Why can't a ρ0 meson decay into two neutral pions?

[Rafaelmado]

TL;DR

Could someone please help me with this problem?

Pions are particles with spin 0 and they form an isospin triplet: π⁺, π⁰, π⁻ (with the superscript indicating the electric charge). Their intrinsic parity is −1 and they are pseudoscalar mesons. In nature we also find other kind of mesons, like the ρ mesons, ρ⁺, ρ⁰ and ρ⁻. As pions, they also form an isospin triplet but they are vector mesons, i.e., they have spin 1 and intrinsic parity −1. The ρ⁰ decays into π⁺π⁻ via the strong interaction, which preserves parity. Prove that a ρ⁰ cannot decay into π⁰π⁰ via the strong interaction. Hints: Remember that pions are bosons and angular momentum is conserved in a reaction.

 

[PeterDonis]

This looks like a homework problem. It needs to be posted in the appropriate homework forum, with the homework template filled out.

Also, please do not use the same title for multiple threads with different questions.