Flavor-symmetry restoration and Symanzik improvement for staggered quarks

We resolve contradictions in the literature concerning the origins and size of unphysical flavor-changing strong interactions generated by the staggered-quark discretization of QCD. We show that the leading contributions are tree level in $\mathcal{O}{(a}^2)$ and that they can be removed by adding three correction terms to the link operator in the standard action. These corrections are part of the systematic Symanzik improvement of the staggered-quark action. We present a new improved action for staggered quarks that is accurate up to errors of $\mathcal{O}{(a}^4{,a}^2{\alpha }_s)$—more accurate than most, if not all, other discretizations of light-quark dynamics.