Radiative Electroweak Symmetry Breaking Model Perturbative All the Way to the Planck Scale

We discuss an extension of the standard model by fields not charged under standard model gauge symmetry in which the electroweak symmetry breaking is driven by the Higgs quartic coupling itself without the need for a negative mass term in the potential. This is achieved by a scalar field $S$ with a large coupling to the Higgs field at the electroweak scale which is driven to very small values at high energies by the gauge coupling of a hidden symmetry under which $S$ is charged. This model can remain perturbative all the way to the Planck scale. The Higgs boson is fully standard-model-like in its couplings to fermions and gauge bosons. However, the effective cubic and quartic self-couplings of the Higgs boson are significantly enhanced.

Figure 1

The RG evolution of quartic couplings ${\lambda }_{H,S,HS}$ in the model with $N_S=1$ (red), 10 (green), and ${10}^2$ (blue) complex scalars for $g_4=0$. The effective potential is minimized at $\mu =\max (m_S,m_H)$ which depends on $N_S$. Boundary conditions at this scale for ${\lambda }_H$ and ${\lambda }_{HS}$ are determined by the observed Higgs boson mass, ${\widehat{\lambda }}_H(m_S)\simeq -1/16$, and ${\lambda }_S$ is set to 0 for simplicity.

Figure 2

The RG evolution of quartic couplings and extra gauge coupling in the model with $N_S=10$. The effective potential is minimized at $\mu =m_S$. Boundary conditions at this scale for ${\lambda }_H$ and ${\lambda }_{HS}$ are determined by the observed Higgs boson mass, ${\widehat{\lambda }}_H(m_S)\simeq -1/16$, and ${\lambda }_S$ is set to 0 for simplicity.

Figure 3

Ratios of predicted effective cubic and quartic couplings and the SM value versus $p$, where $p=N_S{g}_4^2/(16{\pi }^2)$ and $N_S=10$. The dashed line indicates leading order predictions that include the momentum dependent corrections to the Higgs pole mass. Solid curves represent predicted values at one and two loops keeping all the terms coming from derivatives of the effective potential. The gray band shows the $\mu$ dependence of the two loop predictions. We vary $\mu$ from $m_S/\sqrt{2}$ to $\sqrt{2}{m}_S$.