Role of the $\Lambda(1600)$ in the $K^-p \to \Lambda \pi^0\pi^0$ reaction

TL;DR

This paper investigates the role of the $ ext{Lambda}(1600)$ resonance in the $K^- p o ext{Lambda} ext{pi}^0 ext{pi}^0$ reaction using an effective Lagrangian approach, successfully reproducing experimental data and highlighting the resonance's significance.

Contribution

The study introduces a detailed model including the $ ext{Lambda}(1600)$ resonance and non-resonant processes to explain the reaction dynamics and interpret experimental results.

Findings

The $ ext{Lambda}(1600)$ resonance is essential for fitting the total cross section data.

The model accurately reproduces experimental total cross sections.

Predicted invariant mass distributions can be tested in future experiments.

Abstract

Role of the $\Lambda(1600)$ is studied in the $K^- p \to \Lambda \pi^0 \pi^0$ reaction by using the effective Lagrangian approach near the threshold. We perform a calculation for the total and differential cross sections by considering the contributions from the $\Lambda(1600)$ and $\Lambda(1670)$ intermediate resonances decaying into $\pi^0 \Sigma^{*0}(1385)$ with $\Sigma^{*0}(1385)$ decaying into $\pi^0 \Lambda$. Besides, the non-resonance process from $u$-channel nucleon pole is also taken into account. With our model parameters, the current experimental data on the total cross sections of the $K^- p \to \Lambda \pi^0 \pi^0$ reaction can be well reproduced. It is shown that we really need the contribution from the $\Lambda(1600)$ with spin-parity $J^P = 1/2^+$, and that these measurements can be used to determine some of the properties of the $\Lambda(1600)$ resonance. Furthermore, we also plot the $\pi^0 \Lambda$ invariant mass distributions which could be tested by the future experimental measurements.