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 $a_t$ suppresses the discretization error by a power of $a_t{m}_Q$ for a heavy quark of mass $m_Q.$ We discuss the issue of large discretization errors, which scale as $a_s{m}_Q$ with $a_s$ the spatial lattice spacing. By performing one-loop calculations of the speed-of-light renormalization for several possible lattice actions in the limit of $a_t\to 0,$ we show that one can eliminate the large systematic error on the anisotropic lattice.