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pQCD Physics of multiparton interactions

We study production of two pairs of jets in %hard hadron--hadron collisions in view of extracting contribution of {\em double hard interactions} of three and four partons ($3\to4$, $4\to4$). Such interactions, in spite of being power suppressed at the level of the total cross section, become comparable with the standard hard collisions of two partons, $2\to4$, in the {\em back-to-back kinematics} when the transverse momentum imbalances of two pairing jets are relatively small. We express differential and total cross sections for two-dijet production in double parton collisions through the generalized two-parton distributions, $_2$GPDs \cite{BDFS1}, that contain large-distance two-parton correlations of non-perturbative origin as well as small-distance correlations due to parton evolution. We find that these large- and small-distance correlations participate in different manner in 4-jet production, and treat them in the leading logarithmic approximation of pQCD that resums collinear logarithms in all orders. A special emphasis is given to $3\to4$ double hard interaction processes that occur as an interplay between large- and short-distance parton correlations and were not taken into consideration by approaches inspired by the parton model picture. We demonstrate that the $3\to4$ mechanism, being of the same order in $\as$ as the $4\to4$ process, turns out to be {\em geometrically enhanced} compared to the latter and should contribute significantly to 4-jet production. The framework developed here takes into systematic consideration perturbative $Q^2$ evolution of $_2$GPDs. It can be used as a basis for future analysis of NLO corrections to multi-parton interactions (MPI) at LHC and Tevatron colliders, in particular for improving evaluation of QCD backgrounds to new physics searches.