Staggered fermions, zero modes, and flavor-singlet mesons

Understand

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.