NNLO QCD corrections to weak boson fusion Higgs boson production in the $H \to b\bar b$ and $H \to WW^* \to 4l$ decay channels

We compute the next-to-next-to-leading order QCD corrections to Higgs boson production in weak boson fusion followed by its decay to a b$ \overline{b} $ pair or to a pair of leptonically-decaying W bosons. Our calculation allows us to compute realistic fiducial cross sections and assess the impact of fiducial cuts applied to the Higgs boson decay products on the magnitude of QCD radiative corrections in weak boson fusion.