Pseudoscalar flavor-singlets and staggered fermions

TL;DR

This paper reports progress in calculating the pseudoscalar singlet meson spectrum, especially the eta' mass, using 2+1-flavor Asqtad staggered fermions, and examines the topological charge correlation to test theoretical predictions.

Contribution

It provides an update on measuring the eta' mass with staggered fermions and explores the topological charge correlation, contributing to understanding the validity of the fourth-root trick.

Findings

Preliminary eta' mass measurements using staggered fermions.

Strong correlation between ${\rm Tr}(\gamma_5\otimes 1)$ and topological charge.

Insights into the validity of the fourth-root trick in staggered fermions.

Abstract

The Asqtad improved staggered fermion formalism has been a valuable tool in successfully calculating the non-singlet parts of the hadronic spectrum. We are engaged in a project to calculate the spectrum of the pseudoscalar singlet mesons with 2+1-flavor Asqtad staggered gauge configurations. Propagators of flavor-singlet states incorporate contributions from both disconnected and connected diagrams, and hence are sensitive to any differences in the actions governing the sea and valence fermions on the lattice. As such, they also present the possibility of a probe of the validity of the ``fourth-root trick'' in the staggered fermion formulation. We present an update on our progress toward measuring the $\eta'$ mass on 2+1-flavor Asqtad staggered gauge configurations, including a review of methods and preliminary results. We also show a strong correlation between ${\rm Tr}(\gamma_5\otimes 1)$ and the topological charge in these configurations, as predicted by the index theorem.