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 ${\cal O}(\alpha \alpha_s)$ $k_T$-factorization calculations with several tree-level next-to-leading order ${\cal O}(\alpha \alpha_s^2)$ off-shell production amplitudes. For the CCFM scenario, our consideration is based on the ${\cal O}(\alpha \alpha_s^2)$ off-shell gluon-gluon fusion subprocess $g^* g^* \to Z/W + Q\bar Q$ and some subleading ${\cal O}(\alpha \alpha_s^2)$ 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.
Highlights
For the CCFM scenario, our consideration is based on the Oðαα2sÞ off-shell gluon-gluon fusion subprocess gÃgà → Z=W þ QQand some Oðαα2s Þ subprocesses involving quark interactions, taken into account in conventional QCD factorization
We have studied the associated production of Z and W bosons and charm or beauty quark jets at the LHC conditions using the transverse momentum dependent (TMD) factorization framework
We have applied the TMD parton distributions in a proton obtained from the recent parton branching (PB) method as well as from the CCFM evolution equation
Summary
A theoretical description of a number of processes at high energies and large momentum transfer containing multiple hard scales requires so-called transverse momentum dependent (TMD, or unintegrated) parton (quark and gluon) density functions [1] These quantities encode the nonperturbative information on proton structure, including transverse momentum and polarization degrees of freedom and are related to the physical cross sections via different TMD factorization scenarios. In contrast to the CCFM scenario, in the PB calculations (as being the DGLAP-based ones) one has to include usual leading order (LO) OðααsÞ subprocesses properly matched with a number of additional higher-order terms We perform such calculations and the matching procedure following the approach applied recently [20] for c-jet production at the LHC.
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