Anisotropic lattice actions for heavy quark

The anisotropic lattice fermion actions are investigated with the one-loop perturbative calculations aiming at constructing a formulation for heavy quark with controlled systematic uncertainties. For the heavy-light systems at rest the 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 scales 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.