Resonance Model of $πΔ\rightarrow Y K$ for Kaon Production in Heavy Ion Collisions

Abstract

The elementary production cross sections $πΔ\rightarrow Y K$ $(Y=Σ,\,\, Λ)$ and $πN \rightarrow Y K$ are needed to describe kaon production in heavy ion collisions. The $πN \rightarrow Y K$ 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 $πΔ\rightarrow Y K$ at intermediate energies (from the kaon production threshold to3 GeV of $πΔ$ 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 $πΔ\rightarrow ΣK$ 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 $πΔ\rightarrow ΛK$ reactions are taken into account coherently as the intermediate states in the calculations. Also t-channel $K^*(892) \frac{1}{2}(1^-)$ vector meson exchange is included. The results show that $K^*(892)$ exchange is neglegible for the $πΔ\rightarrow ΣK$ reactions, whereas this meson does not contribute to the $πΔ\rightarrow ΛK$ reactions. Furthemore, the $πΔ\rightarrow Y K$ contributions to kaon production in heavy ion collisions are not only non-neglegible but also very different from the $πN \rightarrow Y K$ reactions. An argument valid for $πN \rightarrow Y K$ cannot be extended to $πΔ\rightarrow Y K$ reactions. Therefore, cross sections for $πΔ\rightarrow Y K$ including correctly the different isospins must be