Production of $\Xi(1530)$ in the $K^- p$ scattering process

Abstract

In the present work, we examine the production of $\Xi(1530)$ in the $K^- p \to K^{+} \Xi(1530)^{-}$ and $K^- p \to K^{0} \Xi(1530)^{0}$ reactions utilizing an effective Lagrangian approach. To accurately fit the cross sections for both processes, we include nine $\Lambda$ and $\Sigma$ hyperons and their resonances in both $s$- and $u$-channel processes. Considering the discrepancy of the measured cross sections for $K^- p \to K^+ \Xi(1530)^-$ within the range $\sqrt{s}=[2.087, 2.168]\ \mathrm{GeV}$, we employ two distinct fitting strategies: a uniform weighting scheme (model A) and a different weighting approach (model B). A comparative analysis suggests that model A yields a superior global agreement with experimental data compared to model B. Beyond fitting the cross sections, we also estimate the individual contributions from various intermediate states. Our results reveal that the cross section arising from the $\Sigma(1193)$ intermediate process is dominant. Furthermore, we predict different cross sections for $K^- p\to K^+\Xi(1530)^-$ and $K^- p\to K^0\Xi(1530)^0$ at several representative center-of-mass energies, providing testable predictions for forthcoming J-PARC experiments.