Charm meson production and double parton interactions at the LHC

We discuss production of open charm mesons in proton-proton collisions at the LHC. The cross section for inclusive production of $c \bar c$ pairs is calculated within the $k_{\perp}$-factorization approach in which a major part of higher-order corrections is belived to be effectively included. We use and test the applicability of several unintegrated gluon distributions. Numerical results of the $k_{\perp}$-factorization approach are compared to NLO pQCD collinear predictions. Inclusive differential distributions in transverse momentum and (pseudo)rapidity of several charmed mesons are presented and compared to recent results of the ALICE, ATLAS and LHCb collaborations. We also examine production of neutral charmed meson-antimeson pairs ($D^0 {\overline D^0}$) in unique kinematics of forward rapidities of the LHCb experiment. Kinematical correlations in azimuthal angle $\varphi_{D^0 {\overline D^0}}$, invariant mass $M_{D^0 {\overline D^0}}$ and rapidity difference $Y_{D^0 {\overline D^0}}$ distributions are calculated. Moreover, we also discuss production of two pairs of $c \bar c$ within a simple formalism of double-parton scattering (DPS). We compare results of calculations of single-parton scattering (SPS) and double-parton scattering (DPS) for production of $c \bar c c \bar c$ and for $D^0-D^0$ meson-meson correlations. We compare our predictions for double charm production with recent results of the LHCb collaboration for azimuthal angle $\varphi_{D^0 D^0}$ distribution, dimeson invariant mass $M_{D^0 D^0}$ and rapidity distance between mesons $Y_{D^0 D^0}$. The obtained results clearly certify the dominance of DPS in the production of events with double charm.