Quarkonium: General Information

[buzsh]

So I've been set a computational problem regarding applying the Shroedinger equation to quarkonium and I'm just trying to do some research around the subject because it's nothing like I've ever covered before and quite fascinating. There's quite a few questions that I can't find answers to though as this seems to be a recent and poorly understood and documented area, so I'd really appreciate your thoughts on these.

1) I understand that toponium isn't a thing because the top quarks decay before a bound state can be formed, but as bottomonium and charmonium are a thing, why is it quarkonium doesn't consider the lighter quarks? And how does this differ from a pion?

2) What stops the annihilation of these mesons? I've heard of positronium, but that decays quickly. Do I need to assume that quarkonium follows the same fate because any literature I've found seems to gloss over it? Or do they decay into other quarks first?

3) The potential between them I've found is:
- ^4a/_3r + br
What is the origin of these terms? The first is the strong force, but I only know that because a is labelled the strong coupling constant. It could just as easily be the electromagnetic force with an arrangement like that; I would have assumed the strong force would be a bit more complex. I can't explain the origin of the second term. Is it just a mathematical construct to tidy up the phenomena that quarks never exist on their own or something physical?

Really appreciate any knowledge you can impart on me around the subject. Thank you :)

 

[Einj]

1) There is no intrinsic difference between a pion and, say, a J/psi in the sense that we nature of the binding is still stong force. However, when the two quarks are heavy, as for charmonium and bottomonium, you can study the two-body system in terms of the Born-Oppenheimer approximation and extract the potential from that. This can be done with heavy quarks because they behave fairly non-relativistically.

2) I honestly don't know if that's true for every heavy quarkonium, but in the case of J/psi there is something called the OZI rule that tells you that some J/psi decay modes appear less frequently because they can only happen via three intermediate gluons. Maybe you can solve your doubt starting from this.

3) The potential as a whole is a strong potentiale. That's something peculiar about strong forces, i.e. at very small distances they are pretty similar to e.m. forces, just with a different coupling constant. However, for large distances the potential grows linearly and so the two color sources cannot travel too far away from each other. This is what causes the so-called confinement, i.e. colored particles are always bound into hadrons.
The previous potential is usually obtained from lattice QCD calculations, exactly because you can use the Born-Oppenheimer approx. as I mentioned before.

I hope this is helpful