Scalar Meson Spectroscopy with Lattice Staggered Fermions

TL;DR

This paper investigates scalar meson properties using lattice QCD with staggered fermions, analyzing correlators within rooted staggered chiral perturbation theory to validate the fourth-root procedure and extract low energy couplings.

Contribution

It provides the first detailed analysis of scalar meson correlators in the staggered fermion framework using rSXPT, testing the validity of the fourth-root procedure.

Findings

Correlators are consistent with previous low energy coupling determinations.

Rooted staggered chiral perturbation theory effectively describes scalar meson correlators.

Results support the validity of the fourth-root procedure in lattice QCD.

Abstract

With sufficiently light up and down quarks the isovector ($a_0$) and isosinglet ($f_0$) scalar meson propagators are dominated at large distance by two-meson states. In the staggered fermion formulation of lattice quantum chromodynamics, taste-symmetry breaking causes a proliferation of two-meson states that further complicates the analysis of these channels. Many of them are unphysical artifacts of the lattice approximation. They are expected to disappear in the continuum limit. The staggered-fermion fourth-root procedure has its purported counterpart in rooted staggered chiral perturbation theory (rSXPT). Fortunately, the rooted theory provides a strict framework that permits the analysis of scalar meson correlators in terms of only a small number of low energy couplings. Thus the analysis of the point-to-point scalar meson correlators in this context gives a useful consistency check of the fourth-root procedure and its proposed chiral realization. Through numerical simulation we have measured correlators for both the $a_0$ and $f_0$ channels in the ``Asqtad'' improved staggered fermion formulation in a lattice ensemble with lattice spacing $a = 0.12$ fm. We analyze those correlators in the context of rSXPT and obtain values of the low energy chiral couplings that are reasonably consistent with previous determinations.