Studies of the production of heavy quarkonium states are very important to improve our understanding of QCD and hadron formation, given that the heavy quark masses allow the application of theoretical tools less sensitive to nonperturbative effects. Thanks to a dedicated dimuon trigger strategy, combined with the record-level energy and luminosity provided by the LHC, the CMS experiment could collect large samples of pp collisions at 7 and 8 TeV, including quarkonium states decaying in the dimuon channel. This allowed the CMS collaboration to perform a series of systematic measurements in quarkonium production physics, including double-differential cross sections and polar- izations, as a function of rapidity and pT , for five S-wave quarkonia: J/ψ, ψ(2S), Y(1S), Y(2S), and Y(3S). Some of these measurements extend well above pT � 100 GeV, prob- ing regions of very high pT /mass, where the theory calculations are supposed to be the most reliable. Thanks to its high-granularity silicon tracker, CMS can reconstruct low- energy photons through their conversions to e + e − pairs, thereby accessing the radiative decays of the P-wave quarkonium states, with an extremely good mass resolution, so that the J=1 and J=2 1P states can be resolved. This allows CMS to determine cross-section ratios and feed-down decay fractions involving the χ states, in both the charmonium and bottomonium families. This talk presents some of the most recent CMS quarkonium production results, in pp collisions, in particular the production of Y(1S,2S,3S), the cross-section ratio of charmo- nium and bottomonium P-wave states and the polarization of S-wave c¯ c and b¯ b states.
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