$\Upsilon$(nS) Polarization in pp Collisions at the LHC with the CMS Experiment

The polarizations of the $\Upsilon$(1S), $\Upsilon$(2S) and $\Upsilon$(3S) mesons produced in proton-proton collisions at $\sqrt{s} = 7 \, \mathrm{TeV}$ are measured using a data sample collected with the CMS detector in 2011. The data correspond to an integrated luminosity of $4.9 \, \mathrm{fb^{-1}}$. 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, $\lambda_{\theta}, \, \lambda_{\phi}$ and $\lambda_{\theta \phi}$, is complemented by the determination of the frame-invariant quantity $\tilde{\lambda}$, which provides a useful intrinsic test of the reliability of the whole analysis chain as well as supplementary physical information. The polarization of the three $\Upsilon$ states are found to be small in the considered kinematic region ($10 < p_T < 50$~GeV, $\mid y \mid \, < 1.2$) in all the polarization frames.