We study charmonium correlators in pseudoscalar and vector channels at finite temperature using lattice QCD simulation in the quenched approximation. Anisotropic lattices are used in order to have sufficient numbers of degrees of freedom in the Euclidean temporal direction. We focus on the low energy structure of the spectral function, corresponding to the ground state in the hadron phase, by applying the smearing technique to enhance the contribution to the correlator from this region. We employ two analysis procedures: the maximum entropy method (MEM) for the extraction of the spectral function without assuming a specific form, to estimate the shape of the spectral function, and the standard χ2 fit analysis using typical forms in accordance with the result of MEM, for a more quantitative evaluation. To verify the applicability of the procedures, we first analyze the smeared correlators as well as the point correlators at zero temperature. We find that by shortening the t-interval used for the analysis (a situation inevitable at T>0) the reliability of MEM for point correlators is lost, while it subsists for smeared correlators. Then the smeared correlators at T? 0.9 Tc and 1.1 Tc are analyzed. At T? 0.9 Tc, the spectral function exhibits a strong peak, well approximated by a delta function corresponding to the ground state with almost the same mass as at T=0. At T? 1.1 Tc, we find that the strong peak structure still persists at almost the same place as below Tc, but with a finite width of a few hundred MeV. This result indicates that the correlators possess a nontrivial structure even in the deconfined phase.
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