A possible $\Sigma^*$ or $\Lambda^*$ resonance with $J^P=3/2^-$ in $K^-p\to K\Xi$ scattering

We analyze the $K^-p\to K^+\Xi^-$ and $K^-p\to K^0\Xi^0$ processes in the energy region $1.8<\sqrt{s}<2.8$ GeV within an effective Lagrangian approach. The $\Lambda(1800)$ and $\Sigma(2250)$ resonances, along with the ground states $\Sigma$ and $\Lambda$, are included. Additionally, a possible $J^P=3/2^-$ $\Sigma^*$ or $\Lambda^*$ resonance with a mass around 1.9 GeV and a width of approximately 200 MeV is introduced to describe the structure at 2.0 GeV in the total cross section and reproducing the threshold behavior. The two possible solutions corresponding to $\Sigma^*(3/2^-)$ and $\Lambda^*(3/2^-)$ cannot be distinguished by the existing data. Predictions for the polarization of the final-state $\Xi$ and the cross section of $K^-n \to K^0\Xi^-$ are compared with the experimental data, we find that the results of solution-II with $\Lambda^*(3/2^-)$ are much better. We also discuss the possible interpretations of the introduced $3/2^-$ hyperon as a pentaquark candidate, e.g. an $S$-wave $K\Xi(1530)$ hadronic molecule. However, since the polarization data suffer from rather large uncertainties, more data inputs are needed in future experiments, for example, J-PARC, HIAF and JLab.