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Recent studies on the spectral function of charmonium in lattice QCD suggestsurvival of $J/\psi$ state in the deconfinement phase till relatively hightemperature. Based on the studies, different scenarios of $J/\psi$ suppressionare discussed to understand experimental results in the Heavy Ion Collisionexperiments. The scenarios require the information on the dissociationtemperatures of $\chi_c$ and $\psi'$ as well as that of $J/\psi$. In order toinvestigate these states in finite temperature lattice QCD, we have to consideran effect of a characteristic constant mode in the correlators. As a result ofthe study on the constant mode, we find that most drastic change in charmoniumcorrelators for $\chi_c$ states just above the deconfinement transition arecaused by the constant mode. It may indicate the survival of $\chi_c$ statesafter the deconfinement transition until, at least, $1.4T_c$.

Study of constant mode in charmonium correlators at finite temperature