$D$-meson production at Large Hadron Collider in the Regge limit of QCD

We study the inclusive production of $D^0$, $D^+$, $D^{\star+}$, and $D_s^+$ mesons in proton-antiproton collisions at the Tevatron and in proton-proton collisions at LHC at leading order in the parton Reggeization approach endowed with universal fragmentation functions fitted to $e^+e^-$ annihilation data from CERN LEP1. We have described $D$-meson transverse momentum distributions measured in the central region of rapidity by the CDF Collaboration at Tevatron ($|y|<1$) and ALICE Collaboration at LHC ($|y|<0.5$) within uncertainties and without free parameters, using Kimber-Martin-Ryskin unintegrated gluon distribution function in a proton. The $2\to1$ hard subprocess of gluon production via a fusion of two Reggeized gluons in the PRA framework is proposed for the first time in the case of $D$-meson fragmentation production and proved to be a dominant one. We found our results for $D$-meson central-rapidity production are in the good agreement with experimental data from the LHC and with large-transverse-momenta Tevatron data. The achieved degree of agreement for the LHC exceeds the one obtained by NLO calculations in the conventional collinear parton model and previous LO calculations in $k_T$-factorization without taking into account the $2\to1$ subprocess. The predictions for the $D$-meson production in the central rapidity region for the expected LHC energy of $\sqrt S=14$ TeV are also presented.