Quarkonium production and polarization in pp collisions with the CMS detector

Heavy quarkonium mesons constitute an ideal laboratory to study hadron formation, through the understanding of the properties of quarkonium production and polarization in hadron collisions. The currently most favored approach to model quarkonium production is non-relativistic quantum chromodynamics (NRQCD), taking advantage of the heavy quark masses to simplify QCD calculations. The experimental situation in the pre-LHC era was not satisfactory, given the ambiguous and inconsistent measurements of quarkonium polarization. New experimental input, relying on improved analysis methodologies, is required to advance the understanding of hadron formation. The LHC is a quarkonium factory, providing ideal conditions to study quarkonia in proton-proton collisions. CMS is ideally suited to study the decays of S-wave quarkonia in two muons. Furthermore, given the high granularity silicon tracker, radiative decays of P-wave quarkonia can be reconstructed with excellent momentum resolution through the reconstruction of photon conversions to e$^+$e$^-$ pairs. This allowed CMS to perform measurements of cross-section ratios involving the $\chi$ states, in both the charmonium and bottomonium families. This document discusses results of CMS quarkonium production and polarization data analyses, in proton-proton collisions, at $\sqrt{s}=$7~TeV and 8~TeV, emphasizing the most recent measurements, including the measurement of the polarizations of all five S-wave quarkonium vector states. Results are compared to corresponding results of other experiments, and to state-of-the-art NRQCD model calculations