Prompt inclusive production of J/ψ , ψ′ and χc mesons at the LHC in forward directions within the NRQCD kt -factorization approach: Search for the onset of gluon saturation

Abstract

We discuss prompt production of $J/\ensuremath{\psi}$ mesons in proton-proton collisions at the LHC within the NRQCD ${k}_{t}$-factorization approach using Kimber-Martin-Ryskin (KMR) unintegrated gluon distributions (UGDF). We include both direct color-singlet production ($gg\ensuremath{\rightarrow}J/\ensuremath{\psi}g$) as well as a feed down from ${\ensuremath{\chi}}_{c}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\gamma}$ and ${\ensuremath{\psi}}^{\ensuremath{'}}\ensuremath{\rightarrow}J/\ensuremath{\psi}X$ decays. The production of the decaying mesons (${\ensuremath{\chi}}_{c}$ or ${\ensuremath{\psi}}^{\ensuremath{'}}$) is also calculated within the NRQCD ${k}_{t}$-factorization approach. The corresponding matrix elements for $gg\ensuremath{\rightarrow}J/\ensuremath{\psi}\text{ }\text{ }\mathrm{g}$, $gg\ensuremath{\rightarrow}{\ensuremath{\psi}}^{\ensuremath{'}}g$ and $gg\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c}$ 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 ${\ensuremath{\chi}}_{c}(2)$-to-${\ensuremath{\chi}}_{c}(1)$ at midrapidities much closer to experimental data than obtained in a recent analysis. Differential distributions in rapidity and transverse momentum of $J/\ensuremath{\psi}$ and ${\ensuremath{\psi}}^{\ensuremath{'}}$ 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 $J/\ensuremath{\psi}$ and ${\ensuremath{\chi}}_{c}$ mesons at forward/backward rapidities. We show that it is necessary 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 $J/\ensuremath{\psi}$ production within model uncertainties with a color-singlet component only. Therefore, our theoretical results leave only relatively small room for the color-octet contributions. We discuss relations to other models in the literature. The results for the so-called hybrid model are compared to the results of the original ${k}_{t}$-factorization approach.