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

We present the theoretical study of the process $\chi_{c0}(1P)\to\bar\Sigma\Sigma\pi $ decay, by taking into account the $\pi\Sigma$ and $\pi\bar\Sigma$ 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 $\pi\Sigma$ channel and offers a reaction to test the existence of an $I=1$ state with strangeness $S=-1$ and spin-parity $J^p=1/2^-$ around the $\bar KN$ threshold predicted by some theories and supported by some experiments.