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 ${\lambda }_{\mathrm{s}}\sim g_{\mathrm{g}}^2$ 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 ${\lambda }_{\mathrm{s}}\sim g_{\mathrm{g}}^4$. 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.

• Received 15 September 2018

DOI:https://doi.org/10.1103/PhysRevD.99.015026

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Published by the American Physical Society