Systematic analysis of radiative symmetry breaking in models with extended scalar sector

TL;DR

This paper systematically analyzes radiative symmetry breaking in models with extended scalar sectors, emphasizing the importance of renormalization scale dependence and demonstrating the effectiveness of RG improvement methods for reliable predictions.

Contribution

It reviews common approximation methods for RSB, discusses their limitations, and applies RG improvement to enhance the reliability of results in extended scalar models like SU(2)cSM.

Findings

Different perturbative methods can give varying RSB results due to scale dependence.

RG improvement reduces scale dependence, leading to more consistent predictions.

The analysis highlights the importance of considering loop and tree-level contributions carefully.

Abstract

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.