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

We consider the production of $Z$ bosons associated with beauty quarks at the LHC in the framework of $k_T$-factorization approach. Our consideration is based on the off-shell gluon-gluon fusion subprocess $g^* g^* \to Z Q\bar Q$ at the leading order ${\cal O}(\alpha\alpha_s^2)$ (where the $Z$ boson further decays into a lepton pair) and several subleading ${\cal O}(\alpha \alpha_s^2 )$ and ${\cal O}(\alpha \alpha_s^3 )$ subprocesses involving quark-antiquark and quark-gluon interactions, taken into account in the conventional (collinear) QCD factorization. The contributions from double parton scattering are discussed as well. The transverse momentum dependent (or unintegrated) gluon densities in a proton are derived from Catani-Ciafaloni-Fiorani-Marchesini (CCFM) evolution equation. We achieve reasonably good agreement with the latest data taken by CMS and ATLAS Collaborations. The comparison of our results with next-to-leading-order pQCD predictions, obtained in the collinear QCD factorization, is presented. We discuss the uncertainties of our calculations and demonstrate the importance of subleading quark involving contributions in describing the LHC data in the whole kinematic region