Continuum extrapolation of BK with staggered fermions

We report on recent progress in the calculation of BK using HYP-smeared staggered fermions on the MILC asqtad lattices. Our main focus is on the continuum extrapolation, which is done using (up to) four different lattice spacings—a ≈ 0.12, 0.09, 0.06 and 0.045 fm. Since Lattice 2010, we have reduced the statistical errors on the a ≈ 0.09 fm lattices by a factor of ∼ 3, and roughly doubled the size of the a ≈ 0.045 fm ensemble. We find that these improvements have a very significant impact on the continuum extrapolation, with the a ≈ 0.12 fm data lying outside the range of applicability of simple functional forms. Hence we use only the three smallest lattice spacings to perform the extrapolation, finding B̂K = BK(RGI) = 0.725±0.004(stat)±0.038(sys). This value is consistent with our published value from 2010 (based the three coarsest lattice spacings), but has smaller errors.