Variants of fattening and flavor symmetry restoration

TL;DR

This work investigates fat-link improvements to the Kogut-Susskind fermion action to curb flavor-symmetry breaking, using empirical comparisons of pion spectra across multiple fat-link actions on shared lattice ensembles. It introduces and analyzes several actions (Fat5, Fat7, Fat7tad, Asqtad, Asq, and unitary variants), highlighting coefficients and improvements such as tadpole enhancement, Naik/Lepage corrections, and an approximate unitarization scheme to enable dynamical simulations. The results show substantial reductions in flavor violation, with Fat7tad and Asqtad performing particularly well, and reveal trade-offs between computational cost and discretization quality. The findings support using Asqtad as a practical, improved KS action for dynamical QCD simulations, while Fat7tad offers maximal flavor restoration, thereby guiding future lattice QCD studies involving dynamical quarks.

Abstract

We study the effects of different "fat link" actions for Kogut-Susskind quarks on flavor symmetry breaking. Our method is mostly empirical - we compute the pion spectrum with different valence quark actions on common sets of sample lattices. Different actions are compared, as best we can, at equivalent physical points. We find significant reductions in flavor symmetry breaking relative to the conventional or to the "link plus staple" actions, with a reasonable cost in computer time. We also develop and test a scheme for approximate unitarization of the fat links. While our tests have concentrated on the valence quark action, our results will be useful in designing simulations with dynamical quarks.

Figures (5)

• Figure 1: A simple link and staples in one plane, showing the relative signs of the coupling to a gluon with momentum component $\pi$ in the transverse direction (unparenthesized), and a gluon with momentum $\pi$ in the longitudinal direction (parenthesized).
• Figure 2: The simple link, three link staple, five link staple and seven link staple used in suppressing flavor symmetry breaking. The final path is the five link path used, following Lepage, to correct the small momentum form factor.
• Figure 3: An approximately unitary variant of the three link staple.
• Figure 4: The spectrum of pion masses with the "Link+Staple+Naik" action. The two spectra are at $10/g_{imp}^2=7.3$ and $7.5$ respectively. In both cases we have interpolated in quark mass, assuming that squared meson masses are linear in the quark mass, to the point where $m_G/m_\rho=0.55$. The pion masses are plotted in units of the $\rho$ mass. Each pion is labeled by the gamma matrix specifying its flavor structure. The pattern of near degeneracies predicted in Ref. SHARPE is evident. As expected, the mass splittings among the pions are smaller for the smaller lattice spacing ($10/g_{imp}^2=7.5$).
• Figure 5: The $\delta_2$ for three different actions versus the squared lattice spacing. From left to right, the actions are the conventional "One Link" action, the "Link+Staple+Naik" action, and the "Order $a^2$ tadpole" action. In each case, the $\rho$ mass for the respective action was used to define the length scale. The points come from two flavor runs with $10/g_{imp}^2=7.3$ (rightmost points in each graph), $10/g_{imp}^2=7.5$, and a quenched simulation with single plaquette gauge action at $6/g_{conv}^2=6.15$. The lines drawn in each panel are approximate slopes for the local non-Goldstone pion (lower line) and for the three link flavor ${\bf 1}$ pion (upper line), which is the worst case pion.