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- Homework Statement
- Explain why eta meson can't decay into 3 neutral pions. Use isospin and pions statistics.

- Homework Equations
- `##|\eta >=|I=0,I_{z}=0>## and ##|\pi ^{0} >=|1,0>##

I started combining 2 pions:

##|\pi ^{0},\pi ^{0} >=\sqrt{\frac{2}{3}}|2,0>-\sqrt{\frac{1}{3}}|0,0>##

What should i do now? Should i continue combining the third pion or can i already say that it's forbidden? If yes, why? Is it because the state antisymmetric, impossible for two bosons?

##|\pi ^{0},\pi ^{0} >=\sqrt{\frac{2}{3}}|2,0>-\sqrt{\frac{1}{3}}|0,0>##

What should i do now? Should i continue combining the third pion or can i already say that it's forbidden? If yes, why? Is it because the state antisymmetric, impossible for two bosons?