Prompt inclusive production of $J/\psi$, ${\psi }^{\prime }$ and ${\chi }_c$ mesons at the LHC in forward directions within the NRQCD $k_t$-factorization approach - search for the onset of gluon saturation

Abstract

We discuss prompt production of $J/\psi$ mesons in proton-proton collisions at the LHC within NRQCD $k_t$-factorization approach using Kimber-Martin-Ryskin (KMR) unintegrated gluon distributions (UGDF). 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 NRQCD $k_t$-factorization approach. The corresponding matrix elements for $gg\to J/\psi$ g, $gg\to {\psi }^{\prime }g$ and $gg\to {\chi }_c$ include parameters of the nonrelativistic space wave functions of the quarkonia at $r=0$, which are taken from potential models in the literature. We get the ratio of the corresponding cross section ratio for ${\chi }_c(2)$-to-${\chi }_c(1)$ at midrapidities much closer to experimental data than obtained in a recent analysis. Differential distributions in rapidity and transverse momentum of $J/\psi$ and ${\psi }^{\prime }$ are calculated and compared with experimental data of the ALICE and LHCb collaborations. We discuss a possible onset of gluon saturation effects in the production of $J/\psi$ and ${\chi }_c$ mesons at forward/backward rapidities. We show that it is neccessary to modify the standard KMR UGDF to describe ALICE and LHCb data. A mixed UGDF scenario was proposed. Then we can describe the experimental data for $J/\psi$ production within model uncertainties with color-singlet component only. Therefore our theoretical results leave only a relatively small room for the color-octet contributions.

17 pages, 15 figures

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