Gluon induced contributions to WZ and W gamma production at NNLO

We calculate the contribution of the partonic processes $g\stackrel{\ensuremath{\rightarrow}}{g}\mathrm{WZq}\overline{q}$ and $g\stackrel{\ensuremath{\rightarrow}}{g}W\ensuremath{\gamma}q\overline{q}$ to $\mathrm{WZ}$ and $W\ensuremath{\gamma}$ pair production at hadron colliders, including anomalous triple gauge-boson couplings. We use the helicity method and include the decay of the W and Z bosons into leptons in the narrow-width approximation. In order to integrate over the $q\overline{q}$ final state phase space we use an extended version of the subtraction method to NNLO and remove collinear singularities explicitly. Because of the large gluon density at low x, the gluon induced terms of vector-boson pair production are expected to be the dominant NNLO QCD correction, relevant at CERN LHC energies. However, we show that due to a cancellation they turn out to provide a rather small contribution, anticipating good stability for the perturbative expansion.