Dynamical differential equations compatible with rational qKZ equations

For the Lie algebra $gl_N$ we introduce a system of differential operators called the dynamical operators. We prove that the dynamical differential operators commute with the $gl_N$ rational quantized Knizhnik-Zamolodchikov difference operators. We describe the transformations of the dynamical operators under the natural action of the $gl_N$ Weyl group.Comment: 7 pages, AmsLaTe

Difference Equations Compatible with Trigonometric KZ Differential Equations

The trigonometric KZ equations associated with a Lie algebra \g depend on a parameter \lambda\in\h where \h\subset\g is the Cartan subalgebra. We suggest a system of dynamical difference equations with respect to $\lambda$ compatible with the KZ equations. The dynamical equations are constructed in terms of intertwining operators of \g-modules.Comment: 23 pages, AmsTeX, third version, some misprints were correcte

Higher-twist corrections to gluon TMD factorization

We calculate power corrections to TMD factorization for particle production by gluon-gluon fusion in hadron-hadron collisions.Comment: 29 pages, 3 figures; v2: misprints correcte

Gluon TMD in particle production from low to moderate x

We study the rapidity evolution of gluon transverse momentum dependent distributions appearing in processes of particle production and show how this evolution changes from small to moderate Bjorken x.Comment: 36 pages, 3 figures. arXiv admin note: text overlap with arXiv:1505.0215

Power corrections to TMD factorization for Z-boson production

A typical factorization formula for production of a particle with a small transverse momentum in hadron-hadron collisions is given by a convolution of two leading-twist TMD parton densities with cross section of production of the final particle by the two partons. For practical applications at a given transverse momentum, though, one should estimate at what momenta the power corrections to TMD factorization formula due to higher-twist operators become essential. In this paper we calculate the first power corrections to TMD factorization formula for Z-boson production and Drell-Yan process in high-energy hadron-hadron collisions. At the leading order in $N_c$ power corrections are expressed in terms of leading-twist TMDs by QCD equations of motion.Comment: 44 pages, 3 figures. v2: text changes. arXiv admin note: text overlap with arXiv:1706.0141