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We investigate a new class of improved relativistic fermion action on thelattice with a criterion to give excellent energy-momentum dispersion relationas well as to be consistent with tree-level $O\left(a^{2}\right)$-improvement.Main application in mind is that for heavy quark for which $ma\simeq O(0.5)$.We present tree-level results and a scaling study on quenched lattices.

$O(a^2)$-improved actions for heavy quarks and scaling studies on quenched lattices