Multiparton pp and pA Collisions: From geometry to parton-parton correlations

We derive expressions for the cross-section of the multiparton interactions (MPI) based on the analysis of the relevant Feynman diagrams. We express the MPI cross-sections through the double (triple,⋯) generalized parton distributions (GPDs). In the mean field approximation for the double GPDs, the answer for the double parton cross-section is expressed through the integral over two gluon.nucleon form factor which was measured in the exclusive DIS vector meson production. We explain under what conditions the derived expressions for MPI correspond to an intuitive picture of hard interactions in the impact parameter representation. The mean field approximation in which correlations of the partons are neglected fails to explain the double parton interaction data. Perturbative- QCD-induced correlations enhance the cross-section by a factor of 1.5.2 for large pτ and 0.001 < x < 0.1 explaining the current data. We argue that in the small x kinematics (10^-4 ≤ x ≤ 10^-3) where effects of perturbative correlations diminish, a diffractive nonperturbative mechanism kicks in and generates positive correlations comparable in magnitude with perturbative ones.We explain how our technique can be used for calculations of MPI in the proton.nucleus scattering. The interplay of hard interactions and underlying event is discussed, as well as different geometric pictures for each of the MPI mechanisms . pQCD, nonperturbative correlations and mean field. Predictions for value of σeff for various processes and a wide range of kinematics are given. We show that together different MPI mechanisms give good description of experimental data, both at Tevatron, and LHC, including the central kinematics studied by ATLAS and CMS detectors, and forward (heavy flavors) kinematics studied by LHCb.