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In this paper, we carry out the next-to-leading-order (NLO) studies on $Z \to\Upsilon(1S)+g+g$ via the color-singlet (CS) $b\bar{b}$ state. We find thenewly calculated NLO QCD corrections to this process can significantlyinfluence its leading-order (LO) results, and greatly improve the dependence onthe renormalization scale. By including the considerable feeddowncontributions, the branching ratio $\mathcal{B}_{Z \to \Upsilon(1S)+g+g}$ ispredicted to be $(0.56 \sim 0.95)\times 10^{-6}$, which can reach up to $19\%\sim 31\%$ of the LO predictions given by the CS dominant process $Z \to\Upsilon(1S)+b+\bar{b}$. Moreover, $Z \to \Upsilon(1S)+g+g$ also seriouslyaffect the CS predictions on the $\Upsilon(1S)$ energy distributions,especially when $z$ is relatively small. In summary, for the inclusive$\Upsilon(1S)$ productions in $Z$ decay, besides $Z \to\Upsilon(1S)+b+\bar{b}$, the gluon radiation process $Z \to \Upsilon(1S)+g+g$can provide indispensable contributions as well.

The studies on $Z \to \Upsilon(1S)+g+g$ at the next-to-leading-order QCD accuracy