Observations on staggered fermions at non-zero lattice spacing

TL;DR

This paper investigates the non-local effects of the fourth-root trick in staggered fermions in lattice QCD at finite lattice spacing, arguing that these effects vanish in the continuum limit.

Contribution

It demonstrates that the non-locality introduced by the fourth-root trick is likely an artifact of finite lattice spacing and disappears as the continuum limit is approached.

Findings

Non-local behavior observed in free theory and fixed gauge backgrounds.

Non-local effects diminish and vanish in the continuum limit.

Challenges recent claims about taste-symmetry breaking and mass renormalization.

Abstract

We show that the use of the fourth-root trick in lattice QCD with staggered fermions corresponds to a non-local theory at non-zero lattice spacing, but argue that the non-local behavior is likely to go away in the continuum limit. We give examples of this non-local behavior in the free theory, and for the case of a fixed topologically non-trivial background gauge field. In both special cases, the non-local behavior indeed disappears in the continuum limit. Our results invalidate a recent claim that at non-zero lattice spacing an additive mass renormalization is needed because of taste-symmetry breaking.