Low-lying<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Ω</mml:mi></mml:math>states with negative parity in an extended quark model with Nambu–Jona-Lasinio interaction

Abstract

Here we investigate mixing of the low-lying three- and five-quark $\ensuremath{\Omega}$ states with spin-parity quantum numbers 1/2${}^{\ensuremath{-}}$ and 3/2${}^{\ensuremath{-}}$, employing the quark-antiquark creation triggered by Nambu--Jona-Lasinio (NJL) interaction. Wave functions of the three- and five-quark configurations are constructed by using the extended constituent quark model, within which the hyperfine interaction between quarks is also taken to be the NJL-induced one. Numerical results show that the NJL-interaction-induced pair creation results in vanishing mixing between three- and five-quark $\ensuremath{\Omega}$ configurations with spin-parity $1/{2}^{\ensuremath{-}}$, but mixing between three- and five-quark $3/{2}^{\ensuremath{-}}$ $\ensuremath{\Omega}$ states should be very strong. The mixing decreases energy of the lowest $3/{2}^{\ensuremath{-}}$$\ensuremath{\Omega}$ state to be $1785\ifmmode\pm\else\textpm\fi{}25$ MeV, which is lower than energy of the lowest $1/{2}^{\ensuremath{-}}$ state in this model. This is consistent with our previous predictions within the instanton-induced quark-antiquark creation model.