We examine the problems of calculating the leading relativistic corrections to heavy-quarkonium decays [relative $O\left(v^2\right)$] within the context of QCD. The incorporation of constituent motion in a consistent manner poses nontrivial problems associated with gauge invariance and multiple counting with higher-order contributions in the coupling constant. Although we were unable to resolve these questions in a completely satisfactory manner, we present an improved static limit where the kinematic relativistic corrections are included through binding effects. Our results are gauge invariant and in qualitative agreement with the relative size of relativistic corrections suggested in the analysis of the branching ratio of $\frac{\Gamma \mathrm{}\left(3g\right)\mathrm{}}{\Gamma \left(l\overline{l}\right)}$ in the $\frac{\psi }{J}$ and $\Upsilon$ systems in QCD.

• Received 10 November 1982

DOI:https://doi.org/10.1103/PhysRevD.27.1518