$\bar{K} + N \to K + \Xi$ reaction and $S=-1$ hyperon resonances

The $\bar{K} + N \to K + \Xi$ reaction is studied for center-of-momentum energies ranging from threshold to 3 GeV in an effective Lagrangian approach that includes the hyperon $s$- and $u$-channel contributions as well as a phenomenological contact amplitude. The latter accounts for the rescattering term in the scattering equation and possible short-range dynamics not included explicitly in the model. Existing data are well reproduced and three above-the-threshold resonances were found to be required to describe the data, namely, the $\Lambda(1890)$, $\Sigma(2030)$, and $\Sigma(2250)$. For the latter resonance we have assumed the spin-parity of $J^P=5/2^-$ and a mass of 2265 MeV. The $\Sigma(2030)$ resonance is crucial in achieving a good reproduction of not only the measured total and differential cross sections, but also the recoil polarization asymmetry. More precise data are required before a more definitive statement can be made about the other two resonances, in particular, about the $\Sigma(2250)$ resonance that is introduced to describe a small bump structure observed in the total cross section of $K^- + p \to K^+ + \Xi^-$. The present analysis also reveals a peculiar behavior of the total cross section data in the threshold energy region in $K^- + p \to K^+ + \Xi^-$, where the $P$- and $D$-waves dominate instead of the usual $S$-wave. Predictions for the target-recoil asymmetries of the $\bar{K} + N \to K + \Xi$ reaction are also presented.