Bottomonia production and polarization in the NRQCD with $$k_T$$ kT -factorization. I: $$\Upsilon (3S)$$ Υ(3S) and $$\chi _b(3P)$$ χb(3P) mesons

Abstract

Abstract The $$\Upsilon (3S)$$ Υ(3S) 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 transverse momentum dependent (TMD, or unintegrated) gluon densities in a proton were derived from the Ciafaloni-Catani-Fiorani-Marchesini (CCFM) evolution equation as well as from the Kimber–Martin–Ryskin (KMR) prescription. Treating the non-perturbative color octet transitions in terms of the multipole radiation theory and taking into account feed-down contributions from radiative $$\chi _b(3P)$$ χb(3P) decays, we extract the corresponding non-perturbative matrix elements for $$\Upsilon (3S)$$ Υ(3S) and $$\chi _b(3P)$$ χb(3P) mesons from a combined fit to $$\Upsilon (3S)$$ Υ(3S) transverse momenta distributions measured by the CMS and ATLAS Collaborations at the LHC energies $$\sqrt{s} = 7$$ s=7 and 13 TeV and central rapidities. Then we apply the extracted values to describe the CDF and LHCb data on $$\Upsilon (3S)$$ Υ(3S) production and to investigate the polarization parameters $$\lambda _\theta $$ λθ , $$\lambda _\phi $$ λϕ and $$\lambda _{\theta \phi }$$ λθϕ , which determine the $$\Upsilon (3S)$$ Υ(3S) spin density matrix. Our predictions have a good agreement with the currently available data within the theoretical and experimental uncertainties.