Numerical study of staggered quark action on quenched anisotropic lattices

The staggered quark action on anisotropic lattices is studied. We carry out numerical simulations in the quenched approximation at three values of lattice spacing ($a_{\sigma}^{-1}=1-2$ GeV) with the anisotropy $\xi= a_{\sigma}/a_{\tau}=4$, where $a_{\sigma}$ and $a_{\tau}$ are the spatial and temporal lattice spacings, respectively. The bare anisotropy $\gamma_F$ in the quark action is numerically tuned through the ratio of meson masses in the fine and coarse directions, and through the dispersion relation of a meson, so that the renormalized fermionic anisotropy coincides with that of the gauge field. The discrepancy between these two calibration schemes provides an estimate of the finite lattice artifact, which is found to be sizable in the range of cutoff explored in this work. We also compute the meson masses using correlators with the wall source at the tuned anisotropy parameter. The flavor symmetry breaking effect smoothly decreases as $\beta$ increases. The effect of uncertainty in $\gamma_F$ on the meson masses are examined. We also discuss a perspective on dynamical simulations.