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The $\Upsilon(1S)$ meson production and polarization at high energies isstudied in the framework of the $k_T$-factorization approach. Our considerationis based on the non-relativistic QCD formalism for a bound states formation andoff-shell production amplitudes for hard partonic subprocesses. The directproduction mechanism, feed-down contributions from radiative $\chi_b(mP)$decays and contributions from $\Upsilon(3S)$ and $\Upsilon(2S)$ decays aretaken into account. The transverse momentum dependent (TMD) gluon densities ina proton were derived from the Ciafaloni-Catani-Fiorani-Marchesini evolutionequation and the Kimber-Martin-Ryskin prescription. Treating thenon-perturbative color octet transitions in terms of multipole radiationtheory, we extract the corresponding non-perturbative matrix elements for$\Upsilon(1S)$ and $\chi_b(1P)$ mesons from a combined fit to transversemomenta distributions measured at various LHC experiments. Then we apply theextracted values to investigate the polarization parameters $\lambda_\theta$,$\lambda_\phi$ and $\lambda_{\theta\phi}$, which determine the $\Upsilon(1S)$spin density matrix. Our predictions have a reasonably good agreement with thecurrently available Tevatron and LHC data within the theoretical andexperimental uncertainties.

Bottomonium production and polarization in the NRQCD with $k_T$-factorization. III: $\Upsilon(1S)$ and $\chi_b(1P)$ mesons