Theory ofπ (K)+N→π (K)+ΔReactions

The production of the $\Delta \left(N_{\frac{3}{2},\frac{3}{2}}^{}{}_{}{}^{*}\right)$ and $Y_1^{}{}_{}{}^{*}\mathrm{}\left(1385\right)\mathrm{}$ $P_{\frac{3}{2}}$ isobars by $\pi$, $K$, and $\overline{K}$ mesons is discussed. We assume the Chew-Low static model for $\Delta$ and $Y_1^{}{}_{}{}^{*}$, but do not assume anything about the exchange mechanism such as the $\rho$-meson exchange. It is shown that for fixed small momentum transfer and for fixed energy the decay distributions of $\Delta$ and $Y_1^{}{}_{}{}^{*}$ and the distribution of the Treiman-Yang angle are equal to those predicted by the $\rho$ (or $K^{*}$) meson exchange model with $M1\mathrm{}\to P_{\frac{3}{2}}$ transition. This result is valid both for any elementary meson ($J>\mathrm{}0\mathrm{}$) exchange models and for the Regge-pole models. In the same approximation we obtain relations such as $\frac{d\sigma ({\pi }^{+}p\to {\pi }^0{\Delta }^{++})}{\mathrm{dt}}=\frac{\frac{3}{2}d\sigma ({\pi }^{+}n\to {\pi }^{0}p,\mathrm{spin}\mathrm{flip})}{\mathrm{dt}}$. Making use of the relation, we can predict that the spin-flip part of the $\pi N$ charge-exchange scattering is very large. The Regge-pole model is applied to these processes. In the $\rho$ (or $K^{*}$) Regge-pole exchange model, the angular distributions at a large momentum transfer $t\approx -1\mathrm{}$ ${\mathrm{}\left(\mathrm{BeV}\right)\mathrm{}}^2$ are found to be equal to those predicted by the $\rho$ (or $K^{*}$) meson exchange model with $L2\mathrm{}\to P_{\frac{3}{2}}$ transition.