Continuum extrapolation of $B_K$ with staggered fermions

Abstract

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 $a\approx 0.045$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. Hence we use only the three smallest lattice spacings to perform the extrapolation, finding ${\hat{B}}_K=B_K(\text{RGI})=0.725\pm 0.004(\text{stat})\pm 0.038(\text{sys})$. This value is consistent with our published value from 2010 (based the three coarsest lattice spacings), but has smaller errors.

Comments: 7 pages, 6 figures, references updated