Lattice QCD ensembles with four flavors of highly improved staggered quarks

TL;DR

This paper presents the first phase of generating four-flavor QCD ensembles using the HISQ action with a Symanzik-improved gauge action, spanning lattice spacings from 0.06 to 0.15 fm and light-quark masses near physical. It evaluates scale setting via r1 and f_p4s, analyzes topological susceptibility, and quantifies substantial reductions in taste-symmetry breaking compared with earlier asqtad ensembles. The study also examines autocorrelations and algorithmic choices (RHMC vs RHMD) to optimize computational efficiency, reporting robust sampling of topological sectors and improved gauge configurations. The results establish a solid foundation for high-precision QCD phenomenology and outline plans to extend to finer lattices and publicly release the ensembles.

Abstract

We present results from our simulations of quantum chromodynamics (QCD) with four flavors of quarks: u, d, s, and c. These simulations are performed with a one-loop Symanzik improved gauge action, and the highly improved staggered quark (HISQ) action. We are generating gauge configurations with four values of the lattice spacing ranging from 0.06 fm to 0.15 fm, and three values of the light quark mass, including the value for which the Goldstone pion mass is equal to the physical pion mass. We discuss simulation algorithms, scale setting, taste symmetry breaking, and the autocorrelations of various quantities. We also present results for the topological susceptibility which demonstrate the improvement of the HISQ configurations relative to those generated earlier with the asqtad improved staggered action.

Figures (11)

• Figure 1: Comparison of the RHMC and RHMD algorithms for the $a\approx 0.09$ fm, physical quark mass and $a\approx 0.06$ fm, $m_l=m_s/10$ ensembles. The RHMD points are plotted at the value of the molecular dynamics step size $\epsilon$ for which they were generated, and are given by red squares for the $a\approx 0.09$ fm ensemble, and by green diamonds for the $a\approx 0.06$ fm one. The RHMC points are plotted at $\epsilon=0$, and are given by blue bursts for the $a\approx 0.09$ fm ensemble and by fancy black diamonds for the $a\approx 0.06$ fm one. The left panel shows the plaquette, the central panel the strange-quark $\langle\bar{\psi}\psi\rangle$, and the right panel the light-quark $\langle\bar{\psi}\psi\rangle$, all as a function of $\epsilon^2$. A significant fraction of the total sample for $a\approx 0.09$ fm was run at $\epsilon^2=0.000177$, which is why the error bars at that point are so small. Both the light and strange quark $\langle\bar{\psi}\psi\rangle$ are given in lattice units, and both are calculated in double precision. The points for the $a\approx 0.06$ fm ensemble have been shifted vertically to move them into the range of the graph, the plaquette downward by 0.031643, the strange and light quark $\langle\bar{\psi}\psi\rangle$ upward by 0.0157497 and 0.00185230, respectively.
• Figure 2: The time history of the topological charge for five HISQ gauge configuration ensembles. The histogram to the right of each time history shows the distribution of charges.
• Figure 3: Topological susceptibility vs. taste-singlet pion mass squared in units of $r_0$, comparing results from five HISQ ensembles (filled symbols) with previously published asqtad results ref:topo_susc2 (open symbols). Solid curves are from a joint chiral/continuum fit to the asqtad data for the four lattice spacings shown in the figure. The lowest (black) curve indicates the resulting continuum extrapolation of the asqtad fit with two representative points displaying the extrapolation errors. The (red) dot-dashed curve shows the leading order prediction in chiral perturbation theory. The (green) arrow above the (green) 0.12 fm asqtad curve indicates the asqtad point with a light quark mass comparable to that of the upper solid (green) HISQ square. Similarly, the (blue) arrow above the (blue) 0.09 fm asqtad curve indicates the asqtad point with a light quark mass comparable to the upper solid (blue) HISQ octagon, and the (red) arrow below the (red) 0.06 fm asqtad curve locates the asqtad point with a light quark mass comparable to the solid (red) HISQ diamond.
• Figure 4: Pion taste splitting of pions for asqtad (blue) and HISQ (red) actions. For clarity, the HISQ splittings are also enclosed in dashed-dotted boxes, and nearly degenerate masses have been displaced slightly in the horizontal direction. Differences between the squared masses of various taste pions and that of the Goldstone pion are shown in units of $r_1$, and plotted versus the expected leading dependence of taste violations in the theory, $\alpha_S^2 a^2$, also in $r_1$ units. Here, we use $\alpha_S=\alpha_V$ at scale $q^*\!=\!2/a$. The two diagonal lines are not fits, but merely lines with slope 1, showing the expectation if the splittings are linear in $\alpha_S^2 a^2$. The vertical line at the upper left shows the displacement associated with a factor of three in splittings. The numerical values of the HISQ taste splittings plotted here are given in Table \ref{['tab:taste_degenerate']} of the appendix.
• Figure 5: Same as Fig. \ref{['fig:taste-split-2oa']}, but with $\alpha_S= \alpha_V(q^*\!=\!1.5/a)$.