We examine the role played in double parton interactions (DPI) by the parton--parton correlations originating from perturbative QCD parton splittings. Also presented are the results of the numerical analysis of the integrated DPI cross sections at Te
vatron and LHC energies. To obtain the numerical results the knowledge of the single-parton GPDs gained by the HERA experiments was used to construct the non-perturbative input for generalized double parton distributions. The perturbative two-parton correlations induced by three-parton interactions contribute significantly to resolution of the longstanding puzzle of an excess of multi-jet production events in the back-to-back kinematics observed at the Tevatron.
We demonstrate that perturbative QCD leads to positive 3D parton--parton correlations inside nucleon explaining a factor two enhancement of the cross section of multi-parton interactions observed at Tevatron at $x_ige 0.01$ as compared to the predict
ions of the independent parton approximation. We also find that though perturbative correlations decrease with $x$ decreasing, the nonperturbative mechanism kicks in and should generate correlation which, at $x$ below $10^{-3}$, is comparable in magnitude with the perturbative one for $xsim 0.01$.
We review the recent progress in the theoretical description and experimental observation of multiple parton interactions. Subjects covered include experimental measurements of minimum bias interactions and of the underlying event, models of soft phy
sics implemented in Monte Carlo generators, developments in the theoretical description of multiple parton interactions and phenomenological studies of double parton scattering. This article stems from contributions presented at the Helmholtz Alliance workshop on Multi-Parton Interactions at the LHC, DESY Hamburg, 13-15 September 2010.
We demonstrate that in the back-to-back kinematics the production of four jets in the collision of two partons is suppressed in the leading log approximation of pQCD, compared to the hard processes involving the collision of four partons. We derive t
he basic equation for four-jet production in QCD in terms of the convolution of generalized two-parton distributions of colliding hadrons in the momentum space representation. Our derivation leads to geometrical approach in the impact parameter space close to that suggested within the parton model and used before to describe the four-jet production. We develop the independent parton approximation to the light-cone wave function of the proton. Comparison with the CDF and D0 data shows that the independent parton approximation to the light-cone wave function of the proton is insufficient to explain the data. We argue that the data indicate the presence of significant multiparton correlations in the light-cone wave functions of colliding protons.
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 gene
ralize 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.
