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

TL;DR

The paper addresses the production of Xi(1530) in $K^- p$ scattering and disentangles intermediate-hyperon contributions using an effective Lagrangian approach that includes $s$- and $u$-channel exchanges of nine hyperons and resonances up to spin $J\le 5/2$, with two form-factor schemes and a fitted coupling product $g_Y$. It compares two fitting strategies (Model A with uniform weights and Model B with adjusted weights) due to inconsistent data in a specific energy window, finding that Model A offers the better global description and that the $\,\\Sigma(1193)$ intermediate state dominates the cross sections while $\,\\Lambda(1405)$ is negligible. The study also provides differential cross-section predictions and estimates for cascade channels $K^- p \to K \Xi \pi$ at $p_K=2.87$ GeV, offering testable predictions for forthcoming J-PARC measurements and highlighting energy regions where resonant structures appear near $\\sqrt{s}\\approx 2.1$ GeV and $\\sqrt{s}\\approx 2.3$ GeV. Overall, the results clarify resonance contributions in Xi(1530) production and deliver experimentally testable predictions that can refine our understanding of hyperon dynamics in strange hadron reactions.

Abstract

In the present work, we examine the production of $Ξ(1530)$ in the $K^- p \to K^{+} Ξ(1530)^{-}$ and $K^- p \to K^{0} Ξ(1530)^{0}$ reactions utilizing an effective Lagrangian approach. To accurately fit the cross sections for both processes, we include nine $Λ$ and $Σ$ hyperons and their resonances in both $s$- and $u$-channel processes. Considering the discrepancy of the measured cross sections for $K^- p \to K^+ Ξ(1530)^-$ 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 $Σ(1193)$ intermediate process is dominant. Furthermore, we predict different cross sections for $K^- p\to K^+Ξ(1530)^-$ and $K^- p\to K^0Ξ(1530)^0$ at several representative center-of-mass energies, providing testable predictions for forthcoming J-PARC experiments.

Figures (10)

• Figure 1: Diagrams contributing to the process of $K^{-}p \rightarrow K^{+} \Xi(1530)^{-}$, corresponding to the (a) $s$- and (b) $u$-channel contributions, respectively.
• Figure 2: Diagrams contributing to the process of $K^{-}p \rightarrow K^{0} \Xi(1530)^{0}$, corresponding to the (a) $s$- and (b) $u$-channel contributions, respectively.
• Figure 3: (Color online) The cross sections for $(a)$$K^{-} p \rightarrow K^+ \Xi(1530)^-$ and $(b)$$K^{-} p \rightarrow K^{0} \Xi(1530)^{0}$ depending on the $\sqrt{s}$. The black points with error bars correspond to the experimental data of the cross sections for $K^- p \to K^+ \Xi(1530)^-$ and $K^- p \to K^0 \Xi(1530)^0$ from Refs. Berge:1966zzDauber:1969hgBriefel:1977bpFlaminio:1979iz, while the blue solid curves are obtained with the fitted parameters in Table \ref{['Tab.2']}.
• Figure 4: (Color online) The individual contributions from different intermediate states for the cross sections for $K^{-} p \rightarrow K^{+} \Xi(1530)^{-}$ depending on the $\sqrt{s}$ in model A.
• Figure 5: (Color online) The individual contributions from different intermediate states for the cross sections for $K^{-} p \rightarrow K^{0} \Xi(1530)^{0}$ depending on the $\sqrt{s}$ in model A. It should be noted that the diagrams $(c)$ and $(d)$ are almost the same as those in Fig. \ref{['Fig.4']} since the above-threshold $\Lambda$ resonance contributions are dominated by the s channel, while the $\Sigma$ resonance contributions are exactly the same in both processes.