Producing $Λ(1405)$ and $Λ(1520)$ in $π^-p$ reaction to explore their inner structures

TL;DR

This study investigates the production of hyperon resonances Λ(1405) and Λ(1520) in π^- p scattering using an effective Lagrangian framework augmented by Regge trajectories to describe t-channel and u-channel exchanges. By fitting total and differential cross sections for π^- p → K Λ(1405) and π^- p → K Λ(1520), the authors identify distinct production dynamics: the u-channel dominates Λ(1405) production, while the t-channel drives Λ(1520) production, with markedly different differential cross-section shapes. A constituent counting-rule analysis suggests Λ(1520) aligns with a conventional three-quark configuration (n ≈ 10) whereas Λ(1405) shows an anomalous effective n around 8, signaling a potentially exotic structure. The Dalitz process π^- p → K Λ* → K π Σ is shown to be experimentally feasible for reconstructing Λ*, providing practical guidance for future measurements. The work emphasizes high-precision t-distribution data at large momentum transfer from facilities like AMBER, J-PARC, HIKE, and HIAF to further clarify the production mechanisms and internal structures of these hyperons.

Abstract

In this work, the production mechanisms of the hyperon resonances $Λ(1405)$ and $Λ(1520)$ in the $π^- p$ scattering are investigated within an effective Lagrangian approach incorporating Regge trajectories. By including contributions from $t$-channel $K^*$ and $u$-channel $Σ$ exchanges, we perform global fits to the total and differential cross sections for $π^{-} p \rightarrow KΛ(1405)$ and $π^{-} p \rightarrow KΛ(1520)$. The results show good agreement with available experimental data. For the total cross section of $Λ(1405)$ production, the $u$-channel contribution is dominant, whereas the $t$-channel contribution plays the primary role in $Λ(1520)$ 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 $Λ(1520)$ is consistent with a conventional three-quark configuration, while $Λ(1405)$ shows a clear deviation, suggesting a more exotic structure. Owing to the large branching ratio of $Λ^* \to πΣ$, the Dalitz process $π^{-} p \rightarrow K Λ^{*} \rightarrow K πΣ$ is also calculated. Our results demonstrate that reconstructing $Λ^*$ via the $KπΣ$ 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.

Figures (18)

• Figure 1: Feynman diagrams for $\pi^{-} p\rightarrow K\Lambda^*$.
• Figure 2: The total cross section for the reaction $\pi^{-} p\rightarrow K\Lambda(1405)$. The band stands for the error bar of the three fitting parameters in Table \ref{['1']}.
• Figure 3: The $t$-distribution for the reaction $\pi^{-} p\rightarrow K\Lambda(1405)$ at a center of mass energy of $W = 3.057$ GeV. The experimental data are from Ref. Crennell:1972km. Here, the notation is the same as in \ref{['tcs1']}.
• Figure 4: The $u$-distribution for the reaction $\pi^{-} p\rightarrow K\Lambda(1405)$ at a center of mass energy of $W = 3.057$ GeV. Here, the notation is the same as in \ref{['tcs1']}.
• Figure 5: The differential cross section $d \sigma/d \cos\theta$ of the $\pi^{-} p\rightarrow K\Lambda(1405)$ process as a function of $\cos\theta$ at different c.m. energies. Here, the notation is the same as in \ref{['tcs1']}.