  We consider scale invariant models where the classical scale invariance is
broken perturbatively by radiative corrections at the electroweak scale. These
models offer an elegant and simple solution to the hierarchy problem. If we
further require the cosmological constant to be small then such models are also
highly predictive. Indeed, the minimal such model, comprising a Higgs doublet
and a real singlet, has the same number of parameters as the standard model.
Although this minimal model is disfavoured by recent LHC data, we show that two
specific extensions incorporating neutrino masses and dark matter are fully
realistic. That is, consistent with all experiments and observations. These
models predict a light pseudo-Goldstone boson, $h$, with mass around 10 GeV or
less. A fermionic-bosonic mass relation is also predicted. The specific models
considered, as well as more generic scale invariant models, can be probed at
the LHC.
