Prompt charmonia production and polarization at LHC in the NRQCD with -factorization. Part I: meson

In the framework of the -factorization approach, the production and polarization of prompt mesons in pp collisions at LHC energies is studied. Our consideration is based on the non-relativistic QCD formalism for bound states and off-shell amplitudes for hard partonic subprocesses. 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. The non-perturbative color-octet matrix elements were first deduced from the fits to the latest CMS data on transverse momentum distributions and then applied to describe the ATLAS and LHCb data on production and polarization at  TeV. We perform the estimation of the polarization parameters , , and , which determine the spin density matrix and demonstrate that taking into account the off-shellness of the initial gluons in the color-octet contributions leads to unpolarized production at high transverse momenta, in qualitative agreement with the LHC data.