$\Lambda(1405)$ production in the process $\chi_{c0}(1P)\to \bar{\Lambda}\Sigma\pi$

TL;DR

This paper presents a theoretical analysis of the $ ext{chi}_{c0}(1P)$ decay into $ar{ ext{Lambda}} ext{Sigma} ext{pi}$, exploring the molecular structure of $ ext{Lambda}(1405)$ and testing the existence of predicted $ ext{Sigma}$ states through invariant mass distributions.

Contribution

It introduces a chiral unitary approach to study final state interactions in $ ext{chi}_{c0}(1P)$ decay, revealing features of $ ext{Lambda}(1405)$ and potential new $ ext{Sigma}$ resonances.

Findings

Peak around 1350-1400 MeV in $ ext{pi} ext{Sigma}$ invariant mass

Cusp at $ar{K}N$ threshold in $ ext{pi} ext{Sigma}$ distribution

Peak around 1380 MeV and cusp at $ar{K}N$ threshold in $ ext{pi}ar{ extLambda}$ distribution

Abstract

We have performed a theoretical study on the process $\chi_{c0}(1P)\to \bar{\Lambda}\Sigma\pi$, by taking into account the final state interactions of $\pi\Sigma$ and $\pi\bar{\Lambda}$ based on the chiral unitary approach. As the isospin filters of $I=0$ in the $\pi\Sigma$ channel and $I=1$ in the $\pi\bar{\Lambda}$ channel, this process can be used to study the molecular structure of the $\Lambda(1405)$ resonance, and to test the existence of the predicted states $\Sigma(1380)$ and $\Sigma(1430)$ with spin-parity $J^P=1/2^-$. Our results show that there is a peak around $1350 \sim 1400$~MeV, and a cusp around the $\bar{K}N$ threshold in the $\pi\Sigma$ invariant mass distribution, which should be the important feature of the molecular state $\Lambda(1405)$. We also find a peak around $1380$~MeV, and a cusp around $\bar{K}N$ threshold in the $\pi\bar{\Lambda}$ invariant mass distribution, which are associated to the $\Sigma(1380)$ and $\Sigma(1430)$ resonances.