Systematic study of the polarization effect on the measurements of the $J/ψ$ nuclear modification factor

TL;DR

This paper investigates how the polarization of $J/\psi$ mesons affects the kinematic acceptance used in $R_{\rm AA}$ measurements in heavy-ion and proton-proton collisions. It employs a Toy Monte Carlo framework that propagates polarization parameters in the helicity HX and Collins-Soper CS frames to construct polarization-aware acceptances and a corrected $R_{\rm AA}^{\rm corr.}$ through $R_{\rm AA}^{\rm corr.}=R_{\rm AA}\times \frac{C_{\rm AA}^{p_T,y}}{C_{pp}^{p_T,y}}$, with the input $p_T$ spectrum modeled by $f(p_T)=N\frac{p_T}{(1+(p_T/p_0)^2)^n}$. The results show sizeable forward-rapidity corrections (up to ~16% at low $p_T$) and potentially large central-rapidity effects (up to a factor of 6 at low $p_T$ and 10–70% at higher $p_T$), depending on the collision system and energy, underscoring the need for precise polarization measurements in heavy-ion collisions. Overall, the work highlights that polarization-aware acceptance corrections are essential for accurately interpreting $J/\psi$ interactions with the QGP and for disentangling hot and cold nuclear matter effects.

Abstract

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 $J/ψ$ 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, the recent measurements on the $J/ψ$ polarization in the forward rapidity region in both $p$+$p$ and $A$+$A$ collisions from the LHC experiments suggest that the $J/ψ$ meson has small but non-negligible polarization. In this paper, we show the effects on the kinematic acceptance from the $J/ψ$ polarization to the measurement of $R_{\rm AA}$ in the forward rapidity region using the available data from the ALICE and LHCb experiments and demonstrate the possible maximum effects from polarization in the central rapidity region at the RHIC and LHC energies. The results show that having precise measurements on the quarkonium polarization in heavy-ion collisions is important to obtain the full picture of how heavy quarkonium interacts with the QGP.

Figures (11)

• Figure 1: The polarization parameters $\lambda_{\theta}$, $\lambda_{\phi}$, and $\lambda_{\theta\phi}$ as a function of $p_T$ in \ref{['fig:hx_polar_lhc']} the HX and \ref{['fig:cs_polar_lhc']} CS frame measured from ALICE in Pb+Pb collisions at 5.02 TeV alice_jpsi_pol_pbpb and LHCb in $p$+$p$ collisions at 7 TeV lhcb_jpsi_pol_pp. The rapidity range for these measurements is $2.5 < y < 4.0$. Black lines are a linear function fits to the data points and dashed lines are linear functions fit to the upper and lower bound of the date points. Note that the data points from LHCb are plotted only in the same $y$ region as ALICE.
• Figure 2: The 2-dimensional ($J/\psi$$p_T$ versus $y$) kinematic acceptance ratio of polarized $J/\psi$ with the parameters from the ALICE measurements to the unpolarized $J/\psi$ in \ref{['fig:po_vs_unpo_hx']} HX and \ref{['fig:po_vs_unpo_cs']} CS frame.
• Figure 3: \ref{['fig:jpsi_input_pt']} The $p_T$ spectrum of $J/\psi$ for 0-90% centrality fitted by the function (black line) and details are described in the text. \ref{['fig:correct_spectrum']} The $p_T$ spectra of the $J/\psi$ meson: the input spectrum ($N^{\rm input}$, open boxes), the spectrum with kinematic selections on $J/\psi$ and muons ($N^{\rm in\ Acc.}$, solid black circles), and the corrected spectrum using unpolarized acceptance ($N^{\rm corr.}$, solid triangles).
• Figure 4: The $C_{\rm AA (pp)}$ as a function of $p_T$ in the HX (left) and CS (right) frame in the forward rapidity range ($2.5 < y < 4.0$) in Pb+Pb collisions at 5.02 TeV. The shaded area is due to the uncertainty of the polarization measurements.
• Figure 5: