On relation between Parton Branching Approach and CCFM evolution

Abstract

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 $\mathcal{O}(\alpha {\alpha }_s)$ $k_T$-factorization calculations with several tree-level next-to-leading order $\mathcal{O}(\alpha {\alpha }_s^2)$ off-shell production amplitudes. For the CCFM scenario, our consideration is based on the $\mathcal{O}(\alpha {\alpha }_s^2)$ off-shell gluon-gluon fusion subprocess $g^{\ast }{g}^{\ast }\to Z/W+Q\bar{Q}$ and some subleading $\mathcal{O}(\alpha {\alpha }_s^2)$ 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.

15 pages, 8 figures

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