Study of $J/\Psi$ at high temperatures in anisotropic lattice QCD

The high-temperature $J/\Psi$ mode above the QCD critical temperature $T_c$ is studied using anisotropic quenched lattice QCD. We aim to clarify whether the $J/\Psi$ state above $T_c$ is a localized resonance state or a $c$-$\bar c$ scattering state. We investigate $c$-$\bar c$ modes for $1.1T_c< T <2.1T_c$ using the $O(a)$-improved Wilson quark action at $\beta=6.10$ with renormalized anisotropy $a_s/a_t=4$. To distinguish localized states and scattering states, we calculate the $c$-$\bar c$ correlators on finite lattices with different spatial boundary conditions, i.e., the periodic and the anti-periodic boundary condition. (Note that the $c$-$\bar c$ threshold is raised up in the anti-periodic boundary condition.) As a result, almost no energy difference is found for the lowest $J/\Psi$ mode between the periodic and the anti-periodic boundary conditions at for $1.1T_c< T <2.1T_c$. This fact indicates that the lowest $J/\Psi$ mode can survive as a localized state even above $T_c$ in quenched QCD.