The Role of the $\Delta (1920)$ 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 $\pi N\to \Sigma K$. 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 $\Delta (1920)\frac{3}{2}({\frac{3}{2}}^{+})$ -- are taken into account coherently in the calculations of the $\pi N\to \Sigma K$ 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 $\pi N\to \Sigma k$ reactions, i.e. ${\pi }^{+}p\to {\Sigma }^{+}{K}^{+}$, ${\pi }^{-}p\to {\Sigma }^{-}{K}^{+}$, ${\pi }^{+}n\to {\Sigma }^0{K}^{+}$ (${\pi }^{-}p\to {\Sigma }^{-}{K}^{+}$) and ${\pi }^{0}p\to {\Sigma }^0{K}^{+}$ differ not only by absolute values but also by their energy dependence. This shape differences are due to the mixture of the isospin $I=3/2$ $\Delta (1920)$ with isospin $I=1/2$ nucleon resonances. However, this $I=3/2$ resonance does not give a contribution to the $\pi N\to \Lambda K$ reactions. So the shapes of the total cross sections $\pi N\to \Lambda K$ 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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References in corpus (1)

• Strong Decays of $Q\bar{Q}$ Mesons

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• In-medium effects in strangeness production in heavy-ion collisions at (sub-)threshold energies
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• Proposal for Studying $N^{\ast }$ Resonances with $\bar{p}p\to \bar{p}n{\pi }^{+}$ Reaction
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• Reexamination of the role of the ${\Delta }^{\ast }$ resonances in the $pp\to n{K}^{+}{\Sigma }^{+}$ reaction
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