# Which mesons are possible?

That's probably a plain question but I wonder: Which mesons can exist? The only limitation I'm aware of is the charge (antiparticle+particle). Ok, finally also the color (anticolor+color) but I assume this is not really reducing the possibilities.

Can you please shine a bit light on me?

You can classify mesons via two questions:

1. How do they transform under P and C?

$P$ is the eigenvalue under parity transformations and $C$ is the eigenvalue under charge conjugation. They can take on the values $\pm 1$, so the possibilities are $$PC = \big\{(++), \, (+-),\,(-+),\, (--)\big\}$$

2. What is their quark structure?

Here I'm talking about constituent quarks, that is no quark-antiquark pairs that may appear inside a meson.

If you answer those two questions, you can find an associated name in tables like this one, which is a good summary of all the different mesons.

As you can see in the review I linked above, the lowest possibilities for the total angular momentum $J$ are $$J^{PC} = 0^{++},\, 1^{+-},\, 0^{-+},\, 1^{--}$$ They are the ground state, whereas higher-$J$ represent excited states.
• Yes, since “meson” just means “quark+antiquark”, you can have every combination of six flavors. And since e.g. $u\bar u$ is also possible, there’s $6^2=36$ combinations! These 36 combinations relate to the second question in my answer. Then you can also have 4 different $PC$ structures, which gives $4\times 36=144$ possibilities for the ground state. Then there are who-knows-how-many excited states... – Stephan Nov 16 '17 at 10:57