### Speaker

Doug Toussaint
(University of Arizona)

### Description

[MILC collaboration}
In QCD simulations at small lattice spacings the topological charge $Q$
evolves very slowly, and if this quantity is not properly equilibrated
it could lead to 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
nonperturbative correct chiral theory worked out by Golterman, Sharpe and
Singleton. 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 some confidence that we can reliably estimate the
errors from slow topology change, and even correct for its
leading effects.

### Primary authors

Claude Bernard
(Washington University)
Doug Toussaint
(University of Arizona)