Z-boson decays to heavy quarkonium

We evaluate the decays $Z\to Q+\overline{Q}+S\left(Q\overline{Q}\right)$ of $Z$ bosons to ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\left(Q\overline{Q}\right)$ and ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\left(Q\overline{Q}\right)$ quarkonium states of charm and bottom quarks. We find partial widths of $\Gamma \left(\frac{Z\to c\overline{c}\psi }{J}\right)=47\mathrm{}$ keV, $\Gamma (Z\to c\overline{c}{\eta }_c)=145\mathrm{}$ keV, $\Gamma (Z\to b\overline{b}{\Upsilon }_b)=6.4\mathrm{}$ keV, and $\Gamma (Z\to b\overline{b}{\eta }_b)=6.5\mathrm{}$ keV, that might be observable at the CERN $e^{+}{e}^{-}$ collider LEP. We also calculate the partial widths for $W^{+}\to \frac{c\overline{s}\psi }{J}$, $t\to W^{+}b{\Upsilon }_b$, ${\eta }_Q\to \mathrm{Zgg}$, and $Z\to {\eta }_{c,b}\mathrm{gg}$ decays.