  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.

High Energy Physics - Phenomenology