标题： 关于四夸克算符的异常维数的两环penguin贡献 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QCD中$\Delta F = 1$四夸克算符的反常维度的次领头阶（两环）贡献。我们指出文献中结果存在一个问题。通过分解得到现有结果的步骤，我们确定了问题的来源，这与称为$Q_{11}$的算符有关。我们展示了如何解决这个问题并提供了修正后的反常维度。基于我们的发现，我们提出了一种不同于文献中使用的方法，该方法不受已识别问题的影响，并确认了我们修正后的结果。我们评估了修正的数值影响，这恰好在$5\%$范围内。我们的结果对于在$\Delta F = 1$过程中（如K介子和$B$介子的衰变）对超出标准模型的物理分析中正确重求和次领头对数非常重要。 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 point out 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 $5\%$. 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.