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

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 rooted-staggered fermions---the residual quark mass ${m}_{\mathrm{res}}$ and the mixed valence-sea meson mass splitting ${\ensuremath{\Delta}}_{\mathrm{mix}}$. We find that ${m}_{\mathrm{res}}$, which parametrizes explicit chiral symmetry breaking in the mixed-action theory, is approximately one-quarter the size of our lightest valence quark mass on our coarser lattice spacing and of comparable size to that of simulations by the RBC and UKQCD Collaborations. We also find that the size of ${\ensuremath{\Delta}}_{\mathrm{mix}}$ is comparable to the size of the smallest of the staggered meson taste splittings measured by the MILC Collaboration. 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, some of which should be described by mixed-action chiral perturbation theory ($\mathrm{MA}\ensuremath{\chi}\mathrm{PT}$). Such effects are expected to be mild for many quantities of interest but are expected to be significant in the case of the isovector scalar (${a}_{0}$) correlator. Specifically, once the parameters ${m}_{\mathrm{res}}$, ${\ensuremath{\Delta}}_{\mathrm{mix}}$, and two others that can be determined from the light pseudoscalar meson spectrum are known, the two-particle intermediate state ``bubble'' contribution to the scalar correlator is completely predicted within $\mathrm{MA}\ensuremath{\chi}\mathrm{PT}$. We find that the behavior of the scalar meson correlator is quantitatively consistent with the $\mathrm{MA}\ensuremath{\chi}\mathrm{PT}$ prediction; this supports the claim that $\mathrm{MA}\ensuremath{\chi}\mathrm{PT}$ describes the dominant unitarity-violating effects in the mixed-action theory and can therefore be used to remove lattice artifacts and recover physical quantities.