Eur. Phys. J. C (2021) 81: 1085
https://doi.org/10.1140/epjc/s10052-021-09880-5

Regular Article - Theoretical Physics

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

¹ Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991, Moscow, Russia
² Joint Institute for Nuclear Research, 141980, Dubna, Moscow Region, Russia

Received: 11 May 2021
Accepted: 27 November 2021
Published online: 8 December 2021

Abstract

The $\mathrm{{\rm Y}}(1S)$ 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 $\mathrm{{\rm Y}}(3S)$ and $\mathrm{{\rm Y}}(2S)$ 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 $\mathrm{{\rm Y}}(1S)$ 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 $\mathrm{{\rm Y}}(1S)$ spin density matrix. Our predictions have a reasonably good agreement with the currently available Tevatron and LHC data within the theoretical and experimental uncertainties.