We present a calculation of the $\mathcal{O}({\alpha }_s)$ QCD corrections to the production of a $Z$ boson in association with two photons and to triple-photon production at hadron colliders. All final-state photons are taken as real. For the $Z$ boson, we consider the decays both into charged leptons and into neutrinos including all off-shell effects. Numerical results are obtained via a Monte Carlo program based on the structure of the VBFNLO program package. This allows us to implement general cuts and distributions of the final-state particles. We find that the next-to-leading order QCD corrections are sizable and significantly exceed the expectations from a scale variation of the leading-order result. In addition, differential distributions of important observables change considerably. The prediction of two-photon-associated $Z$ production with $Z$ decays into neutrinos from the charged-lepton rate works well, once we use an additional cut on the invariant mass of the charged-lepton pair.

• Received 27 July 2011

DOI:https://doi.org/10.1103/PhysRevD.84.074028