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.

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... By performing one-loop calculations of the speed-of-light renormalization for several possible lattice actions in the limit of a_t→ 0, we show that one can eliminate the large systematic error on the anisotropic lattice.