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The QCD structure of the electron is defined and calculated. The leading order splitting functions are extracted, showing an important contribution from $\gamma$-$Z$ interference. Leading logarithmic QCD evolution equations are constructed…
Parton recombination is reconsidered in perturbation theory without using the AGK cutting rules in the leading order of the recombination. We use time-ordered perturbation theory to sum the cut diagrams, which are neglected in the GLR…
I present a highly efficient method for evolving parton distributions in perturbative QCD. The method allows evolving the parton distribution functions according to any of the commonly-used truncations of the evolution equations (which…
At present there is no correct theory of evolution of F_2(x,Q^2) at small x. It is a mixture of hard and soft pomeron exchange and perturbative QCD very successfully describes the evolution of the hard-pomeron component. This allows the…
The task of Monte Carlo simulation of the evolution of the parton distributions in QCD and of constructing new parton shower Monte Carlo algorithms requires new way of organizing solutions of the QCD evolution equations, in which…
The small x evolution of the QCD pomeron and the QCD odderon is investigated in the mean field limit of the Color Glass Condensate. The resulting system of coupled nonlinear evolution equations is transformed to the momentum space and…
Recent theoretical progress in understanding high-energy scattering beyond the mean field approximation is reviewed. The role of Lorentz invariance and pomeron loops in the evolution, the relation between high-energy QCD and statistical…
We show that it is possible to use hard-Pomeron behavior to the gluon distribution and singlet structure function at low $x$. We derive a second-order independent differential equation for the gluon distribution and the singlet structure…
The Fortran package QCD-PEGASUS is presented. This program provides fast, flexible and accurate solutions of the evolution equations for unpolarized and polarized parton distributions of hadrons in perturbative QCD. The evolution is…
Linear and non-linear QCD evolutions at high energy suffer from severe issues related to convergence, due to higher order corrections enhanced by large double and single transverse logarithms. We resum double logarithms to all orders by…
Evolution equations describe the effect of consecutively integrating out all quantum fluctuations with momenta larger than some infrared cutoff scale k. We develop a formalism for the introduction of collective degrees of freedom at some…
The QCDNUM program numerically solves the evolution equations for parton densities and fragmentation functions in perturbative QCD. Un-polarised parton densities can be evolved up to next-to-next-to-leading order in powers of the strong…
The Kwiecinski equations for the QCD evolution of the unintegrated parton distributions in the transverse-coordinate space (b) are analyzed with the help of the Mellin-transform method. The equations are solved numerically in the general…
We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…
A new approach to global QCD analysis is developed. The main ingredients are two QCD-based evolution equations. The first one is the Balitsky-Kovchegov nonlinear equation, which sums higher twists while preserving unitarity. The second…
Within the framework of a (1+1)-dimensional model which mimics evolution and scattering in QCD at high energy, we study the influence of the running of the coupling on the high-energy dynamics with Pomeron loops. We find that the particle…
We derive the evolution equation for hadronic scattering amplitude at high energy. Our derivation includes the nonlinear effects of finite partonic density in the hadronic wave function as well as the effect of multiple scatterings for…
This survey is devoted to the asymptotic behavior of solutions of evolution equations generated by maximal monotone operators in Hilbert spaces. The emphasis is in the comparison of the continuous time trajectories to sequences generated by…
We propose a stochastic particle model in (1+1)-dimensions, with one dimension corresponding to rapidity and the other one to the transverse size of a dipole in QCD, which mimics high-energy evolution and scattering in QCD in the presence…
Evolution equations for parton distributions can be approximately diagonalized and solved in moment space without assuming any knowledge of the parton distribution in the region of small x. The evolution algorithm for truncated moments is…