Massive fermions in lattice gauge theory

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Abstract

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 ${b}_{n}{(m}_{q}a)[\mathbf{p}a{]}^{{s}_{n}}$ 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 ${m}_{q}a\ensuremath{\gtrsim}1$. An important by-product of our analysis is an interpretation of the Wilson and Sheikholeslami-Wohlert actions applied to nonrelativistic fermions.

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