Resonance model study of kaon production in baryon baryon reactions for heavy ion collisions

The energy dependence of the total kaon production cross sections in baryon baryon ($N$ and $\Delta$) collisions are studied in the resonance model. We parametrize them in all isospin channels necessary for the microscopic studies of kaon production in heavy ion collisions. This study completes a systematic, consistent investigation of the elementary kaon production reactions for both the pion baryon and baryon baryon reactions. It is shown that the magnitudes of the isospin-averaged total cross sections for the $N N \to N Y K$ and $\Delta N \to N Y K$ ($Y = \Lambda$ or $\Sigma$) reactions are almost equal at energies up to about 200 MeV above threshold. However, the magnitudes for the $\Delta N$ reactions become about 6 times larger than those for the $N N$ reactions at energies about 1 GeV above threshold. Furthermore, this investigation also includes those reactions with a $\Delta$ appearing in the final state, which are usually neglected in theoretical studies of kaon production in heavy ion collisions. In particular, the magnitudes of the isospin-averaged total cross sections for the $N N \to \Delta Y K$ reactions turn out to be comparable to those for the $N N \to N Y K$ reactions at $N N$ invariant collision energies about 3.1 GeV, and about 5 to 10 times larger at $N N$ invariant collision energies about 3.5 GeV.