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We study the in-medium masses of the charmonium states $J/\psi$ and$\eta_{c}$ in the nuclear medium using QCD sum rule approach. These massmodifications arise due to modifications of the scalar and the twist-2 gluoncondensates in the hot hadronic matter. The scalar gluon condensate,$<\frac{\alpha_{s}}{\pi} G^a_{\mu\nu} {G^a}^{\mu\nu}>$ and the twist-2tensorial gluon operator, $<\frac{\alpha_{s}}{\pi} G^a_{\mu\sigma}{{G^a}_\nu}^{\sigma}>$ in the nuclear medium are calculated from the mediummodification of a scalar dilaton field introduced to incorporate trace anomalyof QCD within the chiral SU(3) model used in the present investigation. Theeffects of isospin asymmetry, density and temperature of the nuclear medium onthe in-medium masses of the lowest charmonium states $J/\psi$ and $\eta_{c}$mesons are investigated in the present work. The results of the presentinvestigation are compared with the existing results on the masses of thesestates. The medium modifications of the masses of these charmonium states($J/\psi$ and $\eta_c$) seem to be appreciable at high densities and shouldmodify the experimental observables arising from the compressed baryonic matterproduced in asymmetric heavy ion collision experiments at the future facilityof FAIR, GSI.

$J/\psi$ and $\eta_{c}$ masses in isospin asymmetric hot nuclear matter - a QCD sum rule approach