Prompt inclusive production of $J\mathrm{/}\psi$, ${\psi }^{\mathrm{\prime }}$ and ${\chi }_c$ mesons at $\sqrt{s}$ $=$ $68.5$ $GeV$ energy within NRQCD $k_t$-factorization approach

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