Why doesn't the neutral pion annihilate with itself?

[Mathilda]

Homework Statement

How does the pi-meson (π0) work without annihilating itself?

Homework Equations

|π0 〉1/√2 〉- {|uu − |dd}

u= anti-upquark
d= anti-downquark

The Attempt at a Solution

I do understand that it is a superposition, but why does it work when it is a partice with its own anti.particle?

 

[Orodruin]

What do you mean by "work". The pi mesons are all unstable particles which decay with well known half-lives.