Actually, the quark and antiquark *do* annihilate with each other. It just takes some amount of time for them to do so. The actual time that it takes for any given pion is random, and follows an exponential distribution, but the *average* time it takes is $8.4\times 10^{-17}\,\mathrm{s}$ according to Wikipedia, which we call the lifetime of the neutral pion.

What you've learned is a simplification, in fact (it pretty much always is in physics). The actual state of a pion is a linear combination of the up state and the down state,

$$\frac{1}{\sqrt{2}}(u\bar{u} - d\bar{d})$$

This is how it's able to be its own antiparticle: there aren't separate up and down versions of the neutral pion. Each one is a combination of both flavors.

The orthogonal linear combination,

$$\frac{1}{\sqrt{2}}(u\bar{u} + d\bar{d})$$

doesn't correspond to a real particle. (In a sense it "contributes" to the $\eta$ and $\eta'$ mesons, but I won't go into detail on that.)

The isospin is different. $I=0$ for the $\Lambda^0$ and $I=1$ for the $\Sigma^{0}$. This makes the $\Lambda^0$ an isospin singlet state but the $\Sigma^0$ is part of an isospin triplet.

There are quite few other examples e.g. compare a proton (uud with $I=1/2$) with a $\Delta^{+}$ (uud with $I=3/2$).

## Best Answer

I appreciate this is a cut and paste answer, (which I detest) because I would rather rewrite it to learn something from, but it's 1.00 am here so.... but if you click on the link below it might help. The website below has not been maintained, so you might take a while to resolve it on your machine, sorry.

Extracts From: Sigma Bayon