Effects of non-equilibrated topological charge distributions on pseudoscalar meson masses and decay constants

TL;DR

This paper investigates how non-equilibrated topological charge distributions affect lattice QCD calculations of pseudoscalar meson properties, providing theoretical insights and comparisons with numerical simulations to estimate systematic errors.

Contribution

It extends chiral perturbation theory to include effects of non-equilibrated topological charge on meson masses and decay constants, including heavy-light mesons and staggered taste violations.

Findings

Agreement with MILC lattice data within large statistical errors

Provides a method to correct for or estimate systematic errors from topological charge non-equilibration

Extends partially quenched chiral theory beyond previously known bounds

Abstract

We study the effects of failure to equilibrate the squared topological charge $Q^2$ on lattice calculations of pseudoscalar masses and decay constants. The analysis is based on chiral perturbation theory calculations of the dependence of these quantities on the QCD vacuum angle $\theta$. For the light-light partially quenched case, we rederive the known chiral perturbation theory results of Aoki and Fukaya, but using the nonperturbatively-valid chiral theory worked out by Golterman, Sharpe and Singleton, and by Sharpe and Shoresh. We then extend these calculations to heavy-light mesons. Results when staggered taste-violations are important are also presented. The derived $Q^2$ dependence is compared to that of simulations using the MILC collaboration's ensembles of lattices with four flavors of HISQ dynamical quarks. We find agreement, albeit with large statistical errors. These results can be used to correct for the leading effects of unequilibrated $Q^2$, or to make estimates of the systematic error coming from the failure to equilibrate $Q^2$. In an appendix, we show that the partially quenched chiral theory may be extended beyond a lower bound on valence masses discovered by Sharpe and Shoresh. Subtleties occurring when a sea-quark mass vanishes are discussed in another appendix.