Resonance Model of $\pi \Delta \to YK$ for Kaon Production in Heavy Ion Collisions

Abstract

The elementary production cross sections $\pi \Delta \to YK$ $(Y=\Sigma ,\Lambda )$ and $\pi N\to YK$ are needed to describe kaon production in heavy ion collisions. The $\pi N\to YK$ reactions were studied previously by a resonance model. The model can explain the experimental data quite well \cite{tsu}. In this article, the total cross sections $\pi \Delta \to YK$ at intermediate energies (from the kaon production threshold to3 GeV of $\pi \Delta$ center-of-mass energy) are calculated for the first time using the same resonance model. The resonances, $N(1710)I(J^P)=\frac{1}{2}({\frac{1}{2}}^{+})$ and $N(1720)\frac{1}{2}({\frac{3}{2}}^{+})$ for the $\pi \Delta \to \Sigma K$ reactions, and $N(1650)\frac{1}{2}({\frac{1}{2}}^{-})$, $N(1710)\frac{1}{2}({\frac{1}{2}}^{+})$ and $N(1720)\frac{1}{2}({\frac{3}{2}}^{+})$ for the $\pi \Delta \to \Lambda K$ reactions are taken into account coherently as the intermediate states in the calculations. Also t-channel $K^{\ast }(892)\frac{1}{2}(1^{-})$ vector meson exchange is included. The results show that $K^{\ast }(892)$ exchange is neglegible for the $\pi \Delta \to \Sigma K$ reactions, whereas this meson does not contribute to the $\pi \Delta \to \Lambda K$ reactions. Furthemore, the $\pi \Delta \to YK$ contributions to kaon production in heavy ion collisions are not only non-neglegible but also very different from the $\pi N\to YK$ reactions. An argument valid for $\pi N\to YK$ cannot be extended to $\pi \Delta \to YK$ reactions. Therefore, cross sections for $\pi \Delta \to YK$ including correctly the different isospins must be

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