Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Next-to-leading-order QCD corrections to $Z \to \eta_c(\eta_b)+g+g$   In this paper, we carry out the next-to-leading-order (NLO) studies of $Z \to
\eta_c(\eta_b)+g+g$ (labeled as $"gg"$) through the color-singlet (CS) state of
$c\bar{c}(b\bar{b})[^1S_0^{[1]}]$, with the aim of assessing the impact of this
process on $Z$ decaying into inclusive $\eta_c(\eta_b)$. We find the
newly-calculated QCD corrections to the $gg$ process can notably enhance its
leading-order (LO) results. To be specific, with the renormalization scale
varying in $[m_{c,b},m_Z]$, $\Gamma_{\eta_c gg}$ is increased by about 8-14
times, and about 1.5-2.0 times for $\eta_b$ production. Consequently,
$\Gamma^{\textrm{NLO}}_{Z \to \eta_c+g+g}$ can reach up to about $40-70\%$ of
the LO results given by the CS dominant process $Z \to \eta_c+c+\bar{c}$, and
about $30-40\%$ for the $\eta_b$ case. Moreover, with the significant QCD
corrections, the $gg$ process would exert crucial influence on the CS
predictions of the $\eta_c(\eta_b)$ energy distributions. In conclusion, in the
CS studies of $Z \to \eta_Q+X~(Q=c,b)$, besides $Z \to
\eta_Q[^1S_0^{[1]}]+Q+\bar{Q}$, the process $ Z \to \eta_Q[^1S_0^{[1]}]+g+g$
can as well provide phenomenologically indispensable contributions.

35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph