Why can the omega meson not decay to 3 neutral pions?

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Dilatino
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What reasons prevent the decay

$\omega \rightarrow \pi^0 \pi^0 \pi^0$

from happening?
 
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There are not many things to check if you want to know which decay is possible.

The http://pdg8.lbl.gov/rpp2014v1/pdgLive/Particle.action?node=M001#decayclump_A has the answer.

You can use LaTeX with double # or double $:
##\omega## -> ##\omega##
$$\omega$$ ->$$\omega$$
 
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