Production of Θ+ in γ+D→Λ+Θ+and γ+D→Σ+Θ+ reactions

The $\ensuremath{\gamma}+D\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}+{\mathrm{\ensuremath{\Theta}}}^{+}$ and $\ensuremath{\gamma}+D\ensuremath{\rightarrow}\mathrm{\ensuremath{\Sigma}}+{\mathrm{\ensuremath{\Theta}}}^{+}$ reactions can be used to determine the width of ${\mathrm{\ensuremath{\Theta}}}^{+}$ almost model independently. We calculate the differential cross sections of the $\ensuremath{\gamma}+D\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}+{\mathrm{\ensuremath{\Theta}}}^{+}$, $\ensuremath{\gamma}+D\ensuremath{\rightarrow}\mathrm{\ensuremath{\Sigma}}+{\mathrm{\ensuremath{\Theta}}}^{+}$ and relevant background reactions in the photon energy range $1.2\ensuremath{\leqslant}{E}_{\ensuremath{\gamma}}\ensuremath{\leqslant}2.6\phantom{\rule{0.3em}{0ex}}\mathrm{GeV}$. We determine the most favorable kinematic conditions and observables for the experimental studies of ${\mathrm{\ensuremath{\Theta}}}^{+}$ in the considered processes. We argue that a comparison of the $\ensuremath{\gamma}+D\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}+{\mathrm{\ensuremath{\Theta}}}^{+}$ and $\ensuremath{\gamma}+D\ensuremath{\rightarrow}\mathrm{\ensuremath{\Sigma}}+{\mathrm{\ensuremath{\Theta}}}^{+}$ cross sections should unambiguously determine isospin of ${\mathrm{\ensuremath{\Theta}}}^{+}$.