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The production mechanisms of charmonium states in both hadronic and heavy-ioncollisions hold great significance for investigating the hot and dense QCDmatter. Studying charmonium polarization in ultra-relativistic collisions canalso provide insights into the underlying production mechanisms. With thismotivation, we explore the $J/\psi$ and $\psi$(2S) polarization inproton+proton collisions at $\sqrt{s}$ = 7, 8, and 13 TeV using a pQCD-inspiredMonte-Carlo event generator called PYTHIA8. This work considers reconstructedquarkonia through their dimuons decay channel in the ALICE forward rapidityacceptance range of $2.5 < y_{\mu \mu} < 4$. Further, we calculate thepolarization parameters $\lambda_{\theta}$, $\lambda_{\phi}$, $\lambda_{\theta\phi}$ from the polar and azimuthal angular distributions of the dimuons inhelicity and Collins-Soper frames. This study presents a comprehensivemeasurement of the polarization parameters as a function of transversemomentum, charged-particle multiplicity, and rapidity at the LHC energies. Ourfindings of charmonium polarization are in qualitative agreement with thecorresponding experimental data.

$J/\psi$ and $\psi$(2S) polarization in proton-proton collisions at the LHC energies using PYTHIA8