Next-to-leading order QCD corrections to $Z\to q\bar{q}\gamma$, $q\bar{q}\gamma \gamma$

We consider the rare decay channels of the $Z$ boson: $Z\to \text{two jets}+\gamma$ and $Z\to \text{two jets}+2\gamma$. To obtain the widths and distributions for these processes, we compute the effect of NLO QCD corrections to the processes $Z\to q\bar{q}+\gamma$ and $Z\to q\bar{q}+2\gamma$. We find that these corrections reduce the widths of these processes by about $6.03\mathrm{\%}$ and $12.39\mathrm{\%}$, respectively. The reduction in the partial widths is larger at the jet level. These NLO-improved decay observables may be tested in future runs of the LHC or at future $e^{+}{e}^{-}$ colliders.