$\Sigma^0$ particle decay

Question

I was asked to evaluate whether the following reaction is possible or not:

$$\Sigma^0 \rightarrow \Lambda + \pi^0$$

I have evaluate all conservations law that could prevent it to occur, but i haven't find it! In fact, when i checked the answer, it seems that the reaction does not conserve energy. But i can't understand how this can be realized!

Obviously i know that energy should be conserved, i am mainly worried about how could i realized that, without the necessity to evaluate all Feynman diagrams existing in the theory.

Look an example:

$$p + p \rightarrow p + p + p + \overline{p}$$

Is a possible reaction! But i am now worried about energy conservation, what line of reasoning should i use to conclude that the first one (involving sigma) can't occurs, and the last one can, because of energy conservation?

I am not sure how the rest mass/effective mass of the quarks influence here, since the primer particle can just decay in a particle with less energy.

Answer 1

Conservation of energy is done by considering:

$$ M_{\Sigma} > M_{\Lambda} + m_{\pi} $$

If yes, then it is a go. At the limit of equality, the rest-frame Sigma decays into a Lambda and a pion, also at rest. Ofc, Fermi's Golden Rule is going to say the rate is really low, because there is almost no phase-space (density-of-states). (In fact, a reaction that would violate conservation of energy can be said to be a reaction that has no phase space, even if there is a non-zero amplitude).

Answer 2

Obviously i know that energy should be conserved, i am mainly worried about how could i realized that, without the necessity to evaluate all Feynman diagrams existing in the theory.

Basically. one has to know when studying particle physics, that observations and measurements of particles are what defines it. Feynman diagrams etc come from the mathematical theory, and trying to understand particles assuming that theory molds them is not the way.

Here is the baryon octet from measurements.

note that the sigma zero and the lamda are in the same point in this diagram. To see whether a decay is possible the energy difference between the sigma zero mass and the lamda mass has to be checked.That will show what decays are possible. In fact, checking in the particle data tables , only sigma zero to lamda gamma decays have been measured. The mass difference is too small for the decay you are asked for.