Why doesn't Ω¯ decay to Σ¯ plus π°(pion)?

[ozon]

In David Griffiths' Introduction to Elemantary Particles book, Problem 1.8 makes me confused. It wants me to write possible decay modes of Ω¯. In the parentheses, there is an explanation.It says "The Ω¯ does in fact decay, but by the much slower weak interaction, which does not converse strangeness". So I think only charge conservation is necessary.
Ω¯ ->Σ¯ + π° I think it is possible. Because mass of Ω¯ is greater than mass of Σ¯ + π°. But it is not in possible Ω¯ decays. http://en.wikipedia.org/wiki/Omega_baryon.
I am not a native speaker. I apologize you if I make mistake for writing this topic.

 

[Chopin]

The book mentions strangeness. Are you familiar with what this concept means? If so, try looking up the quantum numbers of the particles in that decay (for instance, see http://en.wikipedia.org/wiki/Omega_baryon, http://en.wikipedia.org/wiki/Sigma_baryon, and http://en.wikipedia.org/wiki/Pi_meson) and see if that gives you any useful information.

 

[Dick]

The book mentions strangeness. Are you familiar with what this concept means? If so, try looking up the quantum numbers of the particles in that decay (for instance, see http://en.wikipedia.org/wiki/Omega_baryon, http://en.wikipedia.org/wiki/Sigma_baryon, and http://en.wikipedia.org/wiki/Pi_meson) and see if that gives you any useful information.

Right. And also look up the quark composition of those baryons. If you are going to change quark composition in going to the product, you have to go through a weak decay. Strangeness is just one aspect of this.

 

[richard wakefield]

It wants me to write possible decay modes of Ω¯. In the parentheses, there is an explanation.It says "The Ω¯ does in fact decay, but by the much slower weak interaction, which does not converse strangeness". So I think only charge conservation is necessary.

The problem refers to previous problem 1.7, which asks for decays through strong interactions. So you are asked to look for decay modes facilitated by strong interactions, where you have to consider conservation of Strangeness. As you have mentioned in your post, you noticed that it is not possible to conserve Strangeness in the given construction of the problem. Griffiths wants to you to see this because it led Gell-Mann to think that the particle should be "metastable". Afterwards the problem informs you that Ω^- does actually decay(you mentioned one of them), but through Weak Interaction(where Strangeness is not conserved) instead of Strong Interaction.