标准模型中$K\toππ$衰变的直接CP破坏和$ΔI=1/2$规则
Direct CP violation and the $ΔI=1/2$ rule in $K\toππ$ decay from the Standard Model
摘要：
我们提出了$ΔI=1/2$，$K\toππ$衰变振幅$A_0$和$\varepsilon'$的晶格QCD计算，$K\toππ$衰变中直接CP破坏的度量，改进了我们2015年对这些量的计算。这两个计算进行了物理运动学上的$32^3\times 64$晶格与逆晶格间距的$a^{-1}=1.3784(68)$ GeV。然而，目前的计算包括近四倍的统计数据和许多技术改进，使我们能够更可靠地隔离$ππ$基态，并更准确地将晶格算子与标准模型中定义的晶格算子联系起来。我们发现${\rm Re}(A_0)=2.99(0.32)(0.59)\times 10^{-7}$ GeV和${\rm Im}(A_0)=-6.98(0.62)(1.44)\times 10^{-11}$ GeV，其中的错误是统计和系统，分别。前者与实验结果${\rm Re}(A_0)=3.3201(18)\times 10^{-7}$ GeV符合得很好。$A_0$的这些结果可以与我们早先对$A_2$的晶格计算相结合，得到${\rm Re}(\varepsilon'/\varepsilon)=21.7(2.6)(6.2)(5.0) \times 10^{-4}$，其中第三个误差代表遗漏的同位旋破缺效应，以及Re $(A_0)$ /Re $(A_2) = 19.9(2.3)(4.4)$。第一个结果与${\rm Re}(\varepsilon'/\varepsilon)=16.6(2.3)\times 10^{-4}$的实验结果一致。第二个与观察到的比率Re $(A_0)/$ Re $(A_2) = 22.45(6)$的比较，证明了这种“$ΔI = 1/2$规则”增强的标准模型起源。
英文摘要：
We present a lattice QCD calculation of the $ΔI=1/2$, $K\toππ$ decay amplitude $A_0$ and $\varepsilon'$, the measure of direct CP-violation in $K\toππ$ decay, improving our 2015 calculation of these quantities. Both calculations were performed with physical kinematics on a $32^3\times 64$ lattice with an inverse lattice spacing of $a^{-1}=1.3784(68)$ GeV. However, the current calculation includes nearly four times the statistics and numerous technical improvements allowing us to more reliably isolate the $ππ$ ground-state and more accurately relate the lattice operators to those defined in the Standard Model. We find ${\rm Re}(A_0)=2.99(0.32)(0.59)\times 10^{-7}$ GeV and ${\rm Im}(A_0)=-6.98(0.62)(1.44)\times 10^{-11}$ GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result ${\rm Re}(A_0)=3.3201(18)\times 10^{-7}$ GeV. These results for $A_0$ can be combined with our earlier lattice calculation of $A_2$ to obtain ${\rm Re}(\varepsilon'/\varepsilon)=21.7(2.6)(6.2)(5.0) \times 10^{-4}$, where the third error represents omitted isospin breaking effects, and Re$(A_0)$/Re$(A_2) = 19.9(2.3)(4.4)$. The first agrees well with the experimental result of ${\rm Re}(\varepsilon'/\varepsilon)=16.6(2.3)\times 10^{-4}$. A comparison of the second with the observed ratio Re$(A_0)/$Re$(A_2) = 22.45(6)$, demonstrates the Standard Model origin of this "$ΔI = 1/2$ rule" enhancement.
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