  It is possible to delay the hierarchy problem, by replacing the standard
Higgs-sector by the Coleman-Weinberg mechanism, and at the same time ensure
perturbative naturalness through the so-called Veltman conditions. As we showed
in a previous study, minimal models of this type require the introduction of an
extra singlet scalar further coupled to new fermions. In this constrained setup
the Higgs mass was close to the observed value and the new scalar mass was
below a TeV scale. Here we first extend the previous analysis by taking into
account the important difference between running mass and pole mass of the
scalar states. We then investigate whether these theories can account for the
750 GeV excess in diphotons observed by the LHC collaborations. New QCD-colored
fermions in the TeV mass range coupled to the new scalar state are needed to
describe the excess. We further show, by explicit computation of the running of
the couplings, that the model is under perturbative control till just above the
masses of the heaviest states of the theory. We further suggest related
testable signatures and thereby show that the LHC experiments can test these
models.
