Two-loop Correction to the Leptonic Decay of Quarkonium

Applying asymptotic expansions at threshold, we compute the two-loop QCD correction to the short-distance coefficient that governs the leptonic decay $\psi \to l^{+}{l}^{-}$ of a S-wave quarkonium state and discuss its impact on the relation between the quarkonium non-relativistic wave function at the origin and the quarkonium decay constant in full QCD.