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

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?

• can you include the masses in the question? Also, what is "vague" about not having enough energy to create a particle, and which particle would be a candidate for strong decay?
– JEB
May 23, 2021 at 18:53

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.