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

Abstract

We investigate double-strangeness exchange reactions, $K^{-}p\to K^{+}{\Xi }^{-}$ and $K^{-}p\to K^0{\Xi }^0$, using an effective Lagrangian approach based on a hybrid Regge-plus-resonance model involving rescattering diagrams. We consider the background processes that include $\Lambda$, $\Sigma$, and $\Sigma (1385)$ 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 $\Lambda (2100,7/2^{-})$ and $\Sigma (2030,7/2^{+})$ resonances contribute significantly, and the $\Sigma (2250)$ resonance favors $J^P=7/2^{-}$. The interference pattern between the $\Lambda (2100,7/2^{-})$ and $\Sigma (2030,7/2^{+})$ 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 $K^{-}p\to K\Xi$ reaction data, proving the significant contribution of the $(\varphi ,\rho ,\omega )$--$(\Lambda ,\Sigma )$ rescattering diagrams.