## Ground state of toponium

27/08/2008

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).