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We consider the production of $Z$ bosons associated with beauty quarks at theLHC using a combined $k_T$ + collinear QCD factorization approach, thatinterpolates between small $x$ and large $x$ physics. Our consideration isbased on the off-shell gluon-gluon fusion subprocess $g^* g^* \to Z Q\bar Q$ atthe leading order ${\cal O}(\alpha\alpha_s^2)$ (where the $Z$ boson furtherdecays into a lepton pair), calculated in the $k_T$-factorization approach, andseveral subleading ${\cal O}(\alpha \alpha_s^2 )$ and ${\cal O}(\alpha\alpha_s^3 )$ subprocesses involving quark-antiquark and quark-gluoninteractions, taken into account in conventional (collinear) QCD factorization.The contributions from double parton scattering are discussed as well. Thetransverse momentum dependent (or unintegrated) gluon densities in a proton arederived from Catani-Ciafaloni-Fiorani-Marchesini (CCFM) evolution equation. Weachieve reasonably good agreement with the latest data taken by CMS and ATLASCollaborations. The comparison of our results with next-to-leading-order pQCDpredictions, obtained in the collinear QCD factorization, is presented. Wediscuss the uncertainties of our calculations and demonstrate the importance ofsubleading quark involving contributions in describing the LHC data in thewhole kinematic region.

Associated production of $Z$ bosons and $b$-jets at the LHC in the combined $k_T$ + collinear QCD factorization approach