Massive fermions in lattice gauge theory

This paper presents a formulation of lattice fermions applicable to all quark masses, large and small. We incorporate interactions from previous light-fermion and heavy-fermion methods, and thus ensure a smooth connection to these limiting cases. The couplings in improved actions are obtained for arbitrary fermion mass [Formula presented] without expansions around small- or large-mass limits. We treat both the action and external currents. By interpreting on-shell improvement criteria through the lattice theory's Hamiltonian, one finds that cutoff artifacts factorize into the form [Formula presented] where p is a momentum characteristic of the system under study, [Formula presented] is related to the dimension of the [Formula presented]th interaction, and [Formula presented] is a bounded function, numerically always of order 1 or less. In heavy-quark systems p is typically rather smaller than the fermion mass [Formula presented] Therefore, artifacts of order [Formula presented] do not arise, even when [Formula presented]. An important by-product of our analysis is an interpretation of the Wilson and Sheikholeslami-Wohlert actions applied to nonrelativistic fermions.