Non-equilibration of topological charge and its effects

TL;DR

This paper investigates the slow evolution of topological charge in lattice QCD simulations, assesses its impact on physical results, and proposes strategies to estimate and correct for these effects using chiral perturbation theory and lattice data.

Contribution

It provides a detailed analysis of topological charge non-equilibration effects in lattice QCD and introduces methods to estimate and mitigate their impact on physical observables.

Findings

Agreement between lattice data and chiral perturbation theory supports error estimation.

Strategies for correcting topological charge effects are proposed.

Confidence in error estimates from slow topology change is demonstrated.

Abstract

In QCD simulations at small lattice spacings, the topological charge Q evolves very slowly and, if this quantity is not properly equilibrated, we could get incorrect results for physical quantities, or incorrect estimates of their errors. We use the known relation between the dependence of masses and decay constants on the QCD vacuum angle theta and the squared topological charge Q^2 together with chiral perturbation theory results for the dependence of masses and decay constants on theta to estimate the size of these effects and suggest strategies for dealing with them. For the partially quenched case, we sketch an alternative derivation of the known $\chi$PT results of Aoki and Fukaya, using the nonperturbatively correct chiral theory worked out by Golterman, Sharpe and Singleton, and by Sharpe and Shoresh. With the MILC collaboration's ensembles of lattices with four flavors of HISQ dynamical quarks, we measure the $Q^2$ dependence of masses and decay constants and compare to the $\chi$PT forms. The observed agreement gives us confidence that we can reliably estimate the errors from slow topology change, and even correct for its leading effects.