Onset of $J/\psi$ melting in a quark-gluon fluid at RHIC

A strong $J/\psi$ suppression in central Au+Au collisions has been observed by the PHENIX experiment at the Relativistic Heavy Ion Collider. We develop a hydro$+J/\psi$ model in which hot quark-gluon matter is described by the full (3+1)-dimensional relativistic hydrodynamics and $J/\psi$ is treated as an impurity traversing through the matter. The experimental $J/\psi$ suppression pattern in midrapidity is reproduced well by the sequential melting of ${\chi }_{\mathrm{c}},{\psi }^{\text{'}}$, and $J/\psi$ in dynamically expanding fluid. The melting temperature of directly produced $J/\psi$ is well constrained by the participant-number dependence of the $J/\psi$ suppression and is found to be about $2T_{\mathrm{c}}$ with $T_{\mathrm{c}}$ being the pseudocritical temperature.

Figure 1

Local temperature in the unit of $T_c$ as functions of the transverse coordinates, $x$ (upper) and $y$ (lower), for various proper time (τ) at midrapidity (${\eta }_s=0$). The impact parameter $b=2.1$ fm (the left panel) corresponds to $\langle N_{\mathrm{part}}\rangle =351$, whereas $b=8.5$ fm (the right panel) corresponds to $\langle N_{\mathrm{part}}\rangle =114$.

Figure 2

Survival probabilities $S_{J/\psi }^{\mathrm{tot}}$ (solid line), $S_{J/\psi }$ (dashed line), and $S_{\chi }$ (dotted line) in the hydro$+J/\psi$ model as a function of the number of participants $N_{\mathrm{part}}$ with $(T_{J/\psi },T_{\chi },f_{\mathrm{FD}})=(2.02T_c,1.22T_c,0.30)$. Filled symbols are the experimental survival probability in the midrapidity of $J/\psi$ in Au+Au collisions at RHIC [7, 11].

Figure 3

Survival probability $S_{J/\psi }^{\mathrm{tot}}$ as a function of the number of participants $N_{\mathrm{part}}$, where melting temperature of $J/\psi$ is $1.90T_c$ (dashed), $1.96T_c$ (dotted), $2.02T_c$ (solid with open circles), $2.08T_c$ (dash-dotted), and $2.14T_c$ (solid).

Figure 4

${\chi }^2$ contour plot in $T_{J/\psi }/T_c-T_{\chi }/T_c$ plane with $f_{\mathrm{FD}}$ being fixed to 0.30. Cross symbol corresponds to $(T_{J/\psi },T_{\chi })=(2.02T_c,1.22T_c)$, which gives minimum ${\chi }^2$. Solid and dashed lines correspond to the $1\sigma$ and $2\sigma$ contours, respectively.

Figure 5

Survival probability $S_{J/\psi }^{\mathrm{tot}}$ as a function of $N_{\mathrm{part}}$, where melting temperatures of $J/\psi$ and χ and feed-down fraction are $2.02T_c$, 1.22$T_c$, and 30%. (a–d) The results using the decay width parametrized by Eq. (6) with α of 0.1, 0.2, 0.3, and 0.4 GeV, respectively.