Transverse-Distance Dependent Parton Densities in the Large-xx Regime

QCD factorization approach in the field-theoretic description of the semi-inclusive hadronic processes in the large Bjorken $x$ approximation implies extraction of the three-dimensional parton distribution functions as a convolution of a collinear jet function and soft transverse-distance dependent (TDD) function defined as a vacuum average of a partially light-like Wilson loop. The soft function can be interpreted, therefore, as an element of generalized loop space. A class of classically conformal-invariant transformations of the elements of this space is generated by the non-local area derivative operator which corresponds to a diffeomorphism in the loop space and determines equations of motion, the latter being associated with the rapidity evolution of the soft TDD functions. We propose a large-$x$ TDD factorization framework and discuss practical applications of this approach to the phenomenology of the TDDs accessible in future experimental programs at the Jefferson Lab 12 GeV and the Electron-Ion Collider.Comment: 6 pages; based on invited talk presented at "Lightcone 2013+: Venturing off the LightCone - Local vs. Global Features", Skiathos, Greece, 20-24 May 2013; submitted to Few Body System

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.Comment: 6 pages, 1 figure. Invited talk presented at the 40th International Symposium on Multiparticle Dynamics, 21 - 25 Sep 2010, Antwerp (Belgium

Fr\'echet derivative for light-like Wilson Loops

We address the equations of motion for the light-like QCD Wilson exponentials defined in the generalized loop space. We attribute an important class of the infinitesimal shape variations of the rectangular light-like Wilson loops to the Fr\'echet derivative associated to a diffeomorphism in loop space what enables the derivation of the law of the classically conformal-invariant shape variations. We show explicitly that the Fr\'echet derivative coincides (at least in the leading perturbative or- der) with the area differential operator introduced in the previous works. We discuss interesting implications of this result which will allow one to relate the rapidity evolution and ultra-violet evolution of phenomenologically important quantum correlation functions (such as 3-dimensional parton distribution functions) and geometrical properties of the light-like cusped Wilson loops.Comment: 13 pages, 6 figures (revised some typos and misprints

On Geometric Scaling of Light-Like Wilson Polygons: Higher Orders in αs\alpha_s

We address the scaling behaviour of contour-shape-dependent ultra-violet singularities of the light-like cusped Wilson loops in Yang-Mills and ${\cal N} = 4$ super-Yang-Mills theories in the higher orders of the perturbative expansion. We give the simple arguments to support the idea that identifying of a special type of non-local infinitesimal shape variations of the light-like Wilson polygons with the Fr\'echet differentials results in the combined geometric and renormalization-group evolution equation, which is applicable beyond the leading order exponentiated Wilson loops.Comment: 8 pages, 2 figure

Taming singularities in transverse-momentum-dependent parton densities

We propose a consistent treatment of divergences emerging in the computation of transverse-momentum-dependent parton densities in leading $\alpha_s$-order of QCD perturbation theory.Comment: 3 pages, 1 figure. Talk presented at the International Workshop on Diffraction in High-Energy Physics, 10-15 Sept, 2010, Otranto (Lecce), Italy. v2: affiliation and references correcte