We discuss inclusive production of open charm in proton-proton scattering at LHC. The calculation is performed within the k t -factorization approach. Different models of unintegrated gluon distributions (UGDF) from the literature are used. The theoretical transverse momentum as well as (pseudo)rapidity distributions of charmed mesons are compared with recent experimental data of ATLAS, ALICE and LHCb collaborations. Only the calculation with Kimber-Martin-Ryskin (KMR) UGDF gives results comparable to experimental ones. All other popular models of UGDF significantly underpredict experimental data. Several sources of uncertainties of the theoretical predictions are also studied in details. In addition we discuss correlations between D andD mesons. Good description of experimental distribution in invariant mass and in relative azimuthal angle between D andD mesons is achieved for the KMR UGDF. The considered correlation observables measured by the LHCb experiment were not discussed in other approaches in the literature.

We discuss production of two pairs of cc within a simple formalism of double-parton scattering (DPS). Surprisingly very large cross sections, comparable to single-parton scattering (SPS) contribution, are predicted for LHC energies. Both total inclusive cross section as a function of energy and differential distributions for √ s are shown. We discuss a perspective how to identify the double scattering contribution.

The double parton distributions (dPDF), both conventional and those corresponding to parton splitting, are calculated and compared for different two-parton combinations. The conventional and splitting dPDFs have very similar shape in x 1 and x 2 . We make a first quantitative evaluation of the single-ladder-splitting contribution to double parton scattering (DPS) production of two S-or Pwave quarkonia, two Higgs bosons and cccc. The ratio of the single-ladder-splitting to conventional contributions is discussed as a function of centre-of-mass energy, mass of the produced system and other kinematical variables. Using a simple model for the dependence of the conventional twoparton distribution on transverse parton separation (Gaussian and independent of x i and scales), we find that the 2v1 contribution is as big as the 2v2 contribution discussed in recent years in the literature. This means that the phenomenological analyses of σ ef f including only the conventional DPS mechanism have to be revised including explicitly the single-ladder-splitting contributions discussed here. The differential distributions in rapidity and transverse momenta calculated for conventional and single-ladder-splitting DPS processes are however very similar which causes their experimental separation to be rather difficult, if not impossible. The direct consequence of the existence of the two components (conventional and splitting) is the energy and process dependence of the empirical parameter σ ef f . This is illustrated in our paper for the considered processes.

We discuss production of cc-pairs within k T -factorization approach (off-shell initial partons) with unintegrated parton distribution functions (uPDFs). We present a consistent prescription which merges the standard leading-order (LO) k T -factorization calculations for this process with tree-level next-to-leading order (NLO) and next-to-next-to-leading order (NNLO) matrix elements. For the first time we include in this framework 2 → 3 and 2 → 4 processes with extra partonic emissions for single particle distributions as well as for correlation observables. The use of the KMR uPDF leads to a good description of the existing charm (D-meson) data already at the leading-order. On the other hand, a new Parton-Branching (PB) uPDF strongly underestimates the same experimental data. A direct inclusion of the higher-orders at tree-level leads to an overestimation of the data, especially for the KMR uPDF. This suggests a significant double-counting.We propose a simple method how to avoid the double-counting. Our procedure leads to a much better description of the experimental data when including the higher-order contributions. Then with the KMR uPDF we get similar results (both for single particle and correlation observables) as for the standard calculations of the 2 → 2 processes. For the PB uPDF inclusion of the higherorders considerably improves description of the experimental data. We conclude that the LO calculation with the KMR uPDF effectively includes the higher-orders which is not the case for the PB uPDF.

We discuss production of D 0 D 0 (andD 0D0 ) pairs related to the LHCb Collaboration results for √ s = 7 TeV in proton-proton scattering. We consider double-parton scattering (DPS) mechanisms of double cc production and subsequent cc → D 0 D 0 hadronization as well as double g and mixed gcc production with gg → D 0 D 0 and gc → D 0 D 0 hadronization calculated with the help of the scale-dependent hadronization functions of Kniehl et al. Single-parton scattering (SPS) mechanism of digluon production is also taken into account. We compare our results with several correlation observables in azimuthal angle ϕ D 0 D 0 between D 0 mesons or in dimeson invariant mass M D 0 D 0 . The inclusion of new mechanisms with g → D 0 fragmentation leads to larger cross sections, than when including only DPS mechanism cc → D 0 D 0 with standard scale-independent fragmentation functions. Some consequences of the presence of the new mechanisms are discussed. In particular a larger σ e f f is needed to describe the LHCb data. There is a signature that σ e f f may depend on transverse momentum of c quarks and/orc antiquarks.