Preprint number: CP3-Origins-2013-39 DNRF90 and DIAS-2013-39
Using the renormalisation group framework we classify different extensions of the standard model according to their degree of naturality. A new relevant class of perturbative models involving elementary scalars is the one in which the theory satisfies simultaneously the Veltman conditions and is conformal at the classical level. We term these extensions perturbative natural conformal (PNC) theories. We show that PNC models are very constrained and thus highly predictive. Among the several PNC examples that we exhibit, we discover a remarkably simple PNC extension of the standard model in which the Higgs is predicted to have the experimental value of the mass equal to 126 GeV. This model also predicts the existence of one more standard model singlet scalar boson with a mass of 541 GeV and the Higgs self-coupling to emerge radiatively. We study several other PNC examples that generally predict a somewhat smaller mass of the Higgs to the perturbative order we have investigated them. Our results can be a useful guide when building extensions of the standard model featuring fundamental scalars.