Upsilonium polarization as a touchstone in understanding the parton dynamics in QCD

In the framework of the $k_t$-factorization approach, the production of $\Upsilon$ mesons at the Fermilab Tevatron and CERN LHC is considered, and the predictions on the spin alignment parameter $\alpha$ are presented. We argue that measuring the polarization of quarkonium states can serve as a crucial test discriminating two competing theoretical approaches to parton dynamics in QCD.