New mechanisms of charm production

We discuss production of charm quarks, mesons as well as nonphotonic electrons in $pp$ scattering at RHIC. The distributions in rapidity and transverse momentum of charm and bottom quarks/antiquarks are calculated in the $k_t$-factorization approach. The hadronization of heavy quarks is done by means of fenomenological fragmentation functions and semileptonic decay functions are found by fitting semileptonic decay data. Good description of the inclusive data at large transverse momenta of electrons is obtained and a missing strength at small transverse momenta of electrons is found. In addition we discuss kinematical correlations between charged leptons from different mechanisms. Reactions initiated by purely QED $\gamma^*\gamma^*$-fusion in elastic and inelastic $pp$ collisions as well as diffractive mechanism of exclusive $c \bar c$ production are included. A good description of the dilepton invariant mass spectrum of the PHENIX collaboration is achieved. Distributions in the dilepton pair transverse momentum and in azimuthal angle between electron and positron are presented. A new mechanism of exclusive production of $c \bar c$ is discussed. Corresponding results are shown and the possibility of its identification is discussed. We discuss also production of two pairs of $c \bar c$ within a simple formalism of double-parton scattering (DPS). Very large cross sections, comparable to single-$c \bar c$ production, are predicted for LHC energies. Both total inclusive cross section as a function of energy and differential distributions are shown. We discuss a perspective how to identify the double scattering contribution.