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

Abstract

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 $K^{\ast }$ and $u$-channel $\Sigma$ exchanges, we perform global fits to the total and differential cross sections for ${\pi }^{-}p\to K\Lambda (1405)$ and ${\pi }^{-}p\to K\Lambda (1520)$. 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 ${\Lambda }^{\ast }\to \pi \Sigma$, the Dalitz process ${\pi }^{-}p\to K{\Lambda }^{\ast }\to K\pi \Sigma$ is also calculated. Our results demonstrate that reconstructing ${\Lambda }^{\ast }$ 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.

11 pages, 18 figures

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