Is the Higgs Boson Associated with Coleman-Weinberg Dynamical Symmetry Breaking?

TL;DR

The paper investigates whether the Higgs potential can arise from Coleman–Weinberg dynamics, governed by RG running and trace anomalies. It develops an all-orders RG framework where the CW potential is $V(\phi) = \tfrac{1}{2}\lambda(\phi)\phi^4$ with $\frac{d\lambda}{d\ln\mu} = \beta(\lambda)$ and the extremum condition $\beta = -4\lambda$, linking mass generation to scale symmetry breaking. The improved stress tensor is central to connecting scale invariance, the trace anomaly, and the RG, with the anomaly expressed as $\widetilde{T}^{\mu}_{\mu} = -\frac{\beta(\lambda)}{\lambda} V(\phi)$. The work also discusses phenomenological implications, including a simple scenario with a dormant Higgs doublet around 380 GeV that could realize a CW-generated Higgs potential and yield observable LHC signatures, as well as a fermion-driven two-loop CW mechanism as an alternative route, all while noting UV challenges like Landau poles.

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, trace anomalies, and emphasize the role of the renormalization group in determining Coleman- Weinberg potentials. 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 $SU(2)\times U(1)$) with a mass of $\sim 380$ 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 $\sim 230$ GeV, can drive a Coleman-Weinberg potential at two-loops. The role of the "improved stress tensor" is emphasized, and we propose a non-gravitational term, analogous to the $θ$-term in QCD, which generates it from a scalar action.

Figures (7)

• Figure 1: Classical $\sim \lambda v^4$ potential.
• Figure 2: Typical RG trajectory $\lambda \sim \beta \ln(v/M)$
• Figure 3: Resulting CW potential, $\sim \beta v^4 \ln(v/M)$
• Figure 4: UV running of the dormant Higgs model, $\lambda_i$ vs. $\ln ( \mu/ v_{weak} )$ (black-$\lambda_3$, red-$\lambda_1$, green-$\lambda_2$, blue-$g_{top}$). This shows Landau singularity at $\ln(\mu/v_{weak}) \sim 3\sim 4$, where $v_{weak}=175$ GeV, or $\mu \sim 3\sim 10$ TeV.
• Figure 5: $H^+H^-$ production at LHC.