A Closed Expression for the Universal R-Matrix in a Non-Standard Quantum Double

In recent papers of the author, a method was developed for constructing quasitriangular Hopf algebras (quantum groups) of the quantum-double type. As a by-product, a novel non-standard example of the quantum double has been found. In the present paper, a closed expression (in terms of elementary functions) for the corresponding universal R-matrix is obtained. In reduced form, when the number of generators becomes two instead of four, this quantum group can be interpreted as a deformation of the Lie algebra [x,h]=2h in the context of Drinfeld's quantization program.Comment: 6 pages, LATEX, JINR preprint E2-93-15

TMD PDFs in the Laguerre polynomial basis

We suggest the modified matching procedure for TMD PDF to the integrated PDF aimed to increase the amount of perturbative information in the TMD PDF expression. The procedure consists in the selection and usage of the non-minimal operator basis, which restricts the expansion to desired general behavior. The implication of OPE allows to systematic account of the higher order corrections. In the case of TMD PDF we assume the Gaussian behavior, which suggests Laguerre polynomial basis as the best for the convergence of OPE. We present the leading and next-to-leading expression of TMD PDF in this basis. The obtained perturbative expression for the TMD PDF is valid in the wide region of $b_T$ (we estimate this region as $b_T\lesssim 2-3$ GeV$^{-1}$ depending on $x$).Comment: 19 pages, 6 figures; corrected abstract, conclusion and various misprints; version submitted to JHE

Generating function for web diagrams

We present the description of the exponentiated diagrams in terms of generating function within the universal diagrammatic technique. In particular, we show the exponentiation of the gauge theory amplitudes involving products of an arbitrary number of Wilson lines of arbitrary shapes, which generalizes the concept of web diagrams. The presented method gives a new viewpoint on the web diagrams and proves the non-Abelian exponentiation theorem.Comment: 8 pages, 3 figures; version accepted by PR