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, which is a relativistic tree-level treatment. This study is the first attempt to complete a systematic consistent investigation of the elementary kaon production reactions for both the pion-baryon and baryon-baryon reactions. Our model suggests that the magnitudes of the isospin-averaged total cross sections for the $N\overrightarrow{N}\mathrm{NYK}$ and $\Delta \overrightarrow{N}\mathrm{NYK}\hspace{0.5em}(Y=\Lambda$ 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 $\mathrm{NN}$ reactions at energies about 1 GeV above threshold. Furthermore, the magnitudes of the isospin-averaged total cross sections for the $N\overrightarrow{N}\Delta \mathrm{YK}$ reactions turn out to be comparable to those for the $N\overrightarrow{N}\mathrm{NYK}$ reactions at $\mathrm{NN}$ invariant collision energies about 3.1 GeV, and about 5 to 10 times larger at $\mathrm{NN}$ invariant collision energies about 3.5 GeV. The microscopic cross sections are parametrized in all isospin channels necessary for the transport model studies of kaon production in heavy-ion collisions. These cross sections are then applied in the relativistic transport model to study the sensitivity to the underlying elementary kaon production cross sections.