Bottomonium production and polarization in the NRQCD with $k_T$-factorization. III: ${\rm Y}(1S)$ and ${\chi }_b(1P)$ mesons

Abstract

The ${\rm Y}(1S)$ meson production and polarization at high energies is studied in the framework of the $k_T$-factorization approach. Our consideration is based on the non-relativistic QCD formalism for a bound states formation and off-shell production amplitudes for hard partonic subprocesses. The direct production mechanism, feed-down contributions from radiative ${\chi }_b(mP)$ decays and contributions from ${\rm Y}(3S)$ and ${\rm Y}(2S)$ decays are taken into account. The transverse momentum dependent (TMD) gluon densities in a proton were derived from the Ciafaloni-Catani-Fiorani-Marchesini evolution equation and the Kimber-Martin-Ryskin prescription. Treating the non-perturbative color octet transitions in terms of multipole radiation theory, we extract the corresponding non-perturbative matrix elements for ${\rm Y}(1S)$ and ${\chi }_b(1P)$ mesons from a combined fit to transverse momenta distributions measured at various LHC experiments. Then we apply the extracted values to investigate the polarization parameters ${\lambda }_{\theta }$, ${\lambda }_{\varphi }$ and ${\lambda }_{\theta \varphi }$, which determine the ${\rm Y}(1S)$ spin density matrix. Our predictions have a reasonably good agreement with the currently available Tevatron and LHC data within the theoretical and experimental uncertainties.

Comments: 28 pages, 14 figures