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 $m_q,$ 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 $b_n{(m}_{q}a\left)\right[\mathbf{p}a{]}^{s_n}$ where p is a momentum characteristic of the system under study, $s_n$ is related to the dimension of the $n$th interaction, and $b_n{(m}_{q}a)$ is a bounded function, numerically always of order 1 or less. In heavy-quark systems p is typically rather smaller than the fermion mass $m_q.$ Therefore, artifacts of order ${(m}_q{a)}^s$ do not arise, even when $m_{q}a\gtrsim 1$. An important by-product of our analysis is an interpretation of the Wilson and Sheikholeslami-Wohlert actions applied to nonrelativistic fermions.