  We study the so-called HEIDI models, which are renormalizable extensions of
the standard model with a higher-dimensional scalar singlet field. We compare
their predictions with the recent results from the LHC. We show that the data
can easily be described by the HEIDI models. However more data are necessary in
order to distinguish these models from the standard model. A particular
prediction is that the width of the Higgs could be in the GeV range. Such a
width could be difficult to establish at the LHC. Suggestions for experiments
beyond the LHC are made.
