Study of the production of heavy quarkonium states at CMS

Studies of the production of heavy quarkonium states are fundamental to improve our understanding of QCD and hadron formation. In fact, the heavy quark masses allow the application of theoretical tools that are relatively insensitive to non-perturbative effects. In this field, the CMS experiment at LHC can give significant contributions. Thanks to a specific dimuon trigger strategy, CMS collected large samples of quarkonium states which decay to dimuons from $pp$ collisions at 7, 8 and 13TeV. Some of the latest CMS quarkonium production results are presented in this paper, such as the measurement of differential production crosssections of $J/\psi$ and $\psi$(2$S$) charmonium and $\Gamma(\mathrm{n}S)$ ($\mathrm{n}$ = 1, 2, 3) bottomonium states in proton-proton collisions at $\sqrt{s}$ = 13TeV, on data samples corresponding to an integrated luminosity of 2.3 fb$^{-1}$ for the $J/\psi$ and 2.7 fb$^{-1}$ for the other mesons. Each double-differential cross-section is measured as a function of rapidity and transverse momentum.