Mixing of the low-lying three- and five-quark<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Ω</mml:mi></mml:math>states with negative parity

Abstract

Mixing of the low-lying three- and five-quark $\ensuremath{\Omega}$ states with spin-parity quantum numbers ${\frac{1}{2}}^{\ensuremath{-}}$ and ${\frac{3}{2}}^{\ensuremath{-}}$ is investigated, employing an instanton-induced quark-antiquark pair creation model, which precludes transitions between ${s}^{3}$ and ${s}^{4}\overline{s}$ configurations. Models with hyperfine interactions between quarks are of three different kinds, namely, one-gluon-exchange (OGE), Goldstone-boson-exchange (GBE), and an instanton-induced interaction (INS). Numerical results show that the instanton-induced pair creation causes strong mixing between the three- and five-quark configurations with spin $3/2$, and that this mixing decreases the energy of the lowest spin $3/2$ states in all three different hyperfine interaction models to $\ensuremath{\sim}1750\ifmmode\pm\else\textpm\fi{}50$ MeV. On the other hand, transition couplings between ${s}^{3}$ and ${s}^{3}q\overline{q}$ states with spin $1/2$ caused by instanton-induced $q\overline{q}$ creation is very small and the resulting mixing of three- and five-quark configurations in the OGE and INS models is negligible, while the mixing of the spin $1/2$ states in GBE model is not; but effects of this mixing on energies of mixed states are also very small. Accordingly, the lowest $\ensuremath{\Omega}$ states with negative parity in all three hyperfine interactions models have spin $3/2$.