Theory ofπ (K)+N→π (K)+ΔReactions

Abstract

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