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arXiv 1012.4178hep-lathep-ph
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$B_K$从2+1风味结构域壁QCD的连续极限

Continuum Limit of $B_K$ from 2+1 Flavor Domain Wall QCD

Y. Aoki, R. Arthur, T. Blum, P. A. Boyle, D. Brömmel, N. H. Christ, C. Dawson, T. Izubuchi, C. Jung, C. Kelly, R. D. Kenway, M. Lightman, R. D. Mawhinney, Shige… 展开作者

Y. Aoki, R. Arthur, T. Blum, P. A. Boyle, D. Brömmel, N. H. Christ, C. Dawson, T. Izubuchi, C. Jung, C. Kelly, R. D. Kenway, M. Lightman, R. D. Mawhinney, Shigemi Ohta, C. T. Sachrajda, E. E. Scholz, A. Soni, C. Sturm, J. Wennekers, R. Zhou

摘要:

利用岩崎规范作用量,在两种不同的晶格间距下,确定了畴壁费米子2+1味的连续极限下的中性K介子混合矩阵元$B_K$.这些格点费米子具有接近精确的手征对称性,因此避免了人工格点算符混合。我们介绍了一个显着的改进,传统的NPR方法,其中裸矩阵元素重整化非微扰的RI-RISK计划,然后转换成MSbar计划使用连续扰动理论。除了RI-100,我们引入并实现了四个非例外的中间动量计划,抑制红外非微扰的不确定性重整化过程。我们计算的转换因子有关的矩阵元素在这个家庭的RI-Sirtons计划和MSbar在一个循环的顺序。使用这些不同的中间方案获得的结果的比较允许未知的高阶贡献的更可靠的估计,因此允许相应地更稳健的系统误差的估计。我们还应用了最近提出的方法,其中扭曲的边界条件被用来控制Symanzik展开的离壳顶点函数,从而更好地控制重正化的连续极限。我们控制手征外推的误差,同时考虑非线性光学SU(2)手征有效理论,和解析质量展开。我们得到了$B_K^{\msbar}(3 GeV) = 0.529(5)_{stat}(15)_χ(2)_{FV}(11)_{NPR}$。这对应于$\hat{B}_K = 0.749(7)_{stat}(21)_χ(3)_{FV}(15)_{NPR}$。将所有误差源相加,得到$\hat{B}_K = 0.749(27)_{combined}$,总误差为3.6%。

英文摘要:

We determine the neutral kaon mixing matrix element $B_K$ in the continuum limit with 2+1 flavors of domain wall fermions, using the Iwasaki gauge action at two different lattice spacings. These lattice fermions have near exact chiral symmetry and therefore avoid artificial lattice operator mixing. We introduce a significant improvement to the conventional NPR method in which the bare matrix elements are renormalized non-perturbatively in the RI-MOM scheme and are then converted into the MSbar scheme using continuum perturbation theory. In addition to RI-MOM, we introduce and implement four non-exceptional intermediate momentum schemes that suppress infrared non-perturbative uncertainties in the renormalization procedure. We compute the conversion factors relating the matrix elements in this family of RI-SMOM schemes and MSbar at one-loop order. Comparison of the results obtained using these different intermediate schemes allows for a more reliable estimate of the unknown higher-order contributions and hence for a correspondingly more robust estimate of the systematic error. We also apply a recently proposed approach in which twisted boundary conditions are used to control the Symanzik expansion for off-shell vertex functions leading to a better control of the renormalization in the continuum limit. We control chiral extrapolation errors by considering both the NLO SU(2) chiral effective theory, and an analytic mass expansion. We obtain $B_K^{\msbar}(3 GeV) = 0.529(5)_{stat}(15)_χ(2)_{FV}(11)_{NPR}$. This corresponds to $\hat{B}_K = 0.749(7)_{stat}(21)_χ(3)_{FV}(15)_{NPR}$. Adding all sources of error in quadrature we obtain $\hat{B}_K = 0.749(27)_{combined}$, with an overall combined error of 3.6%.

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