Measurement of $\Upsilon$(1S), $\Upsilon$(2S) and $\Upsilon$(3S) polarizations in proton-proton collisions at \mbox{$\sqrt{s} = 7$ TeV} with the CMS experiment

The polarizations of the $\Upsilon$(1S), $\Upsilon$(2S) and $\Upsilon$(3S) mesons produced in proton-proton collisions at \mbox{$\sqrt{s}$ = 7 TeV} are measured using a data sample collected with the CMS detector at the LHC, corresponding to an integrated luminosity of approximately 5 fb$^{-1}$. The measurements are based on the analysis of the dimuon decay angular distributions, analyzed in three different polarization frames, and are presented as a function of the $\Upsilon$ transverse momentum, in two rapidity ranges. The measurement of the polarization parameters, $\lambda_{\vartheta}$, $\lambda_{\varphi}$ and $\lambda_{\vartheta\varphi}$ is complemented by the determination of the frame-invariant quantity $\tilde{\lambda}$, which provides an intrinsic test of the whole analysis chain and of the extracted physical information. The results are in disagreement with the available theoretical predictions for high-energy hadron collisions.