Light hadrons with improved staggered quarks: approaching the continuum limit

TL;DR

The paper advances lattice QCD with three dynamical quark flavors using the improved Asqtad action at lattice spacings near $0.09$ and $0.12$ fm to compute the static potential and light hadron spectrum. It conducts a thorough assessment of discretization, finite-volume, precision, integration-step, and autocorrelation effects, and establishes a continuum-extrapolated scale $r_1$ around 0.317 fm, with a consistent $r_0$ in the ~0.46 fm range. The results for pseudoscalar, vector, and baryon masses largely align with experimental values after extrapolations, while explorations of hadronic decays and excited states reveal realistic spectral features and the emergence of multi-state fits in light-quark sectors. The work demonstrates the viability of three-flavor dynamical simulations toward the continuum limit and physical quark masses, while outlining necessary future enhancements in chiral extrapolations and lighter-quark runs.

Abstract

We have extended our program of QCD simulations with an improved Kogut-Susskind quark action to a smaller lattice spacing, approximately 0.09 fm. Also, the simulations with a approximately 0.12 fm have been extended to smaller quark masses. In this paper we describe the new simulations and computations of the static quark potential and light hadron spectrum. These results give information about the remaining dependences on the lattice spacing. We examine the dependence of computed quantities on the spatial size of the lattice, on the numerical precision in the computations, and on the step size used in the numerical integrations. We examine the effects of autocorrelations in "simulation time" on the potential and spectrum. We see effects of decays, or coupling to two-meson states, in the 0++, 1+, and 0- meson propagators, and we make a preliminary mass computation for a radially excited 0- meson.

Figures (16)

• Figure 1: A "shape parameter" for the static potential, $r_0/r_1$. The red octagons are from coarse ($a \approx 0.12$ fm) lattices with three degenerate quark flavors, and the red squares from coarse lattices with two light and one strange quark. At $(M_\pi/M_\rho)^2=0.15$ the upper square is from the $L=28$ run and the lower from the $L=20$ run. The blue crosses are from the fine ($a \approx 0.09$ fm) runs. The single green diamond is from a two flavor simulation. The magenta burst is the continuum and chiral extrapolation discussed in the text, with the smaller error bar the statistical error and the larger the systematic error. In this figure we have chosen to use $(M_\pi/M_\rho)^2$ for the abscissa instead of the $(M_\pi r_1)^2$ used in other figures because this lets us put the entire range of quark masses up to the quenched limit ($M_\pi \rightarrow \infty$) in the graph.
• Figure 2: Pseudoscalar masses as a function of minimum distance included in the fit from the run with $10/g^2=7.09$ and $a m_{l/s}=0.0062/0.031$. The size of the symbols is proportional to the confidence level of the fit, with the size of the symbols in the labels corresponding to 50%. These fits included only a single exponential. Fits selected to quote in the mass tables are marked with arrows.
• Figure 3: Vector meson masses as a function of minimum distance included in the fit from the run with $10/g^2=7.09$ and $a m_{l/s}=0.0062/0.031$.
• Figure 4: Nucleon masses. The blue diamonds and octagons are quenched coarse and fine runs respectively. The red squares are three flavor coarse lattice results, and the red bursts the three flavor fine lattices. The magenta fancy plusses connected by the straight line and the two curved lines are continuum and chiral extrapolations discussed in the text. The fancy diamond is the experimental value, with an error bar from the uncertainty in $r_1$.
• Figure 5: Single elimination jackknife masses for the pion, from the run with $10/g^2=6.76$ and $a m_{l/s}=0.01/0.05$, using fits with $D_{\rm min}=19$.