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 is considered, and the comparisions of calculated $p_T$-distributions and spin alignment parameter $\alpha$ with the D0 experimental data are shown. We argue that measuring the double cross section and the polarization of upsilonium states can serve as a crucial test discriminating two competing theoretical approaches to parton dynamics in QCD.