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In this paper, we carry out the next-to-leading-order QCD corrections to $Z\to \eta_Q+g+g~(Q=c,b)$ (labeled as $gg$) through the color-singlet (CS) stateof $Q\bar{Q}[^1S_0^{[1]}]$, with the aim of assessing the impact of thisprocess on $Z$ bosons decaying into inclusive $\eta_Q$. We find that the QCDcorrections to the $gg$ process can notably enhance its leading-order results,especially for the $\eta_c$ case, which would then greatly increase theexisting predictions of $\Gamma_{Z \to \eta_Q+X}$ given by the CS-dominantprocess $Z \to \eta_{Q}[^1S_0^{[1]}]+Q+\bar{Q}$. Moreover, with thesesignificant QCD corrections, the $gg$ process would exert crucial influence onthe CS-predicted $\eta_Q$ energy distributions. In conclusion, in the CSstudies of $Z \to \eta_Q+X$, besides $Z \to \eta_{Q}[^1S_0^{[1]}]+Q+\bar{Q}$,$Z \to \eta_Q[^1S_0^{[1]}]+g+g$ can provide phenomenologically indispensablecontributions as well.

Impact of $Z \to \eta_{c,b}+g+g$ on the inclusive $\eta_{c,b}$ meson yield in $Z$-boson decay