$\Upsilon$(nS) Polarization Results Summary from CMS and CDF

Studies of heavy quarkonium production and polarization play an important role in the understanding of quantum chromodynamics (QCD). The CMS and CDF $\Upsilon$(nS) polarization analyses are the most comprehensive measurements of quarkonium polarization made so far. The three frame-dependent polarization parameters, $\lambda_{\vartheta}$, $\lambda_{\varphi}$, and $\lambda_{\vartheta\varphi}$, plus the frame-invariant parameter $\tilde\lambda$ are measured in different reference frames as a function of transverse momentum. The results of the two experiments are in good agreement. The polarization parameters are small in the reference frames under study, excluding large transverse or longitudinal polarizations, especially for the $\Upsilon$(3S) state, which is less affected by feed-down contributions with unknown polarization. These observations are in disagreement with the available theoretical expectations for high-energy hadron collisions.