Numerical Study of the Staggered Quark Action on Quenched Anisotropic Lattices

The staggered quark action on anisotropic lattices is studied. We carry outnumerical simulations in the quenched approximation at three values of latticespacing ($a_{\sigma}^{-1}=1-2$ GeV) with the anisotropy $\xi=a_{\sigma}/a_{\tau}=4$, where $a_{\sigma}$ and $a_{\tau}$ are the spatial andtemporal lattice spacings, respectively. The bare anisotropy $\gamma_F$ in thequark action is numerically tuned through the ratio of meson masses in the fineand coarse directions, and through the dispersion relation of a meson, so thatthe renormalized fermionic anisotropy coincides with that of the gauge field.The discrepancy between these two calibration schemes provides an estimate ofthe finite lattice artifact, which is found to be sizable in the range ofcutoff explored in this work. We also compute the meson masses usingcorrelators with the wall source at the tuned anisotropy parameter. The flavorsymmetry breaking effect smoothly decreases as $\beta$ increases. The effect ofuncertainty in $\gamma_F$ on the meson masses are examined. We also discuss aperspective on dynamical simulations.Comment: 19 pages, 15 eps figure