A Relativistic O(a) Improved Action for Heavy Quarks

where sj = dim[Oj ]. In this framework lattice spacing effects can be systematically removed by adding higher dimensional operators to the lattice action. The aim of this work is to design a lattice action such that the coefficients of O(a) and O(a) terms in Eq. (1) can be reduced. For heavy quarks with mQ ≫ ΛQCD, the mass introduces an additional short-distance scale into the problem, and the Symanzik formalism must be modified to separate the short-distance effects of both the lattice spacing and the heavy-quark mass from the long-distance physics. The Fermilab formalism [2] represents one approach to this problem. It allows the coefficients cj in Eq. (1) to depend on the quark mass. Then it takes the Wilson action [3], modified to allow different coefficients for space-like and time-like operators. Improved lattice actions are constructed by adding higher-dimension operators, again with different coefficients for timeand space-like operators. Ref. [2] considers operators up to dimen-