Flavor Symmetry and the Static Potential with Hypercubic Blocking

TL;DR

The paper addresses flavor symmetry violations in staggered fermions and short-distance distortions in the static potential by introducing hypercubic blocking (HYP), a localized fat-link smearing with three tunable parameters optimized to maximize the minimum plaquette. The authors demonstrate in quenched lattices at β=5.7 and 6.0 that HYP dramatically improves flavor symmetry (about a sixfold reduction in mass splittings) and yields static-potential measurements with an order of magnitude improvement in statistical precision, while only affecting short distances (r/a<2). They extract consistent Sommer scale $r_0$ and string tension $\sqrt{\sigma}$ comparable to large-scale results, and show robust performance on finer lattices, supporting future dynamical simulations with HYP staggered fermions and finite-temperature studies (Hyp_thermo). Overall, HYP provides localized smoothing that enhances chiral/flavor properties without sacrificing short-distance physics, enabling more accurate and computationally efficient lattice QCD studies.

Abstract

We introduce a new smearing transformation, the hypercubic (HYP) fat link. The hypercubic fat link mixes gauge links within hypercubes attached to the original link only. Using quenched lattices at beta = 5.7 and 6.0 we show that HYP fat links improve flavor symmetry by an order of magnitude relative to the thin link staggered action. The static potential measured on HYP smeared lattices agrees with the thin link potential at distances r/a >= 2 and has greatly reduced statistical errors. These quenched results will be used in forthcoming dynamical simulations of HYP staggered fermions.

Figures (8)

• Figure 1: Schematic representation of the hypercubic blocking in three dimensions. a) The fat link is built from the four double-lined staples. b) Each of the double-lined links is built from two staples which extend only in the hypercubes attached to the original link. An important point is that the links entering the staples are projected onto SU(3).
• Figure 2: a) The histogram of the smallest plaquette distribution on a set of $4^{4}$$\beta =5.7$ configurations (dashed lines) and after hypercubic blocking (solid lines) on the same configurations. b) Same as a) but the solid lines correspond to one level APE smearing with $\alpha =0.7$.
• Figure 3: The parameter $\delta _{2}$ of eq. (\ref{['delta2']}) for the two lightest non-Goldstone pions $\pi _{i,5}$ (lower points) and $\pi _{i,j}$ (higher points) as the function of the minimum plaquette average of the fat link actions. The pion spectrum is computed on $8^{3}\times 24$, $\beta =5.7$ quenched configurations, the minimum plaquette average on $4^{4}$, $\beta =5.7$ configurations. The dotted ($\pi _{i,5}$) and dashed ($\pi _{i,j}$) lines show how the flavor symmetric limit is approached as the minimum plaquette approaches three.
• Figure 4: a) The relative mass splitting $\Delta _{\pi }$ of eq. (\ref{['Deltapi']}) between the lightest non-Goldstone pion $\pi _{i,5}$ and the Goldstone pion $G$ as the function of $(r_{0}m_{G})^{2}$ on $\beta =5.7$ quenched configurations both for the thin (fancy diamonds) and the HYP (bursts) actions. b) Same as a) but on $\beta =6.0$ quenched configurations where the lattice spacing is reduced by about a factor of 2. The first three points at the lowest $r_{0}m_{G}$ values for the thin link action in both figures are from Ref. Gupta:1991mr.
• Figure 5: The histograms of the smallest plaquette distribution on sets of $8^{4}$ gauge configurations at different $\beta$ values (dashed lines) and after hypercubic blocking (solid lines) on the same configurations.