Heavy Quarks on Anisotropic Lattices: The Charmonium Spectrum

Abstract

We present results for the mass spectrum of $c\bar{c}$ 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 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.

Comments: 36 pages, 6 figurs