## Ground state of toponium

Following the series of posts I started after the beautiful result of BABAR collaboration, now I try to get a prevision for a new resonance, i.e. the ground state of $\bar t t$ quarkonium that is known in literature as toponium. This resonance has a large mass with respect to the others due to t quark being about 37 times more massive than b quark. In this case we have a theoretical reference by Yuri Goncharov (see here) published in Nuclear Physics A (see here). Goncharov assumes a mass for the top quark of 173.25 GeV and gets $\alpha_s(m_t)\approx 0.12$. He has a toponium ground state mass of 347.4 GeV. How does our formula compare with these values?

Let us give again this formula as

$\eta_t(1S)=2m_t-\frac{1}{4}\alpha_s^2m_t+0.876\alpha_s\sqrt{\sigma}$

being $\sqrt{\sigma}=0.44$ GeV. We obtain

$m_{\eta_t}=345.9$ GeV

that is absolutely good being the error of about 0.4% compared to Goncharov’s paper! Now, using the value of PDG $m_t=172.5$ GeV we get our final result

$m_{\eta_t}=344.4$ GeV.

This is the next quarkonium to be seen. Alhtough we can theoretically do this computation, we want just to point out that no toponium could be ever observed due to the large mass and width of the t quark (see here for a computation).

### 4 Responses to Ground state of toponium

1. Igor Ivanov says:

Dear Marco,

> This is the next quarkonium to be seen.

do you really expect toponium to be seen as a separate peak in the energy dependence of the ttbar production cross section given the large width of the t-quark? If not, how else do you expect toponium to be observed?

Igor

2. mfrasca says:

Dear Igor,

You are right of course and I was somewhat imprudent with my last sentence. It could be that t quark cannot form such a bound state due to its large mass and width (e.g. see http://arxiv.org/abs/hep-ph/9704261). I will correct this.

Thank you for pointing out this.

Marco

3. Alejandro Rivero says:

Actually, I have remarked sometimes that the lack of bound state for toponium and top mesons could have deeper significance. If all the bound states of mesons and diquarks are build only from a “SU(5) flavour” instead of “SU(6)” (I put the quotes because flavour models usually put spin in the game) then the number of different mesons is equal, charge to charge, to the number of leptons. (ie six (b,s,d) x (-c,-u) “scalar” combinations against six (tau,mu,e)x(+1/2,-1/2) “fermion” combinations, 12 for the neutrinos, other 6 for positors). And the number of different “scalar diquarks” is the same, charge for charge too. It is a surprise because it does not work generically for any number or generations, it is an exclusive coincidence due to three generations and high top mass. Get a dynamics for it, and you will have the first argument proving the need of three generations.

4. mfrasca says:

Alejandro,