We present a QCD analysis of the effective weak Hamiltonian at hadronic energy scales for strangeness-nonchanging ($\mathrm{\Delta }S=0$) hadronic processes. Performing a leading-order renormalization group analysis in QCD from the W to the $\mathcal{O}(2\text{GeV})$ energy scale, we derive the pertinent effective Hamiltonian for hadronic parity violation, including the effects of both neutral and charged weak currents. We compute the complete renormalization group evolution of all isosectors and the evolution through heavy-flavor thresholds for the first time. We show that the additional four-quark operators that enter below the W mass scale from QCD operator mixing effects form a closed set, and they result in a $12\times 12$ anomalous dimension matrix. Computing the resulting effective Hamiltonian and comparing to earlier results, we affirm the importance of operator mixing effects and find, as an example, that the parity-violating pion-nucleon coupling constant, using the factorization Ansatz and an assessment of the pertinent quark charge of the nucleon in lattice QCD at the 2 GeV scale, is in better agreement with recent experiments.

我们提出了在强子能量尺度上的有效弱哈密顿量的 QCD 分析，用于奇异不变（$\mathrm{\Delta }\mathrm{小号}=0$) 强子过程。在 QCD 中执行从W到$\mathcal{○}(2\text{锗钒})$在能量尺度上，我们推导出强子宇称违反的相关有效哈密顿量，包括中性和带电弱电流的影响。我们首次计算了所有等扇区的完全重整化群演化以及通过重味阈值的演化。我们表明，从 QCD 算子混合效应进入W质量标度以下的额外四夸克算子形成一个封闭集，它们导致$12\times 12$异常维度矩阵。计算得到的有效哈密顿量并与早期结果进行比较，我们确认算子混合效应的重要性，并发现，例如，违反宇称的介子 - 核子耦合常数，使用分解Ansatz和相关夸克电荷的评估2 GeV 尺度的晶格 QCD 中的核子与最近的实验更加一致。