Prompt charmonia production and polarization at LHC in the NRQCD with kt-factorization. Part I: psi(2S) meson

In the framework of kt-factorization approach, the production and polarization of prompt psi(2S) mesons in pp collisions at the 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 Ciafaloni-Catani-Fiorani-Marchesini evolution equation or, alternatively, were chosen in accordance with Kimber-Martin-Ryskin prescription. The non-perturbative color-octet matrix elements were first deduced from the fits to the latest CMS data on psi(2S) transverse momentum distributions and then applied to describe the ATLAS and LHCb data on psi(2S) production and polarization at 7 TeV. We perform the estimation of polarization parameters $\lambda_\theta$, $\lambda_\phi$ and $\lambda_{\theta \phi}$ which determine psi(2S) spin density matrix and demonstrate that taking into account the off-shellness of initial gluons in the color-octet contributions leads to unpolarized psi(2S) production at high transverse momenta, that is in qualitative agreement with the LHC data.