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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 get poor description of the large transversemomentum distributions of $J/\psi$ with the JH-2013 CCFM-based UGDF. Hereexplicit inclusion of $2 \to 3$ processes considerably improves the situation.Similar effects are discussed in the context of the KMR UGDF.

Production of $J/\psi$ quarkonia in color evaporation model based on $k_{T}$-factorization