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

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