Consistent Conformal Extensions of the Standard Model

The question of whether classically conformal modifications of the standard model are consistent with experimental observations has recently been subject to renewed interest. The method of Gildener and Weinberg provides a natural framework for the study of the effective potential of the resulting multiscalar standard model extensions. This approach relies on the assumption of the ordinary loop hierarchy λs∼gg2 of scalar and gauge couplings. On the other hand, Andreassen et al. recently argued that in the (single-scalar) standard model gauge invariant results require the consistent scaling λs∼gg4. In the present paper, we contrast these two hierarchy assumptions and illustrate the differences in the phenomenological predictions of minimal conformal extensions of the standard model.