Weak Production of Nucleon Resonances

We present a dynamical and fully covariant model for the weak production from nucleons of the $N^{*}\mathrm{}\left(1236\right)\mathrm{}$ and higher-mass resonances. The analytic structure and unitarity of the partial-wave helicity amplitudes are incorporated in this model which has a simple $\frac{N}{D}$ form. Above the $\pi \pi N$ threshold, the excitation and rescattering of hadronic eigenstates are considered. For the excitation mechanism we use pion, nucleon, and vector-meson exchange. By using the conserved vector-current theory and a previous calculation for electroproduction, we ascertain beforehand all the necessary normalizations, which result from the final-state enhancement factors, and thereby perform an absolute calculation for weak production. Predictions are given for the differential and total cross sections in the first four resonance regions, and a favorable comparison is made with the existing data from CERN. Our results for the $N^{*}\mathrm{}\left(1236\right)\mathrm{}$ are considerably different from the predictions made by Adler in a calculation which treats that one resonance. Since we derive the cross-section formulas keeping all dependence on the lepton mass, we can examine the interesting behavior as the forward direction is approached. The partially conserved axial-vector current hypothesis, its implications for resonance production, and the role of our model in designing a test of it are also discussed.