Continuum extrapolation of $B_K$ with staggered fermions

Understand

We report on recent progress in the calculation of $B_K$ 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---$a\approx$ 0.12, 0.09, 0.06 and 0.045 fm.
• Since Lattice 2010, we have reduced the statistical errors on the $a\approx 0.09\;$fm lattices by a factor of $\sim 3$, and roughly doubled the size of the $a\approx0.045\;$fm ensemble.
• We find that these improvements have a very significant impact on the continuum extrapolation, with the $a\approx 0.12\;$fm data lying outside the range of applicability of simple functional forms.