In-medium $J/\psi$ mass shift by the $D$ meson loop effect

By an effective Lagrangian plus QCD sum-rule approach, we investigate the mass shift of the $J/\psi$ state in medium, in symmetric nuclear matter with zero and finite temperature, and cold strange matter. The in-medium mass of the $J/\psi$ state is evaluated through the intermediate pseudoscalar $D$-meson loop for the $J/\psi$ self-energy. The effect of medium is incorporated through the in-medium mass of $D$ meson calculated using chiral SU(3) model plus QCD sum-rule approach. The self energy loop integral is regularized using the phenomenological form factor of the dipole form. We compare our results with some of the results in the literature. The present results should be helpful to understand better the expected data from heavy ion collision experiments, such as CBM and PANDA.