General analysis of scale-setting in classically conformal multiscalar models

In this thesis we investigate the fundamental features of radiatively induced spontaneous symmetry breaking (RSSB) in multiscalar models without classical mass terms. Motivated by addressing the hierarchy problem via the extension of the conformal standard model (cSM) we present a general formalism to analyze the generation of non-trivial minima in the one-loop effective potential via a set of exact criticality equations. Given the intuitive nature of these equations we are able to systematically analyze the RSSB in classically conformal multiscalar models. Specifically, we investigate the interplay of contributions by different particles at the scale of condensation and in the renormalization group running of the coupling parameters. We compare the observed features of RSSB to results obtained when using the commonly used Gildener-Weinberg approximation, which additionally assumes the existence of a flat direction at tree-level. Without making further assumptions to classical scale-invariance we already find cases where one-loop gauge contributions can generally be of the same order of magnitude as the scalar tree-level terms. Thus, allowing for the generation of non-trivial vacua without a tree-level flat direction. The analysis using our approach reveals qualitatively new scenarios of RSSB compared to the Gildener-Weinberg approximation and allows for an intuitive investigation of fundamental properties of scale-setting without making further assumptions to classical scale-invariance