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We use a new approach to color evaporation model (CEM) for quarkoniumproduction. The production of $c\bar c$ pairs is performed within$k_T$-factorization approach using different unintegrated gluon distributionfunctions (UGDF) from the literature. We include all recent improvements tocolor evaporation model. We cannot describe simultaneously mid and forwardrapidity data measured at the LHC when using the KMR UGDF with the samenormalization parameter. Furthermore we get somewhat too hard distribution in$J/\psi$ transverse momentum. Correcting the standard KMR distributions forsaturation effects at small values of $x$ improves $J/\psi$ rapiditydistributions, while taking correction for emissions hidden in the KMR UGDF inthe evaluation of $x$ values improves a bit $J/\psi$ transverse momentumdistributions. The modifications improve also description of the LHCb $D$-mesondata.

$J/\psi$-meson production within improved color evaporation model with the $k_{T}$-factorization approach for $c\bar{c}$ production