${\Theta }^{+}$ baryon production in KN and NN reactions

We study ${\Theta }^{+}\mathrm{}\left(1540\right)\mathrm{}$ production in kaon-nucleon $\mathrm{}\left(\mathrm{KN}\right)\mathrm{}$ and nucleon-nucleon $\mathrm{}\left(\mathrm{NN}\right)\mathrm{}$ interactions by assuming that the ${\Theta }^{+}$ is an isosinglet with $J^P={\frac{1}{2}}^{+}.$ Possible t-channel diagrams with $K^{*}$ exchange are considered in both reactions as well as K exchange in NN reactions. The cross section for $n\overrightarrow{p}{\Lambda }^0{\Theta }^{+},$ which has not been considered in previous calculations, is found to be about a factor of 5 larger than that for $n\overrightarrow{p}{\Sigma }^0{\Theta }^{+}$ due to the large coupling of the $\mathrm{KN}\Lambda$ interaction. The cross sections are obtained by setting $g_{\mathrm{KN}\Theta }=1\mathrm{}$ and varying the ratio of $g_{K^{*}N\Theta }{/g}_{\mathrm{KN}\Theta }$ so that future experimental data can be used to estimate these couplings. We also find that the isospin relations hold for these reactions.