Low-lying $\Omega$ states with negative parity in an extended quark model with Nambu-Jona-Lasinio interaction

Here we investigate mixing of the low-lying three- and five-quark $\Omega$ states with spin-parity quantum numbers $\frac{1}{2}^{-}$ and $\frac{3}{2}^{-}$, employing the quark-antiquark creation triggered by Nambu-Jona-Lasinio (NJL) interaction. Wave functions of the three- and five-quark configurations are constructed using the extended constituent quark model, within which the hyperfine interaction between quarks is also taken to be the NJL interaction induced one. Numerical results show that the NJL-induced pair creation results in vanishing mixing between three- and five-quark $\Omega$ configurations with spin-parity $1/2^{-}$, but mixing between three- and five-quark $3/2^{-}$ $\Omega$ states should be very strong. And the mixing decreases energy of the lowest $3/2^{-}$ $\Omega$ state to be $1785\pm25$~MeV, which is lower than energy of the lowest $1/2^{-}$ state in this model. This is consistent with our previous predictions within the instanton-induced quark-antiquark creation model.