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mPlummers

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**Problem Statement:**Hello! I'm trying to learn how to know if a particular interaction is allowed or forbidden. I found 3 decays which i can't understand.

**Relevant Equations:**The decays are:

1) [itex] \eta \rightarrow \pi ^{0}+\gamma [/itex]

2) [itex]\phi \rightarrow \rho^{0}+\gamma[/itex]

3) [itex]\eta \rightarrow \pi ^{0}+\pi ^{0}[/itex]

4) [itex]\eta^{0} \rightarrow \gamma+\gamma+\gamma[/itex]

1) [itex]\eta[/itex] and [itex]\pi[/itex] have zero spin, while the photon has spin equal to 1. It should be forbidden because angular momentum is not conserved.

2) Here the angular momentum is conserved (they all have spin 1, so the total angular momentum for the final state can be 0, 1, 2, in this case has to be 1). But what about the charge conjugation? I know that they all have C = -1, so it should not be conserved because the total C for the final state is -1 x -1 = 1.

3) The angular momentum is conserved, so i would say that the decay is allowed, but i can't find it in the Particle Data Group, so I'm trying to understand if the parity is conserved. All the particles have P=-1. I know that the parity for the final state is [itex]P_{tot} = P_{1}P_{2}(-1)^{L} [/itex]. The problem is that i don't know the value for L. Should i know that or can i set it equal to zero? If i can put L=0, the the parity is not conserved, so the decay is forbidden... but the PDG says it's possible.

4) I think this is the same case of point 3. Angular momentum is conserved, but i don't know how to add parity quantum numbers (how to choose the total L).

Thank you for your attention!

**[Moderator's note: Moved from homework to a technical forum.]**

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