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

Abstract

We study the effects of failure to equilibrate the squared topological charge Q2Q^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 θ\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 Q2Q^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 Q2Q^2, or to make estimates of the systematic error coming from the failure to equilibrate Q2Q^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.Comment: 46 pages, 5 figures; added section on the effect of staggered taste violations and made other improvements for clarity. Version to be published in Phys. Rev.

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