Nonleptonic Decays ofΩ−

Abstract

By making use of the hypothesis of partially conserved axial-vector current and equal-time commutation relations suggested by the quark model, we have found that (i) asymmetries of ${\Omega }^{-}$ nonleptonic decays ($\Omega \to \Lambda +K,\Xi +\pi , \mathrm{and} {\Xi }^{*}+\pi$) are very small, (ii) the $\Omega$ lifetime $\tau \left(\Omega \right)\approx (0.3\mathrm{}\sim 0.8)\times {10}^{-10\mathrm{}}$ sec, (iii) $\frac{\Gamma (\Omega \to \Lambda K)}{\Gamma (\Omega \to \Xi \pi )}\lesssim \frac{1}{30}$ for the $\mathrm{SU}\left(3\right)\mathrm{}$-symmetric $B_{10}{B}_8{P}_8$ coupling and $\sim (\frac{1}{10}-\frac{1}{5})$ for the broken-$\mathrm{SU}\left(3\right)\mathrm{}$-symmetric $B_{10}{B}_8{P}_8$ coupling, and (iv) $\frac{\Gamma (\Omega \to {\Xi }^{*}\pi )}{\Gamma (\Omega \to \Xi \pi )}\approx \frac{1}{3}$.