Bolstering up the existence of $P_s(2080)$

Abstract: We present a detailed study of the partial decay widths of a spin-parity resonance $J<sup>P=3/2<sup>-$ $N<sup>*$ with a mass of $\simeq$ 2070 MeV obtained from the coupled channel s wave vector-baryon $\rho N$, $\omega N$, $\phi N$, $K<sup>*\Lambda$ and $K<sup>*\Sigma$ dynamics. This state, which couples strongly to the $K<sup>*\Sigma$ channel, corresponds to a nucleon with a hidden strange quark content, in analogy to the $P_c$ states discovered by the LHCb collaboration, and we denote it as $P_s(2080)$. A state with such a nature can decay to vector-baryon, pseudoscalar-baryon, and pseudoscalar-baryon resonance channels, involving triangular loops in the latter two cases. As we will show, the partial decay widths to pseudoscalar-baryon resonance channels, like $\pi N<sup>*(1535)$, $\pi N<sup>*(1650)$, $K\Lambda(1405)$, are comparable to those related to ground state baryons in the final state, like $\pi N$, $\eta N$, $K\Lambda$. In this way, reactions involving such lighter baryon resonances in the final state can be used as an alternative source of information on the properties of a $N<sup>*$ with hidden strangeness.