Staggered fermions, zero modes, and flavor-singlet mesons

TL;DR

This paper investigates the eigenvector structure of staggered fermions to ensure they reproduce continuum physics correctly, particularly regarding zero modes and flavor-singlet mesons, and confirms numerically that these conditions are met.

Contribution

It derives conditions on eigenvectors of staggered-fermion Dirac operators to reproduce the 't Hooft vertex and shows these conditions are numerically satisfied with the HISQ action.

Findings

Eigenvector conditions are satisfied in realistic lattice simulations.

Staggered fermions reproduce the 't Hooft vertex in the continuum limit.

Flavor-singlet meson correlators are free of singularities in quark mass.

Abstract

We examine the taste structure of eigenvectors of the staggered-fermion Dirac operator. We derive a set of conditions on the eigenvectors of modes with small eigenvalues (near-zero modes), such that staggered fermions reproduce the 't Hooft vertex in the continuum limit. We also show that, assuming these conditions, the correlators of flavor-singlet mesons are free of contributions singular in $1/m$, where $m$ is the quark mass. This conclusion holds also when a single flavor of sea quark is represented by the fourth root of the staggered-fermion determinant. We then test numerically, using the HISQ action, whether these conditions hold on realistic lattice gauge fields. We find that the needed structure does indeed emerge.