Production of forward heavy-flavour dijets at the LHCb within $k_{T}$-factorization approach

We calculate differential cross sections for $c \bar c$- and $b \bar b$-dijet production in $pp$-scattering at $\sqrt{s} = 13$ TeV in the $k_T$-factorization and hybrid approaches with different unintegrated parton distribution functions (uPDFs). We present distributions in transverse momentum and pseudorapidity of the leading jet, rapidity difference between the jets and the dijet invariant mass. Our results are compared to recent LHCb data on forward production of heavy flavour dijets, measured recently for the first time individually for both, charm and bottom flavours. We found that an agreement between the predictions and the data within the full $k_T$-factorization is strongly related to the modelling of the large-$x$ behaviour of the gluon uPDFs which is usually not well constrained. The problem may be avoided following the hybrid factorization approach. Then a good description of the measured distributions is obtained with the Parton-Branching, the Kimber-Martin-Ryskin, the Kutak-Sapeta and the Jung setA0 CCFM gluon uPDFs. We calculate also differential distributions for the ratio of $c \bar c$ and $b \bar b$ cross sections. In all cases we obtain the ratio close to 1 which is caused by the condition on minimal jet transverse momentum ($p_{T}^{\mathrm{jet}} > 20$ GeV) introduced in the experiment, that makes the role of heavy quark mass almost negligible. The LHCb experimental ratio seems a bit larger. We discuss potentially important for the ratio effect of $c$- or $b$-quark gluon radiative corrections related to emission outside of the jet cone. The found effect seems rather small. More refine calculation requires full simulation of $c$- and $b$-jets which goes beyond of the scope of the present paper.