Impact of Z→ηc,b+g+g on the inclusive ηc,b meson yield in Z -boson decay

Abstract

In this paper, we carry out the next-to-leading-order QCD corrections to $Z\ensuremath{\rightarrow}{\ensuremath{\eta}}_{Q}+g+g(Q=c,b)$ (labeled as $gg$) through the color-singlet (CS) state of $Q\overline{Q}[{^{1}S}_{0}^{[1]}]$, with the aim of assessing the impact of this process on $Z$ bosons decaying into inclusive ${\ensuremath{\eta}}_{Q}$. We find that the QCD corrections to the $gg$ process can notably enhance its leading-order results, especially for the ${\ensuremath{\eta}}_{c}$ case, which would then greatly increase the existing predictions of ${\mathrm{\ensuremath{\Gamma}}}_{Z\ensuremath{\rightarrow}{\ensuremath{\eta}}_{Q}+X}$ given by the CS-dominant process $Z\ensuremath{\rightarrow}{\ensuremath{\eta}}_{Q}[{^{1}S}_{0}^{[1]}]+Q+\overline{Q}$. Moreover, with these significant QCD corrections, the $gg$ process would exert crucial influence on the CS-predicted ${\ensuremath{\eta}}_{Q}$ energy distributions. In conclusion, in the CS studies of $Z\ensuremath{\rightarrow}{\ensuremath{\eta}}_{Q}+X$, besides $Z\ensuremath{\rightarrow}{\ensuremath{\eta}}_{Q}[{^{1}S}_{0}^{[1]}]+Q+\overline{Q}$, $Z\ensuremath{\rightarrow}{\ensuremath{\eta}}_{Q}[{^{1}S}_{0}^{[1]}]+g+g$ can provide phenomenologically indispensable contributions as well.