Understanding Neutral Pions: Superpositions, Particles, & Feynman Diagrams

[dEdt]

So apparently a neutral pion is a superposition of $u\bar{u}$ and $d\bar{d}$. I'm having trouble understanding what this means. I have no problem understanding how the decay products of some scattering experiment could be a superposition of these two states, but how can we treat this superposition as a single particle? And how would you draw the feynman diagram for some process involving a neutral pion?

 

[Simon Bridge]

The neutral pions are decay products from scattering.
There are plenty of examples online of Feynman diagrams involving pions.

 

[andrien]

the decay of neutral pions into two photons happens through the anomaly in divergence of axial vector current.the decay has a triangle diagram.
http://prola.aps.org/abstract/PR/v177/i5/p2426_1
it is available freely here.
http://astrophysics.fic.uni.lodz.pl/100yrs/pdf/12/068.pdf