Charmonium in medium: From correlators to experiment

We set up a framework in which in-medium charmonium properties are constrained by thermal lattice quantum chromodynamics and subsequently implemented into a thermal rate equation enabling the comparison with experimental data in heavy-ion collisions. Specifically, we evaluate phenomenological consequences for charmonium production originating from two different scenarios in which either the free or the internal energy are identified with the in-medium two-body potential between charm and anticharm quarks. These two scenarios represent $J/\psi$ “melting temperatures” of approximately $1.25T_c$ (“weak binding”) and $2T_c$ (“strong binding”), respectively. Within current uncertainties in dissociation rates and charm-quark momentum spectra, both scenarios can reproduce the centrality dependence of inclusive $J/\psi$ yields in nuclear collisions at the Super Proton Synchrotron (SPS) and the Relativistic Heavy-Ion Collider (RHIC) reasonably well. However, the “strong-binding” scenario associated with the internal energy as the potential tends to better reproduce current data on transverse momentum spectra at both SPS and RHIC.

Figure 1

Temperature dependence of in-medium charm quark mass. The solid (dashed) line is for the strong (weak) binding scenario.

Figure 2

Temperature dependence of $J/\psi$ binding energy. The solid (dashed) line is for the strong (weak) binding scenario with $V_{Q\mathrm{Q̄}}$=$U_{Q\mathrm{Q̄}}$($F_{Q\mathrm{Q̄}}$).

Figure 3

(Top panel) Temperature dependence of dissociation rates for $J/\psi$ and ${\chi }_c$ calculated in quasifree approximation for the strong-binding (solid line, $J/\psi$; dot-dashed line, ${\chi }_c$) and weak-binding scenarios (dashed line, $J/\psi$; dash-double-dotted line, ${\chi }_c$). The dotted line indicates the contribution from $J/\psi$ gluo-dissociation rate in the strong-binding scenario using ${\alpha }_s$ $=$ 0.32 in the underlying cross-section expression[32]. (Bottom panel) 3-momentum dependence of the $J/\psi$ dissociation rate in the strong- and weak-binding scenarios (solid and dashed lines, respectively).

Figure 4

Temperature dependence of the strength of the resonance part of the $S$-wave spectral function $Z_{\Psi }(T)$. The solid (dashed) line is for the strong (weak) binding scenario.

Figure 5

Spectral functions in the vector channel. The top (bottom) panel is for the strong (weak) binding scenario.

Figure 6

Ratio of vector channel correlator to the reconstructed correlator. The top (bottom) panel is for the strong (weak) binding scenario.

Figure 7

Spectral functions in the scalar channel. The top (bottom) panel is for the strong (weak) binding scenario. In the weak-binding scenario ${\chi }_{c0}$ has already melted at $T_c$.

Figure 8

Time profiles of temperature for central collisions of heavy nuclei (participant number $N_{\mathrm{part}}$=380) at RHIC ($\sqrt{s}=200$ AGeV; solid line, midrapidity; dashed line, forward rapidity) and SPS ($\sqrt{s}=17.3$ AGeV; dot-dashed line).

Figure 9

Temperature dependence of the in-medium $J/\psi$ equilibrium limit using the statistical model in the QGP within the strong-binding scenario (dot-dashed lines, with and without $D$-meson resonances below and above 1.3 $T_c$$\simeq 234$ MeV, respectively; solid line, smooth interpolation of the previous two cases; see text for details), the weak-binding scenario (dashed line), and in the HG for temperatures below $T_c$ $=$ 180 MeV.

Figure 10

Results of the thermal rate-equation approach for $J/\psi$ production (normalized to Drell-Yan pairs) versus centrality at SPS, compared to NA50 data[68, 69]. Solid lines, total $J/\psi$ yield; dashed lines, suppressed primordial production; dot-dashed lines, regeneration component; dotted lines, primordial production with CNM effects only. Top panel, strong-binding scenario; bottom panel, weak-binding scenario.

Figure 11

Results of the thermal rate-equation approach for the nuclear modification factor versus centrality at midrapidity at RHIC, compared to PHENIX data[70]. Solid lines, total $J/\psi$ yield; dashed lines, suppressed primordial production; dot-dashed lines, regeneration component; dotted lines, primordial production with CNM effects only. Top panel, strong-binding scenario; bottom panel, weak-binding scenario.

Figure 12

Results of the thermal rate-equation approach for the nuclear modification factor versus centrality at forward rapidity compared to PHENIX data[70]. Solid lines, total $J/\psi$ yield; dashed lines, suppressed primordial production; dot-dashed lines, regeneration component; dotted lines, primordial production with CNM effects only. Top panel, strong-binding scenario; bottom panel, weak-binding scenario.

Figure 13

Results of the thermal rate-equation approach for the ratio of $R_{\mathit{AA}}$ for $J/\psi$ at forward and midrapidity versus $N_{\mathrm{part}}$ in strong (solid line) and weak (dashed line) binding scenarios compared to PHENIX data[70]. In the top two curves, CNM effects have been divided out in both numerator and denominator of the ratio.

Figure 14

$J/\psi$ abundance as a function of time in central ($N_{\mathrm{part}}$ $=$ 380) Au-Au collisions at RHIC. Solid lines, total; dashed line, primordial component; dot-dashed line, regeneration component; double dot-dashed line, equilibrium limit of $J/\psi$, $N_{J/\psi }^{\mathrm{eq}}$. Top panel, strong-binding scenario; bottom panel, weak-binding scenario.

Figure 15

Results of the thermal rate-equation approach for $\langle p_t^2\rangle$ versus centrality at SPS (left panels, compared to NA50 data[38, 72]) and RHIC at mid- and forward rapidity (middle and right panels, respectively, compared to PHENIX data[70]). In each panel, $\langle p_t^2\rangle$ is plotted for total $J/\psi$ yield (primordial $+$ regeneration component; solid lines), the suppressed primordial component (dashed line), the regeneration component (dash-dotted line), and primordial production with CNM effects only (dotted lines). The top (bottom) panels correspond to the strong-binding (weak-binding) scenario.

Figure 16

Nuclear modification factor for $J/\psi$ $p_t$ spectra in central 200 AGeV Au-Au collisions including formation-time effects (fte) and $B$-meson feed-down (Bfd) contributions. PHENIX data[70] are compared to our rate-equation calculations in the strong- and weak-binding scenarios (top and bottom panel, respectively).