## Abstract

We present a QCD analysis of the effective weak Hamiltonian at hadronic energy scales for strangeness-nonchanging (ΔS=0) hadronic processes. Performing a leading-order renormalization group analysis in QCD from the W to the O(2GeV) 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 12×12 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.

Original language | English |
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Article number | 137372 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 833 |

DOIs | |

State | Published - Oct 10 2022 |

### Bibliographical note

Funding Information:We acknowledge partial support from the U.S. Department of Energy Office of Nuclear Physics under contract DE-FG02-96ER40989 . We thank the INT for gracious hospitality and acknowledge lively discussions with the workshop participants of “Hadronic Parity Nonconservation II” while this work was being completed.

Publisher Copyright:

© 2022

## ASJC Scopus subject areas

- Nuclear and High Energy Physics