NLO QCD corrections reduce the predicted widths of Z to two jets plus one photon by 6.03% and to two jets plus two photons by 12.39%.
Two numerical numbers corresponding to real and dipole terms are large in the singular re- gion, but their subtraction lies in the regular region
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Next-to-leading order QCD corrections to $Z\to q\bar{q}\gamma$, $q\bar{q}\gamma\gamma$
NLO QCD corrections reduce the predicted widths of Z to two jets plus one photon by 6.03% and to two jets plus two photons by 12.39%.