# How do $\pi^0$ particles exist?

I have been taught that the $\pi^0$ particle contains either an up quark and an anti-up quark or a down and an anti-down. How can these exist without annihilating?

Also, it is its own antiparticle, but it doesn't make sense that the up version and down version would annihilate when they meet.

Or is what I've been taught a simplification - if so, in what state does this particle exist?

• This is basically the same as another question that was asked here before: physics.stackexchange.com/questions/236/… – Matt Reece Jan 11 '11 at 20:15
• @Matt: good catch, I totally forgot about that one. Although personally, I don't think we necessarily need to close this as a duplicate, since it seems like one of those cases where having the same question asked in different ways might be useful. – David Z Jan 11 '11 at 20:17
• It is the same question... about why and how do they exist. But the annihilation method is completely different in positronium than in $\pi^0$, because of the chiral anomaly. Of course that is beyond the scope of the OP and in fact it could be a new question, how different is positronium decay from pi0 decay. – arivero Jan 17 '11 at 1:47

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.)

• What happens if we detect some neutral pion? Is it still a linear combination of up and down states? – AndyK Jul 15 '11 at 22:05
• We don't actually detect the pion itself, we detect the photons produced when it decays. – David Z Jul 15 '11 at 22:17
• Can we conclude from the produced photons what was the exact quark structure of the neutral pion? I mean, can we tell that it was $u\bar{u}$ or $d\bar{d}$? – AndyK Jul 15 '11 at 22:23
• @ANKU: we know the quark structure of the neutral pion, there is nothing to tell. It is the state given in my answer. – David Z Jul 15 '11 at 23:12