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

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 $(\phi,\rho,\omega)$--$(\Lambda,\Sigma)$ rescattering diagrams.