Heavy quark action on the anisotropic lattice

We investigate the $O(a)$ improved quark action on anisotropic lattice as a potential framework for the heavy quark, which may enable precision computation of hadronic matrix elements of heavy-light mesons. The relativity relations of heavy-light mesons as well as of heavy quarkonium are examined on a quenched lattice with spatial lattice cutoff $a_\sigma^{-1} \simeq$ 1.6 GeV and the anisotropy $\xi=4$. We find that the bare anisotropy parameter tuned for the massless quark describes both the heavy-heavy and heavy-light mesons within 2% accuracy for the quark mass $a_\sigma m_Q < 0.8$, which covers the charm quark mass. This bare anisotropy parameter also successfully describes the heavy-light mesons in the quark mass region $a_\sigma m_Q \leq 1.2$ within the same accuracy. Beyond this region, the discretization effects seem to grow gradually. The anisotropic lattice is expected to extend by a factor $\xi$ the quark mass region in which the parameters in the action tuned for the massless limit are applicable for heavy-light systems with well controlled systematic errors.