Producing $\Lambda(1405)$ and $\Lambda(1520)$ in $\pi^-p$ reaction to explore their inner structures

In this work, the production mechanisms of the hyperon resonances $\Lambda(1405)$ and $\Lambda(1520)$ in the $\pi^- p$ scattering are investigated within an effective Lagrangian approach incorporating Regge trajectories. By including contributions from $t$-channel $K^*$ and $u$-channel $\Sigma$ exchanges, we perform global fits to the total and differential cross sections for $\pi^{-} p \rightarrow K\Lambda(1405)$ and $\pi^{-} p \rightarrow K\Lambda(1520)$. The results show good agreement with available experimental data. For the total cross section of $\Lambda(1405)$ production, the $u$-channel contribution is dominant, whereas the $t$-channel contribution plays the primary role in $\Lambda(1520)$ production. Furthermore, the differential cross sections of the two processes exhibit distinctly different shapes, reflecting their distinct underlying reaction mechanisms. An analysis based on the constituent counting rule indicates that $\Lambda(1520)$ is consistent with a conventional three-quark configuration, while $\Lambda(1405)$ shows a clear deviation, suggesting a more exotic structure. Owing to the large branching ratio of $\Lambda^* \to \pi \Sigma$, the Dalitz process $\pi^{-} p \rightarrow K \Lambda^{*} \rightarrow K \pi \Sigma$ is also calculated. Our results demonstrate that reconstructing $\Lambda^*$ via the $K\pi\Sigma$ final state is experimentally feasible. This study provides important theoretical insights into the production dynamics of these hyperon resonances, and suggests future high-precision measurements of the $t$-distribution at large momentum transfer at facilities such as AMBER, J-PARC, HIKE, and HIAF, which can further clarify their reaction mechanisms and structural properties.