Further Improvements to Staggered Quarks

The improved staggered quark action has enabled breakthrough calculations of QCD with three light dynamical quarks. The largest remaining $a^2$ scaling violations come from "taste-changing" interactions, which are significantly reduced over naive quarks because of carefully chosen smearing of the gauge links. Here we examine further improvements to the quark action and show that additional smearing of the links can reduce the taste-changing errors by another factor of two, whilst retaining a fully $a^2$-improved action. The taste-changing errors can be understood within a perturbative calculation of the four-quark operators that appear at one-loop. We also discuss unquenching techniques with such a highly improved action.