Quarkonium formation time in relativistic heavy-ion collisions

We calculate the quarkonium formation time in relativistic heavy-ion collisions from the space-time correlator of heavy quark vector currents in a hydrodynamic background with the initial nonequilibrium stage expanding only in the longitudinal direction. Using in-medium quarkonia properties determined with the heavy quark potential taken to be the free energy from lattice calculations and the fact that quarkonia can only be formed below their dissociation temperatures due to color screening, we find that $\mathrm{{\rm Y}}$(1S), $\mathrm{{\rm Y}}$(2S), $\mathrm{{\rm Y}}$(3S), $J/\psi$, and ${\psi }^{\prime }$ are formed, respectively, at 1.2, 6.6, 8.8, 5.8, and $11.0\text{fm}/c$ after the quark pair are produced in central Au+Au collisions at the top energy of the BNL Relativistic Heavy Ion Collider (RHIC), and these times become shorter in semicentral collisions. We further show, as an example, that including the effect of formation time enhances appreciably the survivability of $\mathrm{{\rm Y}}$(1S) in the produced hot dense matter.

Figure 1

Formation times of charmonia (left panel) and bottomonia (right panel) in a QGP as functions of the temperature of the QGP [18, 22].

Figure 2

Average temperature $T$, the fractions of bottomonium states $F$, and their derivatives $P$ as functions of time in Au+Au collisions at $\sqrt{s_{NN}}=$ 200 GeV for the 0–5% (upper panel) and 50–60% (lower panel) centralities.

Figure 3

Average temperature $T$, the fractions of charmonium states $F$, and their derivatives $P$ as functions of time in Au+Au collisions at $\sqrt{s_{NN}}=$ 200 GeV for the 0–5% (upper panel) and 50–60% (lower panel) centralities.

Figure 4

Thermal decay width of $\mathrm{{\rm Y}} \left(1S\right)$ as a function of temperature (left panel) and its survival probabilities from thermal decay with and without including the formation time as functions of collision centrality (right panel).