Heavy Quarkonium

Abstract

Bound states of heavy $\bar{q}q$ quarks are reviewed within the context of QCD. First of all, we consider the calculations which can be performed {\sl ab initio}, which includes $\bar{t}t$ with principal quantum number $n$ up to four, $\bar{b}b$ states with $n=1$ and (to a lesser extent) $\bar{b}b$ with $n=2$ and $\bar{c}c$ for $n=1$. Among the results, we report a very precise $O(\alpha_s^4)$ evaluation of $b, c$ quark masses from quarkonium spectrum with a potential to two loops, a calculation of the decay $\Upsilon\to e^+e^-$ and a prediction for the splitting $\Upsilon - \eta_b$. We then consider how, with the help of reasonable assumptions, one can extend QCD calculations to other states of heavy quarks. Finally, a few words are said on the treatment of light quark bound states.