$J/\psi$ polarization study at $\sqrt{s_{NN}}=200$ GeV Au+Au collision of PHENIX experiment

The polarization of quarkonium is typically measured via the angular distribution of its decay leptons. This measurement provides a critical test of the quarkonium production mechanism. There were about $1.5 \times 10^9$ Au+Au minimum bias events collected by the PHENIX experiment in Run-4. The estimated number of $J/\psi$ particles to be identified from the PHENIX muon arm data is more than one order of magnitude larger than the $J/ \psi$ samples from Run-2. Due to the limited $J/\psi$ statistics from even this much large data set, very accurate event-by-event acceptance corrections are required to extract quantitative polarization from the data. The current status of this study for PHENIX Run-4 Au+Au data is presented here.