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

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.

Comments: 7 pages, 13 figures, the version for PRD