  Radiative symmetry breaking (RSB) is a theoretically appealing framework for
the generation of mass scales through quantum effects. It can be successfully
implemented in models with extended scalar and gauge sectors. We provide a
systematic analysis of RSB in such models: we review the common approximative
methods of studying RSB, emphasising their limits of applicability and discuss
the relevance of the relative magnitudes of tree-level and loop contributions
as well as the dependence of the results on the renormalisation scale. The
general considerations are exemplified within the context of the conformal
Standard Model extended with a scalar doublet of a new SU(2)$_X$ gauge group,
the so-called SU(2)cSM. We show that various perturbative methods of studying
RSB may yield significantly different results due to renormalisation-scale
dependence. Implementing the renormalisation-group (RG) improvement method
recently developed in arXiv:1801.05258, which is well-suited for multi-scale
models, we argue that the use of the RG improved effective potential can
alleviate this scale dependence providing more reliable results.
