Are there any challenges in the charmonia production and polarization at the LHC?

We analyze the inclusive prompt production of ψ^', χc, J/ψ and ηc mesons at the LHC using the kT-factorization approach. Our consideration is based on the off-shell production amplitudes for hard partonic subprocesses, nonrelativistic QCD formalism for the formation of bound states and transverse momentum dependent (or unintegrated) gluon densities in a proton derived from Catani-Ciafaloni-Fiorani-Marchesini equation. The nonperturbative color octet transitions are treated in terms of the multipole radiation theory. We extract the corresponding long-distance matrix elements from a combined fit to transverse momentum distributions measured at various LHC experiments. We make predictions for the polarization parameters λ_θ, λ_φ, λ_θφ and the frame-independent parameter λ* and compare them to the available ψ^' and J/ψ data. Finally, we present a universal set of parameters that provides a reasonable simultaneous description for the whole body of the LHC data (on the pT distributions, relative production rates and polarization observables) for the whole charmonium family.