One-loop corrections to the processes $e^+e^- \to \gamma, Z_0 \to J/\psi~\eta_c$ and $e^+e^- \to Z_0 \to J/\psi~J/\psi$

The cross sections of $J/\ensuremath{\psi}\text{ }{\ensuremath{\eta}}_{c}$ and $J/\ensuremath{\psi}\text{ }J/\ensuremath{\psi}$ production in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation are calculated at a one-loop accuracy near $Z$-boson pole and at higher energies as well. Both intermediate bosons, $\ensuremath{\gamma}$ and $Z$, are included. It is found that at $Z$ mass, the next-to-leading contribution increases the production cross sections by a factor of 3.5.