Quark-hadron duality and parity violating asymmetry of electroweak reactions in the Δ region

A dynamical model [T. Sato and T.-S. H. Lee, Phys. Rev. C 54, 2660 (1996); 63, 055201 (2001); T. Sato, D. Uno, and T.-S. H. Lee, ibid. 67, 065201 (2003)] of electroweak pion production reactions in the Δ(1232) region has been extended to include the neutral current contributions for examining the local quark-hadron duality in neutrino-induced reactions and for investigating how the axial N-Δ form factor can be determined by the parity violating asymmetry of N(e⃗,e^') reactions. We first show that the recent data of (e,e^') structure functions F₁ and F₂, which exhibit the quark-hadron duality, are in good agreement with our predictions. For possible future experimental tests, we then predict that the structure functions F₁,F₂, and F₃ for (ν,e) and (ν,ν^') processes also show the similar quark-hadron duality. The spin-dependent structure functions g₁ and g₂ of (e,e^') have also been calculated from our model. It is found that the local quark-hadron duality is not seen in the calculated g₁ and g₂, while our results for g₁ and some polarization observables associated with the exclusive p(e⃗,e^'π) and p⃗(e⃗,e^'π) reactions are in reasonably good agreement with the recent data. In the study of parity violating asymmetry A of N(e⃗,e^') reactions, the relative importance between the nonresonant mechanisms and the Δ excitation is investigated by taking into account the unitarity condition. Predictions are made for using the data of A to test the axial N-Δ form factors determined previously in the studies of N(ν_μ,μ^-π) reactions. The predicted asymmetry A are also compared with the parton model predictions for future experimental investigations of quark-hadron duality.