Production of $c \bar c c \bar c$ in double-parton scattering within $k_{t}$-factorization approach -- meson-meson correlations

We discuss production of two pairs of $c \bar c$ in proton-proton collisions at the LHC. Both double-parton scattering (DPS) and single-parton scattering (SPS) contributions are included in the analysis. Each step of DPS is calculated within $k_t$-factorization approach, i.e. effectively including next-to-leading order corrections. The conditions how to identify the DPS contribution are presented. The discussed mechanism unavoidably leads to the production of pairs of mesons: $D_i D_j$ (each containing $c$ quarks) or $\bar D_i \bar D_j$ (each containing $\bar c$ antiquarks). We calculate corresponding production rates for different combinations of charmed mesons as well as some differential distribution for $(D^0 D^0$ + $\bar D^0 \bar D^0)$ production. Within large theoretical uncertainties the predicted DPS cross section is fairly similar to the cross section measured recently by the LHCb collaboration. The best description is obtained with the Kimber-Martin-Ryskin (KMR) unintegrated gluon distribution, which very well simulates higher-order corrections. The contribution of SPS, calculated in the high-energy approximation, turned out to be rather small. Finally, we emphasize significant contribution of DPS mechanism to inclusive charmed meson spectra measured recently by ALICE, ATLAS and LHCb.