Production of dijets with large rapidity separation: Mueller-Navelet mechanism versus double-parton scattering

We discuss hadroproduction of 4-jet final state at the LHC within the double-parton scattering (DPS) mechanism in the context of large-rapidity-distance jets. For planned and/or being currently performed high energy experiments this is the kinematical region where searches for BFKL signal are of the main interest. The DPS contributions are calculated in the LO collinear approach within the so-called factorized Ansatz. We show that the relative contribution of DPS is growing with respect to standard single-parton scattering (SPS) production of dijets and to the BFKL Mueller-Navelet (MN) jet mechanism at large rapidity distance between jets. This is consistent with recent studies of DPS effects in the case of double $D$ and double $J/\!\psi$ meson production. The calculated differential cross sections as a function of rapidity distance between the jets that are the most distant in rapidity are compared with recent results of LL and NLL BFKL calculations for the Mueller-Navelet jet production at $\sqrt{s} = 7$ TeV. The DPS contribution is carefully studied for $\sqrt{s}$ = 7 TeV and $\sqrt{s}$ = 14 TeV and in different ranges of jet transverse momenta.