Geometry of gauge links in operator definitions of transverse-momentum dependent PDFs: A comparative view

Different approaches to the problem of a gauge-invariant operator definition of transverse-momentum dependent parton densities (TMDs) are reviewed and compared from the point of view of their compatibility with the operator definition of collinear (integrated) parton distribution functions. In particular, geometry of the longitudinal and transverse gauge links (Wilson lines) both in unsubtracted quark TMDs and in the associate soft factors is addressed. A possible connection between different operator definitions is also discussed.Comment: 9 pages, 4 figures. Presented at the International Conference "Photon-2011", 22-27 May 2011 Spa, Belgiu

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