The studies on $Z\to \mathrm{{\rm Y}}(1S)+g+g$ at the next-to-leading-order QCD accuracy

In this paper, we carry out the next-to-leading-order (NLO) studies on $Z \to \Upsilon(1S)+g+g$viathecolor-singlet(CS)$b\bar{b}$ state. We find the newly calculated NLO QCD corrections to this process can significantly influence its leading-order (LO) results, and greatly improve the dependence on the renormalization scale. By including the considerable feeddown contributions, the branching ratio ${\mathcal{B}}_{Z\to \mathrm{{\rm Y}}(1S)+g+g}$ is predicted to be $(0.56\sim 0.95)\times {10}^{-6}$, which can reach up to $19% \sim 31%$oftheLOpredictionsgivenbytheCSdominantprocess$Z \to \Upsilon(1S)+b+\bar{b}$\mathrm{.}Moreover,$Z \to \Upsilon(1S)+g+g$ also seriously affect the CS predictions on the $\mathrm{{\rm Y}}(1S)$ energy distributions, especially when $z$ is relatively small. In summary, for the inclusive $\mathrm{{\rm Y}}(1S)$ productions in $Z$ decay, besides $Z \to \Upsilon(1S)+b+\bar{b}$,thegluonradiationprocess$Z \to \Upsilon(1S)+g+g$ can provide indispensable contributions as well.