Inclusive electromagnetic decays of the heavy quarkonium at next to leading log accuracy

Abstract

We show that perturbation theory may give reasonable numbers for the decays of the bottomonium and charmonium ground states to $e^+e^-$ and to $\gamma\gamma$. To reach this conclusion it is important to perform the resummation of logs. In particular, we obtain the value $\Gamma(\eta_b (1S) \to \gamma\gamma)=0.35 \pm 0.1 ({\rm th.}) \pm 0.05 (\lQ)$ KeV.