O(a)-improved quark action on anisotropic lattices and perturbative renormalization of heavy-light currents -: art. no. 074501

We investigate the Symanzik improvement of the Wilson quark action on anisotropic lattices. Taking first a general action with nearest-neighbor and clover interactions, we study the mass dependence of the ratio of the hopping parameters, the clover coefficients, and an improvement coefficient for heavy-light vector and axial vector currents. We show how tree-level improvement can be achieved. For a particular choice of the spatial Wilson coupling, the tree-level formulas simplify, and the lattice theory reaches the naive continuum limit for m(0)a(tau) much less than1, m(0)a(sigma)similar to1. (Here ino is the bare quark mass, and a(tau) and a(sigma) are the temporal and spatial lattice spacings.) For other choices, the continuum limit is reached only for m(0)a(sigma)much less than1. With the well-behaved choice we calculate the renormalization factors of heavy-light bilinear operators at one-loop order of perturbation theory. These results allow us to show, numerically, that these one-loop corrections also behave well for m(0)a(tau)much less than1 and m(0)a(sigma)similar to1.