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 simultaneously satisfies 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.Comment: 18 pages, updated to match published versio
