  We consider the production of a Standard Model Higgs boson decaying to bottom
quarks in association with a vector boson W/Z in hadron collisions. We present
a fully exclusive calculation of QCD radiative corrections both for the
production cross section and for the Higgs boson decay rate up to
next-to-next-to-leading order (NNLO) accuracy. Our calculation also includes
the leptonic decay of the vector boson with finite-width effects and spin
correlations. We consider typical kinematical cuts applied in the experimental
analyses at the Large Hadron Collider (LHC) and we find that the full NNLO QCD
corrections significantly decrease the accepted cross section and have a
substantial impact on the shape of distributions. We point out that these
additional effects are essential to obtain precise theoretical predictions to
be compared with the LHC data.
