Heavy Quarkonium

TL;DR

This paper reviews heavy quarkonium states within QCD, presenting precise calculations of quark masses, decay rates, and state splittings, and discusses extending these methods to other heavy quark states and light quark bound states.

Contribution

It provides ab initio QCD calculations for heavy quarkonium spectra, including quark masses, decay widths, and state splittings, with high precision and potential extensions to other states.

Findings

Precise $O(\alpha_s^4)$ quark mass evaluations from spectra

Calculation of $mbda o e^+e^-$ decay rate

Prediction of $mbda_b - mbda_b$ splitting

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.