The cross section of associated production of a Z boson with heavy flavor jets in pp collisions is calculated using the SHERPA Monte Carlo generator and the analytical combined QCD approach based on k T factorization at small x and conventional collinear QCD at large x. A satisfactory description of the ATLAS and CMS data on the p T spectra of Z bosons and c jets in the whole rapidity, y, region is shown. Searching for the intrinsic charm (IC) contribution in these processes, which could be visible at large y > 1.5, we study observables very sensitive to nonzero IC contributions and less affected by theoretical QCD scale uncertainties. One of such observables is the so-called double ratio, the ratio of the differential cross section of Z þ c production in the central region of jyj < 1.5 and in the forward region 1.5 < jyj < 2.5, divided by the same ratio for Z þ b production. These observables could be more promising for the search of IC at LHC as compared to the observables considered earlier.

We consider the prompt double $$J/\psi $$ J / ψ production in pp collisions at the LHC in the framework of $$k_T$$ k T -factorization QCD approach. Using the fragmentation mechanism, we evaluate the color octet contributions to the production cross sections taking into account the combinatorial effects of multiple gluon radiation in the initial state driven by the Ciafaloni–Catani–Fiorani–Marchesini evolution equation. We demonstrate the importance of these contributions in a certain kinematical region covered by the CMS and ATLAS measurements. On the other hand, the experimental data taken by the LHCb Collaboration at forward rapidities and moderate transverse momenta can be described well by $${{{\mathcal {O}}}}(\alpha _s^4)$$ O ( α s 4 ) color singlet terms and contributions from the double parton scattering mechanism. The extracted value of the effective cross section is compatible with many other estimations based on different final states.

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