Is the Higgs boson associated with Coleman-Weinberg dynamical symmetry breaking?

Abstract

The Higgs mechanism may be a quantum phenomenon, i.e., a Coleman-Weinberg potential generated by the explicit breaking of scale symmetry in Feynman loops. We review the relationship of scale symmetry and trace anomalies, and we show that the Coleman-Weinberg potential can be defined as the solution to a differential renormalization group equation that follows from the trace of the improved stress tensor. We propose a simple phenomenological model with ``maximal visibility'' at the LHC containing a ``dormant'' Higgs doublet [no VEV, coupled to standard model gauge interactions $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$] with a mass of $\ensuremath{\sim}380\text{ }\text{ }\mathrm{GeV}$. We discuss the LHC phenomenology and UV challenges of such a model. We also give a schematic model in which new heavy fermions, with masses $\ensuremath{\sim}230\text{ }\text{ }\mathrm{GeV}$, can drive a Coleman-Weinberg potential at two loops. The role of the ``improved stress tensor'' is emphasized, and we propose a nongravitational term, analogous to the $\ensuremath{\theta}$ term in QCD, which generates it from a scalar action.