Charmonium production in relativistic heavy-ion collisions

Using the two-component model that includes charmonium production from both initial nucleon-nucleon hard scattering and regeneration in the produced quark-gluon plasma, we study $J/\psi$ production in heavy-ion collisions at the Super Proton Synchrotron (SPS), Relativistic Heavy Ion Collider (RHIC), and Large Hadron Collider (LHC). For the expansion dynamics of produced hot dense matter, we use a schematic viscous hydrodynamic model with the specific shear viscosity in the quark-gluon plasma and the hadronic matter taken, respectively, to be two and ten times the lower bound of $1/4\pi$ suggested by the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. For the initial dissociation and the subsequent thermal decay of charmonia in the hot dense matter, we use the screened Cornell potential to describe the properties of charmonia and perturbative QCD to calculate their dissociation cross sections. Including regeneration of charmonia in the quark-gluon plasma via a kinetic equation with in-medium chamonium decay widths, we obtain a good description of measured $J/\psi$ nuclear modification factors in Pb $+$ Pb collisions at $\sqrt{s_{NN}}=1.73$ GeV at SPS and in Au $+$ Au collisions at $\sqrt{s_{NN}}=200$ GeV at RHIC. A reasonable description of the measured nuclear modification factor of high transverse momenta $J/\psi$ in Pb $+$ Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV at LHC is also obtained.

Figure 1

Temperature profiles along the radial direction at initial thermalization time as functions of radial distance in central Pb $+$ Pb collisions at $\sqrt{s_{NN}}=17.3$ GeV at SPS and $\sqrt{s_{NN}}=2.76$ TeV at LHC, and in central Au $+$ Au collisions at $\sqrt{s_{NN}}=200$ GeV at RHIC from viscous hydrodynamics.

Figure 2

Average temperatures of fire cylinder as functions of time in central Pb $+$ Pb collisions at $\sqrt{s_{NN}}=17.3$ GeV at SPS and $\sqrt{s_{NN}}=2.76$ TeV at LHC, and in central Au $+$ Au collisions at $\sqrt{s_{NN}}=200$ GeV at RHIC from the viscous hydrodynamics.

Figure 3

Binding energy of $J/\psi$ in the QGP as a function of temperature for the QCD coupling constant $g=1.87$.

Figure 4

Charmonium dissociation temperatures in the QGP as functions of the QCD coupling constant $g$.

Figure 5

Thermal decay widths of charmonia in the QGP as a function of temperature for the QCD coupling constant $g=1.87$.

Figure 6

Nuclear modification factor $R_{AA}$ of $J/\psi$ (solid line) as a function of the participant number $N_{\mathrm{part}}$ in Pb $+$ Pb collisions at $\sqrt{s_{NN}}=17.3$ GeV at SPS (upper panel) and in Au $+$ Au collisions at $\sqrt{s_{NN}}=200$ GeV at RHIC (lower panel). Dashed and dotted lines represent, respectively, the contributions to $J/\psi$ production from primordial hard nucleon-nucleon scattering and regeneration in the QGP. Experimental data are from Refs. [2, 3].

Figure 7

Nuclear modification factor $R_{AA}$ of $J/\psi$ as a function of the participant number $N_{\mathrm{part}}$ without (upper panel) and with (lower panel) the shadowing effect in Pb $+$ Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV at LHC. Upper and lower solid lines are the $R_{AA}$ of $J/\psi$ for the nuclear absorption cross sections of ${\sigma }_{\mathrm{abs}}=0$ and 2.8 mb, respectively. Dashed, dotted, and dot-dashed lines denote, respectively, the contributions to $J/\psi$ production from primordial hard nucleon-nucleon scattering, regeneration in the QGP, and decay of bottom hadrons.

Figure 8

Transverse momentum $p_T$ spectra of $J/\psi$ from $p+\overline{p}$ annihilation at $\sqrt{s_{NN}}=1.96$ TeV by the CDF Collaboration at Fermi Lab (filled squares and solid line) [29] and of regenerated $J/\psi$ (dashed line) in central Pb $+$ Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV at LHC.

Figure 9

Nuclear modification factor $R_{AA}$ of $J/\psi$ with transverse momentum larger than 6.5 GeV$/c$ versus the number of participants without (upper panel) and with (lower panel) the shadowing effect in Pb $+$ Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV at LHC. Dashed, dotted, and dot-dashed lines represent, respectively, the contributions to $J/\psi$ production from primordial hard nucleon-nucleon scattering, regeneration from QGP, and decay of bottom hadrons. Upper and lower solid lines are the total $R_{AA}$ obtained with the nuclear absorption cross section of 0 and 28 mb, respectively. Experimental data shown by solid squares are from the CMS Collaboration [15].

Figure 10

Ratio $R_{\mathrm{cp}}$ of the $R_{AA}$ of $J/\psi$ with transverse momentum larger than 6.5 GeV$/c$ in a given centrality to that in the peripheral collision versus the centrality of Pb $+$ Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV at LHC. Experimental data shown by solid squares are from the ATLAS Collaboration [14].