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arXiv 1807.01709hep-phhep-exhep-lat
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$ε'/ε$和$K\toππ$衰变的BSM强子矩阵元的双QCD方法

BSM Hadronic Matrix Elements for $ε'/ε$ and $K\toππ$ Decays in the Dual QCD Approach

Jason Aebischer, Andrzej J. Buras, Jean-Marc Gerard

备注：
39 pages, no figures, clarifying comments added, conclusions unchanged, version to appear in JHEP
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摘要：

我们首次计算了所有可能对$K\toππ$衰变有贡献的定域算符的四夸克强子矩阵元，特别是对标准模型之外的比率$ε'/ε$有贡献的定域算符的矩阵元。为此，我们使用双QCD（DQCD）方法。除了7个新的镜像算符从SM的手征翻转，我们计数13个BSM四夸克算符的给定的手征线性相互独立的和上述14个运营商的强子矩阵元是已知的。我们给出了所有这些算符的两种基的结果，一种称为DQCD基，适用于DQCD方法中强子矩阵元的计算;另一种称为SD基，适用于1~GeV以上的短程重整化群演化.我们证明了长距离演化（介子演化）的模式与短距离演化（夸克-胶子演化）的模式相匹配，据我们所知，这是目前在任何其他分析框架中都无法实现的属性。本文的重点是张量-张量和标量-标量BSM算子的手征增强矩阵元。因此，他们可以解释出现的$ε'/ε$异常，这是强烈表明在DQCD与格点量子色动力学的一些支持。另一方面，我们不期望BSM运算符与$ΔI=1/2$规则相关。

英文摘要：

We calculate for the first time all four-quark hadronic matrix elements of local operators possibly contributing to $K\toππ$ decays and in particular to the ratio $ε'/ε$ beyond the Standard Model (BSM). To this end we use the Dual QCD (DQCD) approach. In addition to 7 new mirror operators obtained from the SM ones by flipping the chirality, we count 13 BSM four-quark operators of a given chirality linearly independent of each other and of the aforesaid 14 operators for which hadronic matrix elements are already known. We present results in two bases for all these operators, one termed DQCD basis useful for the calculation of the hadronic matrix elements in the DQCD approach and the other called SD basis suited to the short distance renormalization group evolution above the 1~GeV scale. We demonstrate that the pattern of long distance evolution (meson evolution) matches the one of short distance evolution (quark-gluon evolution), a property which to our knowledge cannot be presently achieved in any other analytical framework. The highlights of our paper are chirally enhanced matrix elements of tensor-tensor and scalar-scalar BSM operators. They could thereby explain the emerging $ε'/ε$ anomaly which is strongly indicated within DQCD with some support from lattice QCD. On the other hand we do not expect the BSM operators to be relevant for the $ΔI=1/2$ rule.

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