Order of the Chiral and Continuum Limits in Staggered Chiral Perturbation Theory

TL;DR

This paper discusses the non-commutativity of continuum and chiral limits in staggered chiral perturbation theory, highlighting differences between quenched and unquenched QCD and implications for lattice calculations.

Contribution

It extends the observation of non-commuting limits from the Schwinger model to four-dimensional SChPT, clarifying the nature of singularities and their impact on lattice QCD results.

Findings

Non-commutativity observed in 2D Schwinger model also appears in 4D SChPT.

Singularities are not linked to rooting trick or taste issues.

Most unquenched QCD quantities do not exhibit these singularities.

Abstract

Durr 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 (SChPT) in quenched or partially quenched quantities constructed to be particularly sensitive to the chiral limit. Although the physics involved in the SChPT examples is quite different from that in the Schwinger model, neither singularity seems to be connected to the trick of taking the nth root of the fermion determinant to remove unwanted degrees of freedom ("tastes"). Further, I argue that the singularities in SChPT are absent in most commonly-computed quantities in the unquenched (full) QCD case and do not imply any unexpected systematic errors in recent MILC calculations with staggered fermions.