Production of charmed meson-meson pairs at the LHC: Single- versus double-parton scattering mechanisms

We discuss hadroproduction of open charmed mesons ($D^0$, $D^{\pm}$, $D^{\pm}_{S}$) at the LHC energy $\sqrt{s} = 7$ TeV. The cross section for inclusive production of $c \bar c$ pairs is calculated within the $k_{\perp}$-factorization (or high-energy factorization) approach which effectively includes higher-order corrections. Results of the $k_{\perp}$-factorization approach are compared to NLO parton model predictions. The hadronization of charm quarks is included with the help of the Peterson fragmentation functions. Inclusive differential distributions in (pseudo)rapidity and transverse momentum for several charmed mesons are calculated and compared to recent results of the ALICE, ATLAS and LHCb experiments. We also take into consideration a mechanism of double charm (two pairs of $c \bar c$) production within a simple formalism of double-parton scattering (DPS). Surprisingly for LHC energies the DPS cross sections are found to be larger than those from the standard SPS mechanism. We compare our predictions for $DD$ meson-meson pair production with recent measurements of the LHCb collaboration, including correlation observables. Our calculations clearly confirm the dominance of DPS in the production of double charm, however some strength seems to be still lacking. Possible missing contribution from the so-called single-ladder-splitting DPS mechanism is also discussed.