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

Abstract

The ϒ(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 χ b (3P) and χ b (2P) decays and contributions from 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 ϒ(2S) and χ b (2P) mesons from a combined fit to ϒ(2S) transverse momenta distributions measured by the CMS and ATLAS Collaborations at the LHC energies √ s = 7 and 13 TeV and from the relative production rate R χ b (2P) ϒ(2S) measured by the LHCb Collaboration at √ s = 7 and 8 TeV. Then we apply the extracted values to investigate the polarization parameters λ θ , λ φ and λ θφ , which determine the ϒ(2S) spin density matrix. Our predictions have a good agreement with the currently available data within the theoretical and experimental uncertainties.

Revisiting the production of $$J/\psi $$ pairs at the LHC

“…taking them into account in the form of CCFM-evolved Transverse Momentum Dependent (TMD) gluon densities in a proton 3 . In this way we preserve consistency with our previous studies [19][20][21][22] and automatically incorporate the wanted effects of initial state gluon radiation. To reconstruct the CCFM evolution ladder, that is the key point of our consideration, we employ the TMD parton shower routine implemented into the Monte-Carlo event generator cascade [56].…”

“…Their input parameters have been fitted to the proton structure function F 2 (x, Q 2 ). At present, both these gluon distributions are widely used in the phenomenological applications 5 (see, for example, [20][21][22]). The renormalization and factorization scales, μ R and μ F , were set to μ 2…”

“…One possible solution, which, however, implies certain modification of the NRQCD rules, has been proposed[19] (see also[20][21][22]). 2 At the moment, full NLO NRQCD predictions for double J/ψ production are not available yet.0123456789().…”

$$\chi _{c1}$$ and $$\chi _{c2}$$ polarization as a probe of color octet channel

“…As a consequence, the strong transverse polarization of 3 S [8] 1 state produced in hard subprocess gets lost (to zero) after two E1 gluon emissions 3 S [8] 1 → 3 P [8] J → J/ψ. This scheme successfully describes the observed S-wave charmonia [28] and bottomonia [29,30] polarizations. As a byproduct it removes tension with the η c production data [31].…”

“…Our study sheds light on the role of CO contributions which were thought unnecessary or even unwanted [13] for χ cJ p T spectra or their relative rates σ (χ c2 )/σ (χ c1 ), but which reveal now in the measured polar anisotropies. To preserve the consistency with our previous studies [28][29][30][31], we follow mostly the same steps and employ the k T -factorization approach [32][33][34][35] to produce the cc pair in the hard parton scattering. The newly added calculations are only for the feeddown contributions from ψ radiative decays.…”