Double-strangeness exchange reactions in a hybrid Regge-plus-resonance approach

We investigate double-strangeness exchange reactions, $K^{-}p\to K^{+}{\mathrm{\Xi }}^{-}$ and $K^{-}p\to K^0{\mathrm{\Xi }}^0$, using an effective Lagrangian approach based on a hybrid Regge-plus-resonance model involving rescattering diagrams. We consider the background processes that include $\mathrm{\Lambda }$, $\mathrm{\Sigma }$, and $\mathrm{\Sigma }(1385)$ Regge trajectories in the $u$ channel and the $s$-channel Born-term diagrams. The $s$-channel hyperon resonances account for the bump structures in the total cross sections. The $s$-channel $\mathrm{\Lambda }(2100,7\mathrm{/}{2}^{-})$ and $\mathrm{\Sigma }(2030,7\mathrm{/}{2}^{+})$ resonances contribute significantly, and the $\mathrm{\Sigma }(2250)$ resonance favors $J^P=7\mathrm{/}{2}^{-}$. The interference pattern between the $\mathrm{\Lambda }(2100,7\mathrm{/}{2}^{-})$ and $\mathrm{\Sigma }(2030,7\mathrm{/}{2}^{+})$ amplitudes is essential for describing forward differential cross sections in the resonance region $2.07<\sqrt{s}<2.15$ GeV. The absence of the $S=-2$ meson leads to the inclusion of the meson-baryon rescattering diagrams to describe the $K^{-}p\to K\mathrm{\Xi }$ reaction data, proving the significant contribution of the $(\phi ,\rho ,\omega )$–$(\mathrm{\Lambda },\mathrm{\Sigma })$ rescattering diagrams.