Igor Olegovich Cherednikov

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 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 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 transversemomentum dependent distribution functions, collinear parton densities at large-x, etc.

Wilson lines in quantum field theory

The objective of this book is to get the reader acquainted with theoretical and mathematical foundations of the concept of Wilson loops in the context of modern quantum field theory. It teaches how to perform independently some elementary calculations on Wilson lines, and shows the recent development of the subject in different important areas of research.This revised second edition also includes historical notes on Wilson loops and lines.

Theory of transverse-momentum parton densities: Solving the puzzle of divergences

The current status of the theoretical understanding of the transverse-momentum dependent parton densities (TMDs) is discussed. Special attention is payed to the difference between the operator definitions of TMDs proposed so far, the treatment of specific divergences, the geometry of the gauge links, and the role of the soft factors. Short-distance factorization is the basic concept for the application of QCD at high energies [1, 2, 3]. The predictive power of QCD in this region has been successfully demonstrated in the case of fully inclusive processes, where the collinear (Feynman) parton distribution functions (PDFs) are applicable as a nonperturbative part of the QCD factorization theorems. Application of the QCD factorization approach to the description of the semi-inclusive hadronic reactions, such as the semi-inclusive DIS, or the Drell-Yan (DY) process, demands an expansion of the concept of parton distribution functions beyond the collinear approximation. It is useful to introduce the transverse-momentum-dependent (TMD) parton distribution (or fragmentation) functions (in what follows I abbreviate them by TMD = transverse-momentum “densities”) are essentially non-perturbative objects, which accumulate information about the intrinsic 3-dimensional motion of partons (quarks and/or gluons) in a hadron. In Refs. [4, 5, 6], the TMDs have been proposed as a generalization of the collinear PDFs:

EVOLUTION OF TRANSVERSE-DISTANCE DEPENDENT PARTON DENSITIES AT LARGE-XB AND GEOMETRY OF THE LOOP SPACE

We discuss possible applications of the equations of motion in the generalized Wilson loop space to the phenomenology of the three-dimensional parton distribution functions in the large-xB approximation. This regime is relevant for future experimental programs to be launched at the (approved) Jefferson Lab 12 GeV upgrade and the (planned) Electron-Ion Collider. We show that the geometrical evolution of the Wilson loops corresponds to the combined rapidity and renormalization-group equation of the transverse-distance dependent parton densities in the large-xB factorization scheme.

Evolution and Dynamics of Cusped Light-Like Wilson Loops in Loop Space

We address a connection between the energy evolution of the polygonal light-like Wilson exponentials and the geometry of the loop space with the gauge invariant Wilson loops of a variety of shapes being the fundamental degrees of freedom. The renormalization properties and the differential area evolution of these Wilson polygons are studied by making use of the universal Schwinger quantum dynamical approach. We discuss the appropriateness of the dynamical differential equations in the loop space to the study of the energy evolution of the collinear and transverse-momentum dependent parton distribution functions.

CASIMIR ENERGY OF CONFINED FIELDS: A ROLE OF THE RG-INVARIANCE

A role of the renormalization group invariance in calculations of the ground state energy for models with confined fermion fields is discussed. The case of the (1+1)D MIT bag model with the massive fermions is studied in detail.

Layout of Wilson lines and light-cone peculiarities of transverse-momentum dependent PDFs

We consider the problems of gauge invariance, path-dependence and treatment of overlapping UV/rapidity divergences peculiar to the transverse-momentum dependent parton distribution functions (TMDs). For different formulations of the TMDs available in the literature, we check the consistency of the TMD matrix elements with the collinear parton distribution functions possessing the well-known operator structure. Comparative on- and off-light-cone layout of the Wilson lines which secure the gauge-invariance of the TMDs is presented and briefly discussed.

Nonperturbative contributions to the quark form factor at high energy

The analysis of nonperturbative effects in high energy asymptotics of the color singlet quark form factor is presented. We show that the nonperturbative effects determine the initial value for the perturbative evolution of the quark form factor and find their general structure with respect to the high energy asymptotics. Within the Wilson integral formalism which is natural for investigation of the soft, IR sensitive, part of the factorized form factor, we discuss the structure of the instanton induced effects in the evolution equation. It is demonstrated that the instanton contributions result in the finite renormalization of the subleading perturbative result and numerically are characterized by small factor reflecting the diluteness of the QCD vacuum within the instanton liquid model. The relevance of the IR renormalon induced effects in high energy asymptotic behavior is discussed. The consequences of the various analytization procedures of the strong coupling constant in the IR domain are considered.