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We study the charmonium spectral functions at finite momentum and thedispersion relation of $\eta_c$ at finite temperature. For the analysis of thespectral function, we use an extended maximum entropy method (MEM). We performthe MEM analysis for the product space of Euclidean correlators in differentchannels or momenta to incorporate information encoded in correlations amongthe Euclidean correlators in MEM. We find that this method can improve theerror of the reconstructed spectral images. To study the dispersion relation,we introduce a definition of the peak position in the spectral image in whichthe associated error can be estimated on the basis of MEM. We find that thedispersion relation of $\eta_c$ at finite temperature follows the Lorentzinvariant form even near the dissociation temperature $T\simeq1.7T_c$.

Charmonium spectra and dispersion relation with improved Bayesian analysis in lattice QCD