The Role of the $\hat{I}”(1920)$ Resonance for Kaon Production in Heavy Ion Collisions

Abstract

The long mean free path of $K^{+}$ mesons in nuclear matter makes this particle a suitable messenger for the dynamics of nucleus-nucleus reactions at intermediate energies (100 MeV to 3 GeV per nucleon). A prerequisite for this is the knowledge of the elementary production cross sections $\ddot{I}€N\to \hat{I}\pounds K$. Here these cross sections are studied for the first time with the explicite inclusion of the relevant baryon resonances up to 2 GeV as intermediate states. The baryon resonances -- $N(1710)I(J^P)=\frac{1}{2}({\frac{1}{2}}^{+}),N(1720)\frac{1}{2}({\frac{3}{2}}^{+})$ and $\hat{I}”(1920)\frac{3}{2}({\frac{3}{2}}^{+})$ -- are taken into account coherently in the calculations of the $\ddot{I}€N\to \hat{I}\pounds K$ process. (We refer to this model as the `resonance model'.) Also $K^{\ast }(892)\frac{1}{2}(1^{-})$ vector meson exchange is included. It is shown that the total cross sections for different channels of the $\ddot{I}€N\to \hat{I}\pounds k$ reactions, i.e. $\ddot{I}{€}^{+}p\to \hat{I}{\pounds }^{+}{K}^{+}$, $\ddot{I}{€}^{-}p\to \hat{I}{\pounds }^{-}{K}^{+}$, $\ddot{I}{€}^{+}n\to \hat{I}{\pounds }^0{K}^{+}$ ($\ddot{I}{€}^{-}p\to \hat{I}{\pounds }^{-}{K}^{+}$) and $\ddot{I}{€}^{0}p\to \hat{I}{\pounds }^0{K}^{+}$ differ not only by absolute values but also by their energy dependence. This shape differences are due to the mixture of the isospin $I=3/2$ $\hat{I}”(1920)$ with isospin $I=1/2$ nucleon resonances. However, this $I=3/2$ resonance does not give a contribution to the $\ddot{I}€N\to \hat{I}›K$ reactions. So the shapes of the total cross sections $\ddot{I}€N\to \hat{I}›K$ for different isospin projections are the same. In spite of this, such cross sections averaged over different isospin projections in the same multiplet

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