Quarkonium production and polarization in high-energy collisions

One of the best ways to understand hadronization in QCD is to study the production of quarkonium. However, the production mechanism of quarkonium is still uncertain. Spin-related measurements like the polarization are strong tests of production models. We show recent results of direct $J/\psi$ production and polarization using the improved color evaporation model in $p+p$ collisions at $\sqrt{s}=7$~TeV, and compare them with LHC data.