  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.
