O(a) improved Wilson quark action on anisotropic lattice

The $O(a)$ improved Wilson quark action on the anisotropic lattice is investigated. 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 the temporal lattice spacings, respectively. Using the dispersion relation of mesons, the bare anisotropy $\gamma_F$ in the quark action is numerically tuned below the charm quark mass region with the statistical accuracy of 1 % level. The systematic uncertainties in the calibration are examined and found to be under control in the continuum limit. Then we compute the light hadron masses and find that they are consistent with the result of the UKQCD Collaboration on the isotropic lattice. The effect of the uncertainty in the calibration on the hadron spectrum for physical quark masses is also found to be under control.