Associated production of

We consider the production of Z bosons associated with beauty quarks at the LHC using a combined $$k_T$$ + collinear QCD factorization approach, which interpolates between small x and large x physics. Our consideration is based on the off-shell gluon–gluon fusion subprocess $$g^* g^* \rightarrow Z Q\bar{Q}$$ at the leading order $$\mathcal{O}(\alpha \alpha _s^2)$$ (where the Z boson further decays into a lepton pair), calculated in the $$k_T$$-factorization approach, and several subleading $$\mathcal{O}(\alpha \alpha _s^2 )$$ and $$\mathcal{O}(\alpha \alpha _s^3 )$$ subprocesses involving quark–antiquark and quark–gluon interactions, taken into account in 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