标题： 关于两圈啄型贡献至四夸克算符的反常维度 显示英文标题

标题： On the two-loop penguin contributions to the Anomalous Dimensions of four-quark operators

摘要： 我们重新审视了量子色动力学中四夸克算符$\Delta F = 1$的次领头阶（两圈）贡献的反常维度。我们设计了一种测试反常维度的方法，我们认为这种方法具有普遍意义，并通过该方法发现了文献中现有结果中的一个问题。通过对导致现有结果的步骤进行剖析，我们确定了问题的根源，这与被称为$Q_{11}$的算符有关。我们展示了如何修正这个问题，并提供了修正后的反常维度。基于我们的发现，我们提出了一个替代的方法，这种方法没有文献中所使用方法存在的缺陷，并且验证了我们的修正结果。我们评估了修正结果的数值影响，在某些演化矩阵的条目中，其影响大约相当于$5\%$。我们的结果对于正确重整次领头对数在超出标准模型物理的分析中非常重要，例如 kaon 和$B$-介子衰变等$\Delta F = 1$过程中。 显示英文摘要

摘要： We revisit the Next-to-Leading Order (two-loop) contributions to the Anomalous Dimensions of $\Delta F = 1$ four-quark operators in QCD. We devise a test for anomalous dimensions, that we regard as of general interest, and by means of which we detect a problem in the results available in the literature. Deconstructing the steps leading to the available result, we identify the source of the problem, which is related to the operator known as $Q_{11}$. We show how to fix the problem and provide the corrected anomalous dimensions. With the insight of our findings, we propose an alternative approach to the one used in the literature which does not suffer from the identified disease, and which confirms our corrected results. We assess the numerical impact of our corrections, which happens to be in the ballpark of $5\%$ in certain entries of the evolution matrix. Our results are important for the correct resummation of Next-to-Leading Logarithms in analyses of physics beyond the Standard Model in $\Delta F = 1$ processes, such as the decays of Kaons and $B$-mesons.