Determination of $B_K$ using improved staggered fermions (I): SU(3) chiral perturbation theory fit

Abstract

We present the results for $B_K$ calculated using HYP-smeared staggered fermions using lattices generated by the MILC collaboration using the asqtad staggered action. We have done the calculation on 8 ensembles of these lattices, including three different lattice spacings ($a=0.12,0.09,0.06$ fm). We fit the data to forms based on those predicted by SU(3) mixed-action partially-quenched staggered chiral perturbation theory. Our preliminary result is $B_K(\text{NDR},\mu =2\text{GeV})=0.528\pm 0.011\pm 0.048$, where the first error is statistical and the second systematic. The error turns out to be larger than that from an analysis using SU(2) chiral perturbation theory.

Comments: 7 pages, 2 figures, Lattice 2009 proceeding