Discretization effects and the scalar meson correlator in mixed-action lattice simulations

TL;DR

This study analyzes discretization effects in a mixed-action lattice QCD setup using domain-wall valence quarks on an Asqtad-improved staggered sea. It identifies two key low-energy constants, $m_{ m res}$ and $\Delta_{ m mix}$, quantifies their sizes across lattice spacings, and tests mixed-action chiral perturbation theory (MAχPT) against the isovector scalar $a_0$ correlator. The results show MAχPT accurately describes the dominant unitarity-violating bubble contributions, supporting the use of MAχPT to remove lattice artifacts and reliably extract physical quantities such as the kaon bag parameter $B_K$. Overall, the work validates mixed-action lattice simulations as a practical, controlled approach for precise weak matrix-element calculations with predictable discretization effects that vanish toward the continuum limit.

Abstract

We study discretization effects in a mixed-action lattice theory with domain-wall valence quarks and Asqtad-improved staggered sea quarks. At the level of the chiral effective Lagrangian, discretization effects in the mixed-action theory give rise to two new parameters as compared to the lowest order Lagrangian for staggered fermions -- the residual quark mass, m_res, and the mixed valence-sea meson mass-splitting, Delta_mix. We find that the size of m_res is approximately four times smaller than our lightest valence quark mass on our coarser lattice spacing, and comparable to that of simulations by RBC and UKQCD. We also find that the size of Delta_mix is comparable to the smallest of the staggered meson taste-splittings measured by MILC. Because lattice artifacts are different in the valence and sea sectors of the mixed-action theory, they give rise to unitarity-violating effects that disappear in the continuum limit. Such effects are expected to be mild for many quantities of interest, but are significant in the case of the isovector scalar (a_0) correlator. Specifically, once m_res, Delta_mix, and two other parameters that can be determined from the light pseudoscalar spectrum are known, the two-particle intermediate state "bubble" contribution to the scalar correlator is completely predicted within mixed-action chiral perturbation theory (MAChPT). We find that the behavior of the scalar meson correlator is quantitatively consistent with the MAChPT prediction; this supports the claim that MAChPT describes the dominant unitarity-violating effects in the mixed-action theory and can be used to remove lattice artifacts and recover physical quantities.

Figures (12)

• Figure 1: Chiral extrapolation of $m_{\textrm{res}}$ on the coarse lattices. The curve shows the extrapolation/interpolation for points where the domain-wall pion mass is tuned to equal the lightest (taste pseudoscalar) staggered pion mass. For comparison, we show the determination of $m_{\textrm{res}}$ by the LHP Collaboration, which uses this tuning Renner:2004ck.
• Figure 2: Comparison of $r_1 m_{\textrm{res}}$ on the coarse ($a\approx 0.12$ fm) and fine ($a\approx 0.09$ fm) MILC lattices. The curves are the interpolation/extrapolation to the LHPC tuning. The value of $r_1 m_{\textrm{res}}$ on the fine lattices is approximately three times smaller than it is on the coarse lattices.
• Figure 3: Determination of the mixed-action parameter $\Delta_{\textrm{mix}}$ on the coarse and fine MILC lattices. The vertical axis is a carefully chosen linear combination of squared meson masses, the left side of Eq. (\ref{['eq:DelMix']}), such that a linear extrapolation of this quantity in the staggered quark mass gives the parameter $\Delta_{\textrm{mix}}$ as the y-intercept. The small diamonds (squares) are the coarse (fine) data. For comparison, the large diamonds (squares), show the values of the staggered taste splittings measured by MILC on the coarse (fine) lattices.
• Figure 4: Leading contributions to the scalar current. The first diagram corresponds to the propagation of an $a_0$ meson and the second is one of three "bubble" diagrams. While this figure shows a $\pi$ and an $\eta$ propagating, there are contributions from $\pi-\pi$ and $K-\overline{K}$ intermediate states as well.
• Figure 5: Comparison of the scalar correlator generated with a point source on 206 configurations and with a random-wall source on 184 configurations. The data shown is for $am_v$=0.01 on the 0.007/0.05 coarse ensemble.