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A Numerical Study of Improved Quark Actions on Anisotropic Lattices

Tadpole improved Wilson quark actions with clover terms on anisotropic lattices are studied numerically. Using asymmetric lattice volumes, the pseudo-scalar meson dispersion relations are measured for 8 lowest lattice momentum modes with quark mass values ranging from the strange to the charm quark with various values of the gauge coupling $β$ and 3 different values of the bare speed of light parameter $ν$. These results can be utilized to extrapolate or interpolate to obtain the optimal value for the bare speed of light parameter $ν_{opt}(m)$ at a given gauge coupling for all bare quark mass values $m$. In particular, the optimal values of $ν$ at the physical strange and charm quark mass are given for various gauge couplings. The lattice action with these optimized parameters can then be used to study physical properties of hadrons involving either light or heavy quarks.