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

Non-equilibration of topological charge and its effects