Rooted staggered fermions: good, bad or ugly?

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.

Figures (5)

• Figure 1: Update on pion mass results using rooted improved staggered fermions. The scale is set with $r_1$. $Z$-factors account for logarithmic scaling of quark masses. See text for further explanation.
• Figure 2: Results for correlation-length exponent for $d=2$ Ising model with long-range interactions.
• Figure 3: Results for the strong coupling constant, in the potential scheme, versus scale Masonalpha.
• Figure 4: RG framework and notation. Details are discussed in text.
• Figure 5: Condensates in the Schwinger model plotted versus quark mass in dimensionless units DH. Results for $N_f=1$ and $2$ are shown, using both (rooted) staggered and overlap fermions. Each result shows a central value and a 1-$\sigma$ error band. The asterisk shows the known continuum result for the $N_f=1$ massless theory. The "$(-1)^\nu$ curve is explained in the text.