Paper detail

On relation between Parton Branching Approach and CCFM evolution

We consider the associated production of electroweak gauge bosons and charm or beauty quark jets at the LHC using the $k_T$-factorization framework. We apply the transverse momentum dependent (TMD) parton distributions in a proton obtained from the Parton Branching (PB) method as well as from the Catani-Ciafaloni-Fiorani-Marchesini (CCFM) evolution equation. For the PB approach, our prescription merges the standard leading order ${\cal O}(αα_s)$ $k_T$-factorization calculations with several tree-level next-to-leading order ${\cal O}(αα_s^2)$ off-shell production amplitudes. For the CCFM scenario, our consideration is based on the ${\cal O}(αα_s^2)$ off-shell gluon-gluon fusion subprocess $g^* g^* \to Z/W + Q\bar Q$ and some subleading ${\cal O}(αα_s^2)$ subprocesses involving quark interactions, taken into account in conventional (collinear) QCD factorization. We find that the $W + c$ and $Z + b$ cross sections, calculated within the PB and CCFM-based schemes with the proper choice of leading and next-to-leading subprocesses, are in good agreement with each other, thus establishing a correspondence between these two scenarios. A comparison with the latest LHC experimental data is given and the necessity for the proper off-shell treatment of the production amplitudes in determination of the parameters of the TMD parton density is demonstrated.