Perturbative study of anisotropic lattice actions for heavy quarks

Anisotropic lattice fermion actions are investigated with one-loop perturbative calculations aiming at constructing a formulation for a heavy quark with controlled systematic uncertainties. For heavy-light systems at rest an anisotropic lattice with small temporal lattice spacing at suppresses the discretization error by a power of atmQ for a heavy quark of mass mQ. We discuss the issue of large discretization errors, which scale as asmQ with as the spatial lattice spacing. By performing one-loop calculations of the speed-of-light renormalization for several possible lattice actions in the limit of at→0, we show that one can eliminate the large systematic error on the anisotropic lattice