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$ΔS=0$ Hadronic Parity Violation in Next-to-Leading Order QCD: Anomalous Dimension Matrices and Their Implications

We construct the effective Hamiltonian for hadronic parity violation in strangeness-nonchanging ($ΔS=0$) processes in next-to-leading order (NLO) in QCD, for all isosectors, and at a renormalization scale of 2 GeV, thus extending our earlier leading-order (LO) analysis. Hadronic parity violation, studied in the context of the low-energy interactions of nucleons and nuclei, exposes the complex interplay of weak and strong interactions in these systems, and thus supports our extension to NLO. Here we exploit the flavor-blind nature of QCD interactions to construct the needed anomalous dimension matrices from those computed in flavor physics, which we then use to refine our effective Hamiltonian and finally our predicted parity-violating meson-nucleon coupling constants, to find improved agreement with few-body experiments.