  We calculate the fully differential next-to-next-to-leading-order (NNLO)
corrections to vector-boson fusion (VBF) Higgs production at proton colliders,
in the limit in which there is no cross-talk between the hadronic systems
associated with the two protons. We achieve this using a new
"projection-to-Born" method that combines an inclusive NNLO calculation in the
structure-function approach and a suitably factorised next-to-leading-order
(NLO) VBF Higgs plus 3-jet calculation, using appropriate Higgs plus 2-parton
counter events. An earlier calculation of the fully inclusive cross section had
found small NNLO corrections, at the 1% level. In contrast, the cross section
after typical experimental VBF cuts receives NNLO contributions of about 4%,
while differential distributions show corrections of up to 6-7% for some
standard observables. The corrections are often outside the NLO
scale-uncertainty band.
