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

Abstract

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) state of $Q\bar{Q}{[}^1{S}_0^{[1]}]$, with the aim of assessing the impact of this process on $Z$ bosons decaying into inclusive ${\eta }_Q$. We find that the QCD corrections to the $gg$ process can notably enhance its leading-order results, especially for the ${\eta }_c$ case, which would then greatly increase the existing predictions of ${\Gamma }_{Z\to {\eta }_Q+X}$ given by the CS-dominant process $Z\to {\eta }_Q{[}^1{S}_0^{[1]}]+Q+\bar{Q}$. Moreover, with these significant QCD corrections, the $gg$ process would exert crucial influence on the CS-predicted ${\eta }_Q$ energy distributions. In conclusion, in the CS studies of $Z\to {\eta }_Q+X$, besides $Z\to {\eta }_Q{[}^1{S}_0^{[1]}]+Q+\bar{Q}$, $Z\to {\eta }_Q{[}^1{S}_0^{[1]}]+g+g$ can provide phenomenologically indispensable contributions as well.

Comments: 17 pages, 5 figures, and 2 tables; accepted for publication in Physical Review D