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QCD Analysis of ∆S = 0 Hadronic Parity Violation

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Speaker(s) / Presenter(s):
Girish Muralidhara (University of Kentucky)

We present a QCD analysis of the effective weak Hamiltonian at hadronic energy scales for strangeness-nonchanging (∆S = 0) hadronic processes. Performing a leading-order renormalization group analysis in QCD from the weak to the O(2 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 electroweak scale from QCD operator mixing effects form a closed set, and they result in a 12×12 anomalous dimension matrix. We use the resulting effective Hamiltonian to determine the parity-violating meson-nucleon coupling constants, h^1_π , h^{ 0,1,2}_ ρ , h^{0,1}_ ω , employing the factorization Ansatz and assessments of the pertinent quark charges of the nucleon in lattice QCD at the 2 GeV scale. On this basis, we connect to earlier calculations of low-energy, hadronic parity-violating observables in few-nucleon systems to make theoretical predictions that we compare with recent experimental results, for a global view of the relative importance of the various isosectors. 

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