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 mq, 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 close-quote s Hamiltonian, one finds that cutoff artifacts factorize into the form bn(mqa)[pa]sn where p is a momentum characteristic of the system under study, sn is related to the dimension of the nth interaction, and bn(mqa) is a bounded function, numerically always of order 1 or less. In heavy-quark systems p is typically rather smaller than the fermion mass mq. Therefore, artifacts of order (mqa)s do not arise, even when mqa approx-gt 1. An important by-product of our analysis is an interpretation of the Wilson and Sheikholeslami-Wohlert actions applied to nonrelativistic fermions. copyright 1997 The American Physical Society