Two-Loop Corrections to the Leptonic Decays of Quarkonium

Abstract

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