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arXiv 2102.09308hep-phhep-lat
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四夸克算符$K\toππ$和真空矩阵元的SU（3）分析

SU(3) analysis of four-quark operators: $K\toππ$ and vacuum matrix elements

Antonio Pich, Antonio Rodríguez-Sánchez

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46 pages, 7 figures. Published version
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摘要：

局部四夸克算符的强子矩阵元在非轻子K介子衰变中起着核心作用，而真空矩阵元涉及相同种类的算符出现在包含色散关系中，例如那些与$τ$衰变分析相关的。使用一个$SU(3)_L\otimes SU(3)_R$分解的运营商，我们得到这些矩阵元素之间的一般关系，扩展了众所周知的结果，链接在两个不同的部门的观测。两个相关的唯象应用。首先，我们利用测得的$τ$衰变的强子谱函数，确定了电弱企鹅效应对K介子CP破坏比$\varepsilon'/\varepsilon$的贡献。其次，我们拟合我们的$SU(3)$动力学参数的$K\toππ$矩阵元素的最新晶格数据。这种数值拟合与以前的分析方法的结果的比较提供了一个有趣的解剖的$ΔI = \frac{1}{2}$增强，确认旧的建议，其潜在的动力学起源。

英文摘要：

Hadronic matrix elements of local four-quark operators play a central role in non-leptonic kaon decays, while vacuum matrix elements involving the same kind of operators appear in inclusive dispersion relations, such as those relevant in $τ$-decay analyses. Using an $SU(3)_L\otimes SU(3)_R$ decomposition of the operators, we derive generic relations between these matrix elements, extending well-known results that link observables in the two different sectors. Two relevant phenomenological applications are presented. First, we determine the electroweak-penguin contribution to the kaon CP-violating ratio $\varepsilon'/\varepsilon$, using the measured hadronic spectral functions in $τ$ decay. Second, we fit our $SU(3)$ dynamical parameters to the most recent lattice data on $K\toππ$ matrix elements. The comparison of this numerical fit with results from previous analytical approaches provides an interesting anatomy of the $ΔI = \frac{1}{2}$ enhancement, confirming old suggestions about its underlying dynamical origin.

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