Systematic sensitivity study of the $J/\psi$ nuclear modification factor to polarization assumptions

Heavy quarkonium is one of the key candidates to study the fundamental properties of Quark-Gluon Plasma (QGP) created in heavy-ion ($A$+$A$) collisions. Comparing the production of the $J/\psi$ meson in proton+proton ($p$+$p$) and $A$+$A$ collisions, namely the nuclear modification factor ($R_{\rm AA}$), provides the quantitative understanding of the QGP. Normally, the $R_{\rm AA}$ is measured under the assumption that the quarkonium is unpolarized. However, recent measurements on the $J/\psi$ polarization in the forward rapidity region from the LHC experiments suggest that the $J/\psi$ meson has a small but non-negligible polarization. In this paper, we evaluate the systematic sensitivity of the kinematic acceptance to the $J/\psi$ polarization assumptions in the measurement of $R_{\rm AA}$. Using available data from the ALICE and LHCb experiments in the forward rapidity region, and exploring extreme polarization scenarios in the central rapidity region at RHIC and LHC energies, we demonstrate the maximum envelope of systematic uncertainties induced by unknown polarization states. The results indicate that the unpolarized assumption introduces a dominant, unquantified systematic uncertainty. Having precise measurements of quarkonium polarization in heavy-ion collisions is critical to obtaining an accurate interpretation of how heavy quarkonium interacts with the QGP.