Quark-Hadron Duality and Parity Violating Asymmetry of Electroweak Reactions in the Delta Region

A dynamical model of electroweak pion production reactions in the Delta(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-Delta form factor can be determined by the parity violating asymmetry of N(\vec{e},e') reactions. We first show that the recent data of (e,e') structure functions F_1 and F_2, 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 F_1, F_2, and F_3 for (\nu,e) and (\nu,\nu') processes also show the similar Quark-Hadron Duality. The spin dependent structure functions g_1 and g_2 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 g_1 and g_2, while our results for g_1 and some polarization observables associated with the exclusive p(\vec{e},e' pi) and \vec{p}(\vec{e},e' pi) reactions are in reasonably good agreement with the recent data. In the investigation of parity violating asymmetry A of N(\vec{e},e') reactions, it is found that the non-resonant contribution is small at the Delta peak and a measurement of A can be used to distinguish two previously determined axial N-Delta transition form factors. The predicted asymmetry A are also compared with the Parton Model predictions for future experimental investigations of Quark-Hadron Duality.