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arXiv · 1110.2576

Continuum extrapolation of $B_K$ with staggered fermions

Weonjong Lee·Yong-Chull Jang·Hyung-Jin Kim·Jangho Kim·Kwangwoo Kim·Boram Yoon·Taegil Bae·Chulwoo Jung·Jongjeong Kim·Stephen R. Sharpe·SWME Collaboration
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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 $a\approx0.045\;$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. 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.

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Weonjong Lee, Yong-Chull Jang, Hyung-Jin Kim, Jangho Kim, Kwangwoo Kim, Boram Yoon, Taegil Bae, Chulwoo Jung, Jongjeong Kim, Stephen R. Sharpe, SWME Collaboration. 2011-11-02. Continuum extrapolation of $B_K$ with staggered fermions. https://arxiv.org/abs/1110.2576

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