Radiative Symmetry Breaking in Classically Conformal Extensions of the Standard Model

Abstract

We examine the dynamical breakdown of the electroweak symmetry in classically conformal extensions of the Standard Model of Particle Physics known as Higgs Portal Models. Since quantum corrections are responsible for symmetry breaking in these extensions, we study the effective potential up to one-loop order and discuss the application of the renormalisation group to ensure the validity of perturbation theory for arbitrary field values. We emphasise how a judicious choice of the renormalisation scale can minimise the effect of large logarithmic contributions from quantum corrections. In particular, we present a method to re-sum the largest logarithms in models with several scalar fields without resorting to multi-scale techniques. In this way, the improved potential admits a perturbative expansion if the renormalised coupling parameters are small. Non-trivial minima of the effective potential correspond to vacua of the underlying quantum field theory and signal the dynamical breakdown of symmetry. By identifying such points, we conclude that certain Higgs Portal Models can accommodate the radiative generation of the electroweak scale, as well as physics beyond the Standard Model. We also comment on the available literature on the subject and discuss the advantages and shortcomings of the different approaches to radiative symmetry breaking.