On the Absence of O(a) Errors in Staggered-Quark Discretizations

TL;DR

This paper shows that the perceived O(a) errors in staggered-quark discretizations are artifacts of flavor field definitions, and the true taste mixing errors are only at O(a^2), clarifying the nature of discretization errors.

Contribution

It introduces a new coordinate-space flavor field definition that eliminates O(a) taste mixing errors, demonstrating that actual errors are only at O(a^2).

Findings

O(a) taste mixing is an artifact of flavor field definitions.

New flavor field definition suppresses O(a) errors by two powers of a.

Taste mixing errors are only from high-virtuality gluon exchange, at O(a^2).

Abstract

We demonstrate that the O(a) taste mixing exhibited in standard textbook presentations of staggered quarks is an artifact of the particular definition of the flavor fields in those presentations, and has nothing to do with the underlying precision of staggered-quark actions, despite continuing comments to the contrary in the current literature. To illustrate this point we introduce a new coordinate-space definition of the flavor fields that suppresses the O(a) term by two additional powers of a. In fact there are no errors at all from this mechanism. The only source of taste mixing comes from the exchange of highly-virtual gluons and enters in O(a^2). We review the idiosyncrasies of Symanzik improvement for naive/staggerd-quark actions, and show how these results follow from that program.