Why can't $\Sigma$ baryons decay strongly?

Question

First of all, I must say this is a homework question. The complete question includes particles like $p$, $e^-$, $\Lambda$ and $\Omega$.

It's pretty easy to understand why $\Omega$ and $\Lambda$ have to decay weakly; $\Omega$ has three $s$ quarks so, no other baryon to turn into without changing strangeness. As for $\Lambda$, it is the lightest baryon with unit strangeness.

But when it comes to, for example, $\Sigma^0$ it can decay to $\Lambda + \gamma$. And while this particular process doesn't come from a strong interaction, I can't think of any reason why a process like $\Sigma^0 \rightarrow \Lambda + A$ where $A$ is a strangeless particle can't be possible. I'm not sure if the reason should be that there's simply no particle A that can fit that decay. The mass difference between $\Lambda$ and $\Sigma^0$ is pretty small, so maybe that is the case, but it sounds a little bit vague. Am I missing something?

Answer 1

I'm not sure if the reason should be that there's simply no particle A that can fit that decay. The mass difference between Λ and Σ0 is pretty small, so maybe that is the case, but it sounds a little bit vague.

The mass of the $Σ^0$ = 1.192MeV of $Λ$=1.115 MeV, the difference is 77 Mev. At the center of mass that is the energy available for a decay. The smallest mass particle with a quark content is the $π^0$= 139 MeV, is what your are missing.

There is not enough energy in the center of mass of a $Σ^0$ to produce a $π^0$ $Λ$ decay.