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

Abstract

In this paper, we carry out the next-to-leading-order (NLO) studies on $Z\to {\rm Y}(1S)+g+g$ via the color-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 ${\mathcal{B}}_{Z\to {\rm Y}(1S)+g+g}$ is predicted to be $(0.56\sim 0.95)\times 10^{-6}$, which can reach up to $19\%\sim 31\%$ of the LO predictions given by the CS dominant process $Z\to {\rm Y}(1S)+b+\bar{b}$. Moreover, $Z\to {\rm Y}(1S)+g+g$ also seriously affect the CS predictions on the ${\rm Y}(1S)$ energy distributions, especially when $z$ is relatively small. In summary, for the inclusive ${\rm Y}(1S)$ productions in $Z$ decay, besides $Z\to {\rm Y}(1S)+b+\bar{b}$, the gluon radiation process $Z\to {\rm Y}(1S)+g+g$ can provide indispensable contributions as well.

Comments: 13 pages, 6 figures; discussions, references, and minor clarifications added; accepted for publication in the European Physical Journal C