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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 finalmeson-baryon pair based on the chiral unitary approach. We show that theprocess filters the isospin $I=1$ in the $\pi\Sigma$ channel and offers areaction to test the existence of an $I=1$ state with strangeness $S=-1$ andspin-parity $J^p=1/2^-$ around the $\bar KN$ threshold predicted by sometheories and supported by some experiments.

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