ar X iv : h ep - l at / 0 20 90 90 v 1 8 S ep 2 00 2 1 Heavy - light meson in anisotropic lattice QCD ∗

We examine whether the O(a) improved quark action on anisotropic lattices can be used as a framework for the heavy quark, which enables precision computation of matrix elements of heavy-light mesons. To this end, it is crucial to verify that a mass independent and nonperturbative tuning of the parameters is possible. As a first step, we observe the dispersion relation of heavy-light mesons on a quenched lattice using the action which is nonperturbatively tuned only for the leading terms. On a lattice with the spatial cutoff a −1 σ ≃ 1.6 GeV and the anisotropy ξ = 4, the relativity relation holds within 2% accuracy in the quark mass region aσmQ ≤ 1.2 with the bare anisotropy parameter tuned for the massless quark. We also apply the action to a calculation of heavy-light decay constants in the charm quark mass region.