  We present a computation of the next-to-next-to-leading order (NNLO) QCD
corrections to the production of a Higgs boson in association with a W boson at
the LHC and the subsequent decay of the Higgs boson into a b-bbar pair,
treating the b-quarks as massless. We consider various kinematic distributions
and find significant corrections to observables that resolve the Higgs decay
products. We also find that a cut on the transverse momentum of the W boson,
important for experimental analyses, may have a significant impact on kinematic
distributions and radiative corrections. We show that some of these effects can
be adequately described by simulating QCD radiation in Higgs boson decays to
b-quarks using parton showers. We also describe contributions to Higgs decay to
a b-bbar pair that first appear at NNLO and that were not considered in
previous fully-differential computations. The calculation of NNLO QCD
corrections to production and decay sub-processes is carried out within the
nested soft-collinear subtraction scheme presented by some of us earlier this
year. We demonstrate that this subtraction scheme performs very well, allowing
a computation of the coefficient of the second order QCD corrections at the
level of a few per mill.
