# Massive Fermions in Lattice Gauge Theory

## TL;DR

This paper develops a unified lattice fermion formulation valid for all quark masses, ensuring smooth connections between light and heavy quark regimes, and analyzes cutoff artifacts and improvement criteria.

## Contribution

It introduces a comprehensive lattice fermion approach applicable to all quark masses, incorporating interactions and external currents without mass limit expansions.

## Key findings

- Cutoff artifacts factorize into mass- and momentum-dependent terms.
- Order $(m_q a)^s$ artifacts are avoided even for large $m_q a$.
- Provides interpretation of Wilson and Sheikholeslami-Wohlert actions for nonrelativistic fermions.

## 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 evaluated 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 $b_n(m_qa)[\vek{p}a]^{s_n}$, where $\vek{p}$ is a momentum characteristic of the system under study, $s_n$ is related to the dimension of the $n$th interaction, and $b_n(m_qa)$ is a bounded function, numerically always~$\order(1)$ or less. In heavy-quark systems $\vek{p}$ is typically rather smaller than the fermion mass~$m_q$. Therefore, artifacts of order $(m_qa)^s$ do not arise, even when $m_qa\gsim1$. An important by-product of our analysis is an interpretation of the Wilson and Sheikholeslami-Wohlert actions applied to nonrelativistic fermions.