QCD Analysis of $\Delta S=0$ Hadronic Parity Violation

TL;DR

This paper performs a detailed QCD analysis of the effective weak Hamiltonian for $\Delta S=0$ hadronic processes, including operator mixing and renormalization group evolution, to improve understanding of hadronic parity violation.

Contribution

It introduces a comprehensive leading-order QCD renormalization group analysis for $\Delta S=0$ processes, including heavy-flavor thresholds and operator mixing effects, providing more accurate effective Hamiltonians.

Findings

Enhanced agreement of parity-violating pion-nucleon coupling with experiments.

First complete calculation of operator evolution through heavy-flavor thresholds.

Demonstration of a closed set of four-quark operators under QCD mixing.

Abstract

We present a QCD analysis of the effective weak Hamiltonian at hadronic energy scales for strangeness-nonchanging ($\Delta S=0$) hadronic processes. Performing a leading-order renormalization group analysis in QCD from the $W$ to the ${\cal O}(2\,\rm GeV)$ 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.