Related papers: Algebraic models for the hierarchy structure of ev…
We study the scale dependence of the twist-3 quark-gluon parton distributions using the observation that in the multi-color limit the corresponding QCD evolution equations possess an additional integral of motion and turn out to be…
We develop a theory of the Klein-Gordon equation on curved spacetimes. Our main tool is the method of (non-autonomous) evolution equations on Hilbert spaces. This approach allows us to treat low regularity of the metric, of the…
We suggest a new procedure for extrapolating the parton distributions from HERA to much higher energies. The procedure suggested consists of two steps. First, we solve the non-linear evolution equation. Second, we introduce a correcting…
We generalize the model of transition-metal nanocluster growth in aqueous solution, proposed recently [Phys. Rev. E \textbf{87}, 022132 (2013)]. In order to model time evolution of the system, kinetic equations describing time dependence of…
We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolution equations with compact nonlinearities. We show, in particular, that compact nonlinear perturbations of a linear evolution equation can be…
In a consistently formulated pQCD framework incorporating non-zero mass heavy quark partons, there is still the freedom to define parton distributions obeying either mass-independent or mass-dependent evolution equations, contrary to…
Measurements of the diffractive structure function, $F_2^D$, of the proton at HERA are used to extract the partonic structure of the Pomeron. Regge Factorization is tested and is found to describe well the existing data within the selected…
The known analytic properties of the Compton amplitude at small $Q^2$ place significant constraints on its behaviour at large $Q^2$. This calls for a re-evaluation of the role of perturbative evolution in past fits to data.
Recently a Hamiltonian formulation for the evolution of the universe dominated by multiple oscillatory scalar fields was developed by the present author and was applied to the investigation of the evolution of cosmological perturbations on…
Large-distance effects, which lead to the spin-flip part of the hadron -pomeron coupling in QCD -models, are discussed. We study spin asymmetries in exclusive reactions and in diffractive $Q \bar Q$ and vector meson production which are…
This work reviews recent developments in the Parton Branching (PB) method, focusing on its application to Transverse Momentum Dependent (TMD) parton distributions and the implementation of TMD evolution equations in Monte Carlo generators.…
We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes…
We show that simple parametrisations at small x of the proton structure function work so well in limited regions of the $(x,Q^2)$ plane because they are approximately "self-consistent" solutions of the QCD evolution equation. For a class of…
In this article, we show that a technique for showing well-posedness results for evolutionary equations in the sense of [13] established in [16] applies to a broader class of non-autonomous integro-differential-algebraic equations. Using…
Evolution equations of YFS and DGLAP types in leading order are considered. They are compared in terms of mathematical properties and solutions. In particular, it is discussed how the properties of evolution kernels affect solutions.…
We analize the renormalization group equations of supersymmetric QCD with N=1 for the evolution of parton distributions. For this purpose we develope a simple recursive algorithm in x-space to include both regular regions and supersymmetric…
Following the Good-and-Walker picture, hard diffraction in the high-energy/small-x limit of QCD can be described in terms of eigenstates of the scattering matrix off a Color Glass Condensate. From the CGC non-linear evolution equations, it…
Perturbative QCD predicts that at sufficiently large $Q^2$ and small $x$ nucleon structure functions should exhibit scaling in the two variables $\sqrt{\ln\smallfrac{1}{x}\ln\ln Q^2}$ and $\sqrt{\ln\smallfrac{1}{x}\big/\ln\ln Q^2}$,…
The concepts and methods used for the study of disordered systems have proven useful in the analysis of the evolution equations of quantum chromodynamics in the high-energy regime: Indeed, parton branching in the semi-classical…
The concept of evolutionary development of structures constituted a \emph{real} revolution in biology: it was possible to understand how the very complex structures of life can arise in an out-of-equilibrium system. The investigation of…