Next-to-leading-log renormalization-group running in heavy-quarkonium creation and annihilation

Abstract

In the framework of potential nonrelativistic QCD, we obtain the next-to-leading-log renormalization-group running of the matching coefficients for the heavy-quarkonium production currents near threshold. This allows us to obtain S-wave heavy-quarkonium production or annihilation observables with next-to-leading-log accuracy within perturbative QCD. In particular, we give expressions for the decays of heavy quarkonium to ${e}^{+}{e}^{\ensuremath{-}}$ and to two photons. We also compute the $O(m{\ensuremath{\alpha}}^{8}{\mathrm{ln}}^{3}\ensuremath{\alpha})$ corrections to the hydrogen spectrum.