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Inclusive production of J/$ψ$ and $ψ'$ mesons at the LHC

We discuss the prompt production of $J/ψ$ mesons in proton-proton collisions at the LHC within a NRQCD $k_{t}$-factorization approach using Kimber-Martin-Ryskin (KMR) unintegrated gluon distributions (UGDF). We include both direct color-singlet production ($gg \to J/ψ$g) as well as a feed-down from $χ_{c} \to J/ψγ$ and $ψ' \to J/ψX$. The production of the decaying mesons ($χ_{c}$ or $ψ'$)is also calculated within NRQCD $k_{t}$-factorization. The corresponding matrix elements for $gg \to J/ψ$, $gg \to ψ'$ and $gg \to χ_{c}$ include parameters of the nonrelativistic spatial wave functions of quarkonia at $r=0$, which are taken from potential models from the literature. We get the ratio of the corresponding of the cross sections for $χ_{c}(2)$-to-$χ_{c}(1)$ much closer to experimental data than obtained in recent analyses. Differential distributions in rapidity of $J/ψ$ and $ψ'$ are calculated and compared to experimental data of the ALICE and LHCb collaborations. We discuss possible onset of gluon saturation effects at forward/backward rapidities. One can describe the experimental data for $J/ψ$ production within model uncertainties with color-singlet component only. Therefore our theoretical results leave only a relatively small room for the color-octet contributions.