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

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.