Mass Shift and Width Broadening of $J/\psi$ in Hot Gluonic Plasma from QCD Sum Rules

We investigate possible mass shift and width broadening of $J/\psi$ in hot gluonic matter using QCD sum rules. Input values of gluon condensates at finite temperature are extracted from lattice QCD data for the energy density and pressure. Although stability of the moment ratio is achieved only up to $T/T_c\simeq 1.05$, the gluon condensates cause a decrease of the moment ratio, which results in a change of the spectral properties. Using the Breit-Wigner form for the phenomenological side, we find that the mass shift of $J/\psi$ just above $T_c$ can reach maximally 200 MeV and the width can broaden to dozens of MeV.

Figure 1

Gluon condensates as a function of $T/T_c$.

Figure 2

Ratio of the moment from the OPE for various $T/T_c$.

Figure 3

The moment ratio of the phenomenological side as a function of $\Gamma$ for various masses. Left figure shows $n=9$ case and right one shows $n=14$ case.

Figure 4

Relation between mass shift and width at finite temperature. Left figure shows the case of ${\alpha }_{qq}(T)$ and right one shows the case of $\tilde{\alpha }(T)$.

Figure 5

Temperature dependence of the $m_{J/\psi }$ (left vertical axis) in $\Gamma \to 0$ limit (maximum mass shift) and ${\Gamma }_{J/\psi }$ (right vertical axis) in $\delta m\to 0$ limit (no mass shift). Mass and width are indicated by open symbols and closed ones, respectively.