${\chi }_{c0}(1P)$ decay into $\bar{\mathrm{\Sigma }}\mathrm{\Sigma }\pi$ in search of an $I=1$, $1\mathrm{/}{2}^{-}$ baryon state around $\bar{K}N$ threshold

We present the theoretical study of the process ${\chi }_{c0}(1P)\to \bar{\mathrm{\Sigma }}\mathrm{\Sigma }\pi$ decay, by taking into account the $\pi \mathrm{\Sigma }$ and $\pi \bar{\mathrm{\Sigma }}$ final state interactions of the final meson-baryon pair based on the chiral unitary approach. We show that the process filters the isospin $I=1$ in the $\pi \mathrm{\Sigma }$ channel and offers a reaction to test the existence of an $I=1$ state with strangeness $S=-1$ and spin-parity $J^p=1\mathrm{/}{2}^{-}$ around the $\bar{K}N$ threshold predicted by some theories and supported by some experiments.