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Why can the hyperon $\Omega^{-}$ not decay by strong interaction? It seems that strangeness must be violated, but why is it the only way?

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As an answer to the second question, strangeness tends not to be conserved in weak interaction or decay. –  Alyosha Oct 29 '12 at 12:19
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Are you looking for something beyond "Because the strong interaction respects flavor."? If so, can you be more specific? –  dmckee Oct 29 '12 at 13:01

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The reason is because it is the lightest baryon with strangeness 3, the mass energy of lightest strange object of s=1 (the kaons) is greater than 1/3 it's mass, so it can't decay into these.

It is a general principle of energy conservation and strangeness conservation: the lightest example of any conserved quantum numbers can't decay without changing this number. In this case you need the strangeness to go down, and this requires weak decay, because, as dmckee says in his comment, the strong interaction respects flavor.

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