Prompt charmonia production and polarization at LHC in the NRQCD with $k_T$-factorization. II. $\chi_c$ mesons

In the framework of the $k_T$-factorization approach, the production of prompt ψ(2S) mesons in pp collisions at the LHC energies is studied. Our consideration is based on the off-shell amplitudes for hard partonic subprocesses g*g*→χ$_{cJ}$ and nonrelativistic QCD formalism for bound states. The transverse-momentum-dependent (unintegrated) gluon densities in a proton were derived from the Ciafaloni-Catani-Fiorani-Marchesini evolution equation or, alternatively, were chosen in accordance with the Kimber-Martin-Ryskin prescription. Taking into account both color-singlet and color-octet contributions, we deduce the corresponding nonperturbative long-distance matrix elements from the fits to the latest ATLAS data on χ$_{c1}$ and χ$_{c2}$ transverse-momentum distributions at $\sqrt{s} =$ 7 TeV. We find that these distributions at small and moderate pT are formed mainly by the color-singlet components. We successfully described the data on the relative production rates σ(χ$_{c2}$)/σ(χ$_{c1}$) presented by the ATLAS, CMS, and LHCb Collaborations. We find that the fit points to unequal wave functions of χ$_{c1}$ and χ$_{c2}$ states