Building upon the work of the Fermilab and Tsukuba groups, we discuss improved lattice actions capable of describing onium and heavy-light systems with errors of order (~pa)2 but accurate to arbitrary order in(ma)n, wherea is the lattice spacing, ~p is the spatial momentum of the heavy quark(s) andm the heavy quark mass. We demonstrate using both a tree-level example and an inductive proof that this accuracy can be achieved for hadronic masses using an action containing only three mass-dependent parameters: the bare quark mass ( 0), an anisotropy coefficient (ζ ) of the Dirac spatial derivative term and a coefficient (cP) of the chromomagnetic Pauli term. Further improvement terms are needed to calculate matrix elements involving spinor fields or composite operators. This represents a simplification of earlier results and makes practical the non-perturbative evaluation of these coefficients.
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