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We visualize the fundamental property of pQCD: the smaller size of the colorless quark-gluon configurations leads to a more rapid increase of its interaction with energy. Within the frame of dipole model we use the $k_t$ factorization theorem to generalize the DGLAP approximation and/or leading $ln(x_0/x)$ approximation and evaluate the interaction of quark dipole with a target. In the limit of fixed $Q^2$ and $xto 0$ we found the increase with energy of transverse momenta of quark(antiquark) within q$bar q$ pair produced by strongly virtual photon. The average $p^2_t$ is evaluated analytically within the double logarithmic approximation. We demonstrate that the invariant mass$^2$ of the q$bar q$ pair increases with the energy as $M^2_0(x_0/x)^{lambda}$, where $lambdasim 0.4alpha_sN_c/pi$ for transverse photons, and as $sim M^2_0 exp{0.17[(4alpha_sN_c/pi)log(x_0/x)]^{1/2}}$ for longitudinal photons, where $M^2_0 approx 0.7Q^2$ at the energies of the order $s_0sim 10^4$ GeV$^2$ ($x_0sim 10^{-2}$). The magnitude of the effect depends strongly on the small $x$ behavior of the gluon distribution. Similar pattern of the energy dependence of $M^2$ is found in the LO DGLAP approximation generalized to account for $k_t$ factorization. We discuss the impact of the found phenomenon on the dependence of the coherence length on the initial energy and demonstrate that the shape of final hadron state in DIS has biconcave form instead of pancake. Some implications of the found phenomena for the hard processes in pp collisions are discussed.
The high-multiplicity pp collisions at the Large Hadron Collider energies with various heavy-ion-like signatures have warranted a deeper understanding of the underlying physics and particle production mechanisms. It is a common practice to use experi
We discuss strategies for comparisons of nonperturbative QCD predictions for parton distribution functions (PDFs) with high-energy experiments in the region of large partonic momentum fractions $x$. Analytic functional forms for PDFs cannot be unique
We develop the formalism for the evaluation of density-density correlators in lattice QCD that includes techniques for the computation of the all-to-all propagators involved. A novel technique in this context is the implementation of the one-end tric
We sketch the basic ideas of the lattice regularization in Quantum Field Theory, the corresponding Monte Carlo simulations, and applications to Quantum Chromodynamics (QCD). This approach enables the numerical measurement of observables at the non-pe
We derive the transverse momentum dependent (TMD) factorization and resummation formula of the unpolarized transverse momentum distribution ($j_T$) for the single hadron production with the thrust axis in electron-positron collision. Two different ki