Measurement of the YnS polarizations in pp collisions as a function of charged particle multiplicity

As a first step in a broad study of QCD medium effects on quarkonium polarization, the polarizations of the $\Upsilon$(1S), $\Upsilon$(2S), and $\Upsilon$(3S) mesons are measured in proton-proton collisions at \mbox{$\sqrt{s} = 7$\,TeV} as a function of the charged particle multiplicity, $N_{\rm ch}$. The measurements are performed using a dimuon data sample collected in 2011 by the CMS experiment, corresponding to an integrated luminosity of 4.9\,fb$^{-1}$. The results are extracted from the analysis of the dimuon decay angular distributions, analyzed in three different polarization frames; they are presented as a function of $N_{\rm ch}$, for two ranges in $\Upsilon$ transverse momentum ($10 < p_{\rm T} < 15$ and $15 < p_{\rm T} < 35$\,GeV), integrated within the rapidity range $|y|<1.2$. 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 a very useful intrinsic test of the reliability of the whole analysis chain. The polarizations do not show significant changes as a function of $N_{\rm ch}$, excluding strong changes of the production processes between low- and high-multiplicity pp collisions.