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

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 ultrav...

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Bibliographic Details
Published inarXiv.org
Main Authors Cherednikov, I O, Mertens, T, F F Van der Veken
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 31.10.2012
Subjects
Differential equations
Distribution functions
Evolution
Loops
Mathematical analysis
Physics - High Energy Physics - Phenomenology
Physics - High Energy Physics - Theory
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1208.1631