Charmonium mass in hot and dense hadronic matter

We investigate mass shifts of charmonia driven by change of the gluon condensate below but near transition temperatures at finite baryonic chemical potential. Extending previous prescription on the relation between gluon condensates and thermodynamic quantities, we model the gluon condensates of hadronic matter at finite temperature and baryonic chemical potential such that the scalar gluon condensate fits with the latest lattice QCD data. By making use of the QCD sum rule and the second-order Stark effect, we find that the smoother transition in the full QCD can lead to moderate mass shifts of charmonia even below the transition temperature. We also find larger mass shift at fixed temperature as chemical potential increases. Existing data on charmonium-charmonium ratio is found to be consistent with the statistical hadronization scenario, including the obtained mass shift.