Mixing of the low-lying three- and five-quark $\Omega$ states with negative parity

Abstract

Mixing of the low-1/2^{-}$ and $3/2^{-}$ is investigated, employing an instanton-induced quark-antiquark pair creation model, which precludes transitions between $s^{3}$ and $s^{4}\bar{s}$ configurations. Models with hyperfine interactions between quarks of three different kinds, namely, one-gluon-exchange, Goldstone-boson-exchange (GBE) and an instanton-induced interaction (INS) are called OGE, GBE and INS models, respectively. 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 $\sim 1750\pm50$ MeV. On the other hand, transition couplings between $s^3$ and $s^{3}q\bar{q}$ states with spin 1/2 caused by instanton-induced $q\bar{q}$ 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 $\Omega$ states with negative parity in all three hyperfine interactions models have spin 3/2.