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

TL;DR

This paper theoretically investigates the decay of $ ext{chi}_{c0}(1P)$ into $ar ext{Sigma} ext{Sigma} ext{pi}$, exploring the potential existence of an isospin-1, $J^p=1/2^-$ baryon state near the $ar{K}N$ threshold using chiral unitary methods.

Contribution

It introduces a novel reaction mechanism to test for an $I=1$, $J^p=1/2^-$ baryon state around the $ar{K}N$ threshold, incorporating final state interactions within a chiral unitary framework.

Findings

Filters isospin $I=1$ in the $ ext{pi} ext{Sigma}$ channel.

Provides a reaction to detect the $I=1$ baryon state.

Supports the existence of the state near the $ar{K}N$ threshold.

Abstract

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.