Scaling studies of QCD with the dynamical HISQ action

TL;DR

This work evaluates the scaling behavior of QCD simulations using the highly improved staggered quark (HISQ) action, comparing against asqtad across three lattice spacings with 2+1+1 dynamical flavors. By examining hadron masses, pseudoscalar decay constants, and the topological susceptibility at a fixed unphysical light-quark mass, the study demonstrates that HISQ significantly reduces lattice artifacts, enabling near-continuum results on coarser lattices. The analysis also compares scale setting via $r_1$ and the HPQCD-favored $f_{ss}$, highlighting how scale choices affect cross-action comparisons while confirming improved scaling with HISQ. Collectively, the results indicate substantial efficiency gains for precise lattice QCD calculations and motivate further studies across different light-quark masses to robustly control chiral and continuum extrapolations.

Abstract

We study the lattice spacing dependence, or scaling, of physical quantities using the highly improved staggered quark (HISQ) action introduced by the HPQCD/UKQCD collaboration, comparing our results to similar simulations with the asqtad fermion action. Results are based on calculations with lattice spacings approximately 0.15, 0.12 and 0.09 fm, using four flavors of dynamical HISQ quarks. The strange and charm quark masses are near their physical values, and the light-quark mass is set to 0.2 times the strange-quark mass. We look at the lattice spacing dependence of hadron masses, pseudoscalar meson decay constants, and the topological susceptibility. In addition to the commonly used determination of the lattice spacing through the static quark potential, we examine a determination proposed by the HPQCD collaboration that uses the decay constant of a fictitious "unmixed s bar s" pseudoscalar meson. We find that the lattice artifacts in the HISQ simulations are much smaller than those in the asqtad simulations at the same lattice spacings and quark masses.

Figures (11)

• Figure 1: Autocorrelation $C_{\Delta t}$ in simulation time of the plaquette (left panel), strange quark $\bar{\psi}\psi$ (center panel) and topological charge (right panel). Note that the horizontal scale is different in each of the three panels. Errors on the autocorrelation were estimated by dividing the time series into five subsets and averaging the autocorrelations from each subset. The vertical arrows in the left panel indicate the time separation between stored lattices, used in computing the potential, spectrum and other quantities.
• Figure 2: The static quark potential with the HISQ and the asqtad actions. The HISQ results are from the $a\approx 0.09$ fm run, and the asqtad results are from a lattice with almost the same lattice spacing and light-quark mass about 0.2 times the correct strange quark mass ($am_l = 0.00465$). In order to match the potentials, the plot is in units of $r_1$, while rulers in units of the lattice spacing are shown at $r_1 V(r) = 0$. A constant has been added to each potential so that $V(r_1)=0$. The solid lines (essentially superimposed) show the fit from Eq. (\ref{['eqn:potform']}) for the two runs, (evaluated with $\lambda$ set to zero). The inset magnifies a part of this plot at short distance to show the lattice artifacts discussed in the text.
• Figure 3: Taste splittings among the pions. The asqtad results used configurations with 2+1 flavors of dynamical quarks, and the HISQ results 2+1+1 flavors. The quantity plotted is $r_1^2 \left( M_\pi^2 - M_G^2 \right)$, where $M_\pi$ is the mass of the non-Goldstone pion and $M_G$ is the mass of the Goldstone pion. Reading from top to bottom, the non-Goldstone pions are the $\pi_s$ (box), $\pi_0$ (fancy box), $\pi_i$ (fancy plus), $\pi_{io}$ (plus), $\pi_{ij}$ (diamond), $\pi_{i5}$ (cross) and $\pi_{05}$ (octagon). $r_1^2 \left( M_\pi^2 - M_G^2 \right)$ is known to be almost independent of the light-quark mass. The vertical bar at the upper left shows the size of a factor of three, roughly the observed reduction in taste splittings, while the sloping solid line shows the theoretically expected dependence on lattice spacing. Nearly degenerate points have been shifted horizontally to improve their visibility.
• Figure 4: Vector meson ($\rho$) masses in units of $r_1$. Here the bold (red) points are the HISQ simulations with $m_l=0.2 m_s$, and the lighter (blue) points are asqtad results for various light quark masses. The $a\approx 0.06$ fm asqtad point immediately to the right of the $a\approx 0.09$ fm HISQ point has been displaced to the right to make it visible. It in fact falls on top of the $a\approx 0.09$ fm HISQ point. The cross sign at lower left is the physical $\rho$ mass. The error on the physical mass point is just the error on the physical value of $r_1$.
• Figure 5: Nucleon masses in units of $r_1$. Here the bold (red) points are the HISQ simulations with $m_l=0.2 m_s$, and the lighter (blue) points are asqtad results for various light quark masses. The cross at lower left is the physical nucleon mass. The solid magenta line is a continuum extrapolation of a chiral perturbation theory fit to the asqtad nucleon masses, while the dotted green lines are from the same fit at finite lattice spacing lat07_baryons.