Feasibility study for measuring $J/\Psi$ polarization using early LHC data collected with the CMS detector

We present a feasibility study for measuring the polarization of prompt $J/\Psi$ mesons produced in proton-proton collisions at $\sqrt{s} = $~10~TeV as a function of the $J/\Psi$ transverse momentum. The study is based on simulated samples of $J/\Psi$ candidate events corresponding to 1~pb$^{-1}$ of data expected to be collected by the CMS detector in early LHC running. We use Monte Carlo pseudo-experiments to study potential biases in the fit procedure used to extract the polarization parameter, $\alpha$, and in the determination of our expected sensitivity. These measurements are expected to provide some insight into the current observed disagreement between the non-relativistic QCD theory and recent CDF $J/\Psi$ polarization measurements made using data collected at the Tevatron collider.