We present a new method to calculate meson spectral functions (SPFs) on the
lattice based on a variational method. Because, on a finite volume lattice, the
meson SPFs have discrete spectra only, a suitable way to extract such discrete
signals is needed. Using a variational method, we can calculate several
discrete quantities such as the position and the area of spectral peaks for
low-lying states. Moreover data accuracy can be improved by increasing the
number of basis functions. In this report, we first confirm our method in the
free quark case and show that our method works well. Then, we apply the method
to a quenched lattice QCD simulation and calculate the charmonium SPFs for S
and P-waves at zero temperature. Our results for the ground state are well
consistent with the position and the area of the lowest peaks of charmonium
SPFs calculated by the conventional maximum entropy method. For first excited
states, the signals may be reliablly extracted with our method because the
charmonium mass converges to a value close to the experimental one when the
number of basis functions is increased. We also investigate the SPFs for S-wave
charmonia at below and above Tc​. Our results suggest that J/ψ and
ηc​ may survive up to 1.4Tc​.Comment: 7 Pages, 6 figures, talk presented at the XXVIII International
Symposium on Lattice Field Theory, June 14-19 2010, Villasimius, Ital