Understanding the Pi-0 Meson Quark Makeup: An Explanation of its Composition

[UniPhysics90]

I understand that the pi⁺ meson is made up of an up and an anti down quark, and the opposite for the pi^- meson.

What I'm not really understanding is the makeup of the pi⁰ quark: http://img219.imageshack.us/i/piol.png/ *Sorry, couldn't get the image tags to work :(*

there is 3 main points I don't get about this:

1. Why does this have 4 quarks whilst plus and minus have two?
2. Why the minus sign, why not a plus?
3. Why the factor of 1/root2 out the front?

I've tried searching on the internet, but I can barely find the makeup of this meson anywhere, let alone an explanation.

Thanks!

 

[ParticleGrl]

The pion isn't made up of 4 quarks. Rather, its a superposition of two different 2-quark states,(u anti-u, and d ant-d).

This isn't entirely accurate, but if you aren't familiar with quantum mechanics you might consider thinking of the pion as quark,anti-quarks constantly annihilating into gluons, which split back into quark-antiquark pairs. The 1/sqrt(2) out front keeps this superposition normalized.

The minus sign is a bit harder to explain, but it comes from the fact that the 3 pions fit into a mathematical structure known as isospin. If you are familiar with ladder operators and spin in quantum mechanics, you might recognize the structure as similar to that of the spin triplet.

 

[zincshow]

One way to view this is half the time you measure it you will see a u/anti-u, the other half of the time you measure it you will see a d/anti-d pair. Both pairs have only 2 quarks and no charge. The root-2 factor is the fancy math way to demonstrate the 50% probability of what you measure.