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$B K$ using HYP-smeared staggered fermions in $N f=2+1$ unquenched QCD by Bae, Taegil; Jang, Yong-Chull; Jung, Chulwoo; Kim, Hyung-Jin; Kim, Jongjeong; Kim, Kwangwoo; Lee, Weonjong; Sharpe, Stephen R.; Yoon, Boram is a scholarly article available to read on EtoBox.

What is $B K$ using HYP-smeared staggered fermions in $N f=2+1$ unquenched QCD about?

We present results for kaon mixing parameter $B_K$ calculated using HYP-smeared improved staggered fermions on the MILC asqtad lattices. We use three lattice spacings ($a\approx 0.12$, $0.09$ and $0.06\;$fm), ten different valence quark masses ($m\approx m_s/10-m_s$), and several light sea-quark masses in order to control the continuum and chiral extrapolations. We derive the next-to-leading order staggered chiral perturbation theory (SChPT) results necessary to fit our data, and use these results to do extrapolations based both on SU(2) and SU(3) SChPT. The SU(2) fitting is particularly straightforward because parameters related to taste-breaking and matching errors appear only at next-to-next-to-leading order. We match to the continuum renormalization scheme (NDR) using one-loop perturbation theory. Our final result is from the SU(2) analysis, with the SU(3) result providing a (less accurate) cross check. We find $B_K(\text{NDR}, \mu = 2 \text{GeV}) = 0.529 \pm 0.009 \pm 0.032$ and $\hat{B}_K =B_K(\text{RGI})= 0.724 \pm 0.012 \pm 0.043$, where the first error is statistical and the second systematic. The error is dominated by the truncation error in the matching factor. Our resul

Author

Bae, Taegil; Jang, Yong-Chull; Jung, Chulwoo; Kim, Hyung-Jin; Kim, Jongjeong; Kim, Kwangwoo; Lee, Weonjong; Sharpe, Stephen R.; Yoon, Boram

Published

2010

Language

EN