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• W2041567341 startingPage "3144" @default.
• W2041567341 abstract "Two topics are treated in this paper: the explanation of the $|ensuremath{Delta}I|=frac{1}{2}$ rule based on the symmetric quark model and the tests for this explanation in ${ensuremath{Omega}}^{ensuremath{-}}$ nonleptonic decays. From the color-quark, the three-triplet, and the paraquark models, the $|ensuremath{Delta}I|=frac{1}{2}$ rule follows for the octet-hyperon, the ${ensuremath{Omega}}^{ensuremath{-}}$, and the kaon weak nonleptonic decays as a consequence of current algebra, pion PCAC (partially conserved axial-vector current), and dispersion relations. Gronau's successful numerical results for the octet-hyperon decay amplitudes also follow in these alternatives to the Bose-quark model. However, though the origin of both explanations is the Fierz reshuffling property of the $Vifmmodepmelsetextpmfi{}A$ interactions, the explanations of the $|ensuremath{Delta}I|=frac{1}{2}$ rule are quite distinct, e.g., in the Bose-quark model this rule is exact whereas in the other versions it is only approximate, being violated by continuum contributions to the absorptive parts. Because $〈0|{mathcal{H}}_{w}|K〉$ and $〈ensuremath{pi}|{mathcal{H}}_{w}|K〉$ vanish in the symmetric quark model, the usual current-algebra soft-pion argument for $|ensuremath{Delta}I|=frac{1}{2}$ rule and the ${K}^{*}$-pole-dominance assumption (as a Feynman diagram) for ${K}_{0}^{1}ensuremath{rightarrow}2ensuremath{pi}$ are not convincing. On the other hand, the ordinary Fermi-quark model supplemented with octet dominance can be excluded, as it predicts $frac{D}{F}=3$ in the SU(3) limit for the matrix element of the parity-conserving Hamiltonian for two baryons in the nucleon octet $frac{D}{F}ensuremath{simeq}ensuremath{-}0.85$ from $P$-wave fits). The $ensuremath{Lambda}{K}^{ensuremath{-}}$ decay mode of the ${ensuremath{Omega}}^{ensuremath{-}}$ should be predominantly $P$ wave (parity-conserving), whereas the $ensuremath{Xi}ensuremath{pi}$ mode should have the $P$ wave strongly suppressed and comparable to the $D$ wave (parity-violating). This implies $frac{ensuremath{Gamma}({ensuremath{Omega}}^{ensuremath{-}}ensuremath{rightarrow}ensuremath{Xi}ensuremath{pi})}{ensuremath{Gamma}({ensuremath{Omega}}^{ensuremath{-}}ensuremath{rightarrow}ensuremath{Lambda}{K}^{ensuremath{-}})}ensuremath{ll}1$. The estimated total ${ensuremath{Omega}}^{ensuremath{-}}$ decay rate is consistent with the present experimental number." @default.
• W2041567341 created "2016-06-24" @default.
• W2041567341 creator A5063973728 @default.
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• W2041567341 date "1973-11-01" @default.
• W2041567341 modified "2023-09-26" @default.
• W2041567341 title "|ΔI|=12Rule From the Symmetric Quark Model" @default.
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• W2041567341 doi "https://doi.org/10.1103/physrevd.8.3144" @default.
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