Bottomonia production and polarization in the NRQCD with -factorization. II: and mesons

N. A. Abdulov; A. V. Lipatov

doi:10.1140/epjc/s10052-020-8056-x

EPJ

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2020) 80: 486
https://doi.org/10.1140/epjc/s10052-020-8056-x

Regular Article - Theoretical Physics

Bottomonia production and polarization in the NRQCD with -factorization. II: $\Upsilon (2S)$ and $\chi _b(2P)$ mesons

N. A. Abdulov¹^,2 and A. V. Lipatov²^,3^*

¹ Faculty of Physics, Lomonosov Moscow State University, Moscow, 119991, Russia
² Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, 119991, Russia
³ Joint Institute for Nuclear Research, Dubna, Moscow Region, 141980, Russia

^* e-mail: lipatov@theory.sinp.msu.ru

Received: 18 March 2020
Accepted: 16 May 2020
Published online: 30 May 2020

Abstract

The $\Upsilon (2S)$ production and polarization at high energies is studied in the framework of $$k_T$$ -factorization approach. Our consideration is based on the non-relativistic QCD formalism for bound states formation and off-shell production amplitudes for hard partonic subprocesses. The direct production mechanism, feed-down contributions from radiative $\chi _b(3P)$ and $\chi _b(2P)$ decays and contributions from $\Upsilon (3S)$ decays are taken into account. The transverse momentum dependent gluon densities in a proton were derived from the Ciafaloni–Catani–Fiorani–Marchesini evolution equation, Kimber-Martin-Ryskin prescription and Parton Branching method. Treating the non-perturbative color octet transitions in terms of the mulitpole radiation theory, we extract the corresponding non-perturbative matrix elements for $\Upsilon (2S)$ and $\chi _b(2P)$ mesons from a combined fit to $\Upsilon (2S)$ transverse momenta distributions measured by the CMS and ATLAS Collaborations at the LHC energies $\sqrt{s} = 7$ and 13 TeV and from the relative production rate $R^{\chi _b(2P)}_{\Upsilon (2S)}$ measured by the LHCb Collaboration at $\sqrt{s} = 7$ and 8 TeV. Then we apply the extracted values to investigate the polarization parameters $\lambda _\theta$ , $\lambda _\phi$ and $\lambda _{\theta \phi }$ , which determine the $\Upsilon (2S)$ spin density matrix. Our predictions have a good agreement with the currently available data within the theoretical and experimental uncertainties.