We propose a method to evaluate spectral functions on the lattice based on a variational method. On a lattice with a finite spatial extent, spectral functions consist of discrete spectra only. Adopting a variational method, we calculate the locations and the heights of spectral functions at low-lying discrete spectra. We first test the method in the case of analytically solvable free Wilson quarks at zero and finite temperatures and confirm that the method well reproduces the analytic results for low-lying spectra. We find that we can systematically improve the results by increasing the number of trial states. We then apply the method to calculate the charmonium spectral functions for $S$ and $P$-wave states at zero-temperature in quenched QCD and compare the results with those obtained using the conventional maximum entropy method (MEM). The results for the ground state are consistent with the location and the area of the first peak in spectral functions from the MEM, while the variational method leads to a mass which is closer to the experimental value for the first excited state. We also investigate the temperature dependence of the spectral functions for $S$-wave states below and above $T_c$. We obtain no clear evidences for dissociation of $J/\psi$ and ${\eta }_c$ up to $1.4T_c$.

• Received 18 April 2011

DOI:https://doi.org/10.1103/PhysRevD.84.094504