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

Abstract

Starting from the temperature dependence of the energy density and pressure from lattice QCD calculation, we extract the temperature dependence of the electric and magnetic condensate near $T_c$. While the magnetic condensate hardly changes across $T_c$, we find that the electric condensate increases abruptly above $T_c$. This induces a small but an equally abrupt decrease in the mass of $J/\psi$, 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 $J/\psi$ above $T_c$, which also increases fast. These changes can be identified as the critical behavior of $J/\psi$ across $T_c$ associated with the phase transition. We find that the mass shift and with broadening of $J/\psi$ at 1.05 $T_c$ will be around -100 MeV and 100 MeV respectively.

5 pages, 4 figures, revised version to appear in Phys.Rev.D

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