps figures; v2: misprints corrected, minor changes in the conclusions, references updated; v3: extended to 8 pages, important updates in Sect. 3, matches the version published in Phys. Rev. D

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Cited by in corpus (8)

• Gluon and Wilson loop TMDs for hadrons of spin $\le$ 1
• Webs and Posets
• Loop space and evolution of the light-like Wilson polygons
• Evolution of Light-Like Wilson Loops with a Self-Intersection in Loop Space
• On Geometric Scaling of Light-Like Wilson Polygons: Higher Orders in ${\alpha }_s$
• Fréchet derivative for light-like Wilson Loops
• Transverse-Distance Dependent Parton Densities in the Large-$x$ Regime
• Evolution and dynamics of cusped light-like Wilson loops (Hadron 2013)