Charmonium decays: J/ψ→e+e− and ηc→γγ

We compute the O(αs2) correction to the decay rate ηc→γγ and discuss its implications for precision quarkonium physics. We study the suitability of the ratio Γ(J/ψ→e+e−)/Γ(ηc→γγ), in which the non-perturbative or soft effects cancel through O(αs), for extracting fundamental parameters of QCD at low energies. We show that when O(αs2) corrections are included, this ratio cannot be predicted with a high degree of confidence.