Order of the chiral and continuum limits in staggered chiral perturbation theory

Abstract

D\"urr and Hoelbling recently observed that the continuum and chiral limits do not commute in the two dimensional, one flavor, Schwinger model with staggered fermions. I point out that such lack of commutativity can also be seen in four-dimensional staggered chiral perturbation theory ($\mathrm{S}\ensuremath{\chi}\mathrm{PT}$) in quenched or partially quenched quantities constructed to be particularly sensitive to the chiral limit. Although the physics involved in the $\mathrm{S}\ensuremath{\chi}\mathrm{PT}$ examples is quite different from that in the Schwinger model, neither singularity seems to be connected to the trick of taking the ${\mathrm{n}}^{\mathrm{th}}$ root of the fermion determinant to remove unwanted degrees of freedom (``tastes''). Further, I argue that the singularities in $\mathrm{S}\ensuremath{\chi}\mathrm{PT}$ are absent in standard quantities in the unquenched (full) QCD case and do not imply any unexpected systematic errors in recent MILC calculations with staggered fermions.