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

Abstract

Abstract The $$\Upsilon (2S)$$ Υ(2S) production and polarization at high energies is studied in the framework of $$k_T$$ kT -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 $$\chi _b(3P)$$ χb(3P) and $$\chi _b(2P)$$ χb(2P) decays and contributions from $$\Upsilon (3S)$$ Υ(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 $$\Upsilon (2S)$$ Υ(2S) and $$\chi _b(2P)$$ χb(2P) mesons from a combined fit to $$\Upsilon (2S)$$ Υ(2S) transverse momenta distributions measured by the CMS and ATLAS Collaborations at the LHC energies $$\sqrt{s} = 7$$ s=7 and 13 TeV and from the relative production rate $$R^{\chi _b(2P)}_{\Upsilon (2S)}$$ RΥ(2S)χb(2P) measured by the LHCb Collaboration at $$\sqrt{s} = 7$$ s=7 and 8 TeV. Then we apply the extracted values to investigate the polarization parameters $$\lambda _\theta $$ λθ , $$\lambda _\phi $$ λϕ and $$\lambda _{\theta \phi }$$ λθϕ , which determine the $$\Upsilon (2S)$$ Υ(2S) spin density matrix. Our predictions have a good agreement with the currently available data within the theoretical and experimental uncertainties.