We discuss prompt production of $J/\psi$ mesons in proton-proton collisions at the $\sqrt{s}=68.5\mathrm{GeV}$ energy within the nonrelativistic quantum chromodynamics $k_t$-factorization approach using different unintegrated gluon distribution functions (UGDFs). We include both direct color-singlet production ($gg\to J/\psi g$) as well as a feed-down from ${\chi }_c\to J/\psi \gamma$ and ${\psi }^{\prime }\to J/\psi X$ decays. The production of the decaying mesons ${\chi }_c$ or ${\psi }^{\prime }$ is also calculated within the nonrelativistic quantum chromodynamics $k_t$-factorization approach. Differential distributions in the rapidity and transverse momentum of $J/\psi$ are calculated and compared with experimental data of LHCb collaboration. The LHCb fixed target data allow us to test UGDFs in a new range of $x$.

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• Hadron production
• Particle phenomena
• Particle production
• Mesons