Challenges and Problems in Charmonium Production at the SPD NICA

The SPD NICA is planned to operate as a universal facility for study of the unpolarized and polarized transverse momentum dependent (TMD) gluon distribution functions (PDF) of a nucleon using various hard probes. The first one is the charmonium production processes. The experiment aims to provide access to the gluon TMD PDFs, like the Sivers function and the Boer–Mulders function of a proton. In this article, we present an overview of theoretical predictions for \({J \mathord{\left/ {\vphantom {J \psi }} \right. \kern-0em} \psi }\), \({{\chi }_{c}}\), and \({{\eta }_{c}}\) production in the unpolarized and polarized \(pp\)-collisions at the \(\sqrt s = 27\) GeV. We use the TMD parton model as it is postulated in the generalized parton model (GPM) and two models for \(c\bar {c}\)-pair hadronization into a final charmonium, namely the nonrelativistic QCD (NRQCD) and the Improved Color Evaporation Model (ICEM).