Heavy quarks on anisotropic lattices: The charmonium spectrum

We present results for the mass spectrum of $c\overline{c}$ mesons simulated on anisotropic lattices where the temporal spacing $a_t$ is only half of the spatial spacing $a_s.$ The lattice QCD action is the Wilson gauge action plus the clover-improved Wilson fermion action. The two clover coefficients on an anisotropic lattice are estimated using mean links in the Landau gauge. The bare velocity of light ${\nu }_t$ has been tuned to keep the anisotropic, heavy-quark Wilson action relativistic. Local meson operators and three box sources are used in obtaining clear statistics for the lowest lying and first excited charmonium states of ${}^1{S}_0,$ ${}^3{S}_1,$ ${}^1{P}_1,$ ${}^3{P}_0$ and ${}^3{P}_1.$ The continuum limit is discussed by extrapolating from quenched simulations at four lattice spacings in the range 0.1–0.3 fm. Results are compared with the observed values in nature and other lattice approaches. Finite volume effects and dispersion relations are checked.