Two-loop Correction to the Leptonic Decay of Quarkonium

Abstract

Applying asymptotic expansions at threshold, we compute the two-loop QCD correction to the short-distance coefficient that governs the leptonic decay $ψ\to l^+ l^-$ 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.

Figures (1)

• Figure 1: Diagrams that contribute to $\Gamma_{\rm QCD}$. Symmetric diagrams exist for $D_{2,3,5}$. The last diagram summarizes vacuum polarization contributions from massless fermions ($D_6$), gluons ($D_7$), ghosts ($D_8$) and the massive fermion with mass $m_Q$ ($D_9$).