Properties of $J/ψ$ at $T_c$: QCD second-order Stark effect

Abstract

Starting from the temperature dependencies of the energy density and pressure from lattice QCD calculation, we extract the temperature dependencies of the electric and magnetic condensate near Tc. While the magnetic condensate hardly changes across Tc, we find that the electric condensate increases abruptly above Tc. This induces a small but an equally abrupt decrease in the mass of J/ψ, which can be calculated through the second-order Stark effect. Combining the present result with the previously determined QCD sum rule constraint, we extract the thermal width of J/ψ above Tc, which also increases fast. These changes can be identified as the critical behavior of J/ψ across Tc associated with the phase transition. We find that the mass shift and width broadening of J/ψ at 1.05 Tc will be around −100 MeV and 100 MeV respectively.

In-medium modification ofP-wave charmonia from QCD sum rules

“…Therefore the results of the width might be less reliable. In reality there should be mass shifts in this temperature region caused by change of the chromo-electric field, i.e., second-order Stark effect [24,25]. Hence, a small mass shift with large width broadening would not be a realistic combination.…”

$R_{AA}$ of $J/ψ$ near mid-rapidity in heavy ion collisions at $\sqrt{s_{NN}}=200$ GeV

“…Therefore, the effects of a sudden decrease in the mass and a sudden increase in the width at the phase transition point, as advocated in Ref. [6,43], might just compensate each other in R AA , making it difficult to identify such effects from a measurement of R AA alone.…”

“…However, the situation was found to be more involved as recent lattice QCD results showed that J/ψ might survive past the critical temperature (T c ) and dissolve only at a higher temperature (T d ∼ 2T c ) [2,3]. If so, it is important to know the detailed temperature dependencies of the properties of the J/ψ above T c , as large thermal width for example might still lead to a very small survival rate of the J/ψ [4][5][6]. Moreover, if the quark-gluon plasma is formed and the number of charm quarks are large, there is an additional production mechanism that has to be estimated and comes from the formation of J/ψ through the regeneration of charm and anti-charm that are well described by statistical approaches [7][8][9][10].…”

Critical behavior of J/ψ across the phase transition from QCD sum rules

“…See Ref. [13] for a recent investigation. Here we show the possible maximum change of the mass and width, in which the other quantity is assumed to remain with the vacuum value.…”