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 $Q^2$ 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.

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. D

References in corpus (6)

• Critical slowing down and error analysis in lattice QCD simulations
• Finite volume QCD at fixed topological charge
• Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks
• Staggered Chiral Perturbation Theory and the Fourth-Root Trick
• Effective field theories for QCD with rooted staggered fermions
• Diffusion of topological charge in lattice QCD simulations

Cited by in corpus (18)

• FLAG Review 2019
• FLAG Review 2021
• $B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD
• Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD
• $B_s\to D_s\ell \nu$ Form Factors for the full $q^2$ range from Lattice QCD with non-perturbatively normalized currents
• $B\to K$ and $D\to K$ form factors from fully relativistic lattice QCD
• FLAG Review 2024
• Charmonium properties from lattice QCD + QED: hyperfine splitting, $J/\psi$ leptonic width, charm quark mass and $a_{\mu }^c$
• Sp(4) gauge theories on the lattice: Quenched fundamental and antisymmetric fermions
• Lattice QCD form factor for $B_s\to D_s^{\ast }l\nu$ at zero recoil with non-perturbative current renormalisation
• $|V_{us}|$ from $K_{\ell 3}$ decay and four-flavor lattice QCD
• Contribution of the QCD $\Theta$-term to nucleon electric dipole moment
• QCD $\theta$-vacuum energy and axion properties
• D-meson semileptonic decays to pseudoscalars from four-flavor lattice QCD
• Bottomonium precision tests from full lattice QCD: hyperfine splitting, ${\rm Y}$ leptonic width and $b$ quark contribution to $e^{+}{e}^{-}\to$ hadrons
• Strong coupling constant and quark masses from lattice QCD
• Form factors for the processes $B_c^{+}\to D^0{\ell }^{+}{\nu }_{\ell }$ and $B_c^{+}\to D_s^{+}{\ell }^{+}{\ell }^{-}(\nu \overline{\nu })$ from lattice QCD
• Parallel Tempered Metadynamics: Overcoming potential barriers without surfing or tunneling