Rare exclusive decays of the Z-boson revisited

The realization that first- and second-generation Yukawa couplings can be probed by decays of the Higgs boson to a meson in association with a photon has renewed interest in such rare exclusive decays. We present here a detailed study of the rare $Z$-boson processes $Z \to J/\psi+\gamma$, $Z \to \Upsilon+\gamma$, and $Z \to \phi+\gamma$ that can serve as benchmarks for the analogous Higgs-boson decays. We include both direct-production and fragmentation contributions to these decays, and consider the leading QCD corrections and the relativistic corrections to the $J/\psi$ and $\Upsilon$ processes. We present numerical predictions for the branching ratios that include a careful accounting of the theoretical uncertainties.