Radiative symmetry breaking at the Fermi scale and flat potential at the Planck scale

Abstract

We investigate a possibility of the "flatland scenario", in which the electroweak gauge symmetry is radiatively broken via the Coleman-Weinberg mechanism starting from a completely flat Higgs potential at the Planck scale. We show that the flatland scenario is realizable only when an inequality K<1 among the coefficients of the beta-functions is satisfied. We show several models satisfying the condition.

Figures (3)

• Figure 1: The RG flows of $\lambda_\Phi$ and $\lambda_{\mathrm{mix}}$ in $(2,1,1)$ model. $v_\Phi=10$ TeV, $m_\phi=81.4$ GeV and $y_M(v_\Phi)=0.378$. $K$ is close to $1$ and the quartic coupling $\lambda_\Phi$ is small. Accordingly, the scalar mass becomes very light compared with $v_\Phi$.
• Figure 2: $M_{Z'}$ vs $M_{\nu_R}$and $m_\phi$ for the $(2,1,1)$ model. $M_{\nu_R}$ is almost proportional to $M_{Z'}$.
• Figure 3: $M_{Z'}$ vs $\alpha_{B-L}(v_\Phi)$ for the $(2,1,1)$ and $(1,1,1)$ models.