QCD corrections and anomalous couplings in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Z</mml:mi><mml:mi>γ</mml:mi></mml:math>production at hadron colliders

The processes $p\stackrel{(\ensuremath{-})}{p}\ensuremath{\rightarrow}Z\ensuremath{\gamma}+\stackrel{\ensuremath{\rightarrow}}{X}{\mathcal{l}}^{+}{\mathcal{l}}^{\ensuremath{-}}\ensuremath{\gamma}+X$ $(\mathcal{l}=e,\ensuremath{\mu})$ and $p\stackrel{(\ensuremath{-})}{p}\ensuremath{\rightarrow}Z\ensuremath{\gamma}+\stackrel{\ensuremath{\rightarrow}}{X}\overline{\ensuremath{\nu}}\ensuremath{\nu}\ensuremath{\gamma}+X$ are calculated to $\mathcal{O}({\ensuremath{\alpha}}_{s})$ for general $\mathrm{ZZ}\ensuremath{\gamma}$ and $Z\ensuremath{\gamma}\ensuremath{\gamma}$ couplings. The impact of $\mathcal{O}({\ensuremath{\alpha}}_{s})$ QCD corrections on the observability of $\mathrm{ZZ}\ensuremath{\gamma}$ and $Z\ensuremath{\gamma}\ensuremath{\gamma}$ couplings in $Z\ensuremath{\gamma}$ production at the Fermilab Tevatron and the CERN Large Hadron Collider (LHC) is discussed.