Rooted staggered fermions: good, bad or ugly?

TL;DR

This paper critically reviews the validity of the fourth-root trick in lattice QCD, examining recent progress, potential issues, and implications for continuum limits and physical results.

Contribution

It provides a comprehensive critical analysis of recent developments regarding the fourth-root trick and its impact on the validity of rooted staggered fermion simulations.

Findings

Recent progress suggests potential validity of the fourth-root trick

Concerns remain about the continuum limit and theoretical consistency

Implications for quark mass calculations and finite temperature/density studies

Abstract

I give a status report on the validity of the so-called ``fourth-root trick'', i.e. the procedure of representing the determinant for a single fermion by the fourth root of the staggered fermion determinant. This has been used by the MILC collaboration to create a large ensemble of lattices using which many quantities of physical interest have been and are being calculated. It is also used extensively in studies of QCD thermodynamics. The main question is whether the theory so defined has the correct continuum limit. There has been significant recent progress towards answering this question. After recalling the issue, and putting it into a broader context of results from statistical mechanics, I critically review the new work. I also address the related issue of the impact of treating valence and sea quarks differently in rooted simulations, discuss whether rooted simulations at finite temperature and density are subject to additional concerns, and briefly update results for quark masses using the MILC configurations. An answer to the question in the title is proposed in the summary.