Isospin-½ nucleon-resonance production by aV,Aweak neutral current

We define a set of ratios characterizing the production of the isospin-½ resonances $D_{13}\mathrm{}\left(1514\right)\mathrm{}$ and $S_{11}\mathrm{}\left(1505\right)\mathrm{}$, as well as the isospin-$\frac{3}{2}$ resonance $P_{33}\mathrm{}\left(1232\right)\mathrm{}$, by electromagnetic and weak (charged and neutral) currents. Assuming the most general weak neutral current with $V$, $A$ spatial structure, we calculate the matrix elements needed to extract the production ratios in three dynamical models for resonance production: the Born-approximation model, the nonrelativistic quark model, and the quark-bag model. For the special case of the Weinberg-Salam theory neutral current, the three models suggest that for $0\le {{sin}^2\theta }_W\le 0.5$ the ratios $\frac{D_{13}}{P_{33}}$ and $\frac{S_{11}}{P_{33}}$ observed in neutral-current ${\pi }^0$ or $\eta$ production on a free nucleon target should be substantially smaller (by a factor of 2 to 4) than the corresponding ratios observed in charged-current ${\pi }^0$ or $\eta$ production. We also attempt to predict the ratios $\frac{D_{13}}{P_{33}}$ and $\frac{S_{11}}{P_{33}}$ to be expected in charged-current production from the corresponding ratios observed in electroproduction, but here the three models do not agree, and so we can only state a wide possible range in which the values of the ratios may lie. We briefly discuss the chargeexchange corrections needed for comparison with experiments on complex nuclear targets; we find for an aluminum target that the reduction factors quoted above are halved, so that in neutral-current-induced reactions the ratios $\frac{D_{13}}{P_{33}}$ and $\frac{S_{11}}{P_{33}}$ are smaller by a factor of 1 to 2 than the corresponding ratios observed in charged-current-induced reactions.