Flavor-Symmetry Restoration and Symanzik Improvement for Staggered Quarks

TL;DR

The paper addresses unphysical flavor-changing interactions in staggered-quark lattice QCD, showing the dominant mechanism is one-gluon exchange with high lattice momentum $q \approx \zeta\pi/a$. It develops a Symanzik-improved action by replacing the link $U_\mu$ with a fat link $V_\mu$ and introducing two additional corrections, $V'_\mu$ and a higher-derivative term, to cancel both flavor-changing and flavor-conserving ${O}(a^{2})$ effects, yielding an action accurate to ${O}(a^{4}, a^{2}\alpha_s)$ at tree level. The coefficients $c(\zeta^{2})$ for the three independent pion splittings can be tuned nonperturbatively to remove residual tadpole effects. This approach provides a highly accurate, practical framework for light-quark lattice QCD, enabling reliable simulations at lattice spacings around ${0.1-0.3}$ fm with reduced flavor-breaking artifacts.

Abstract

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 $\order(a^2)$ 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 $\order(a^4,a^2α_s)$ --- more accurate than most, if not all, other discretizations of light-quark dynamics.