Radiative generation of the Higgs potential

Abstract

We consider the minimal extension of the Standard Model with a generalized B-L gauge symmetry U(1)_X for generating the Higgs potential radiatively. Assuming that the full scalar potential vanishes at the vacuum instability scale, we achieve the goal in terms of two free parameters, the X gauge coupling and the right-handed neutrino Yukawa coupling. The X gauge symmetry is broken spontaneously by the Coleman-Weinberg mechanism while the scale symmetry breakdown induces electroweak symmetry breaking through the radiative generation of appropriate scalar quartic couplings. We show that there is a reasonable parameter space that is consistent with a correct electroweak symmetry breaking and the observed Higgs mass.

Figures (3)

• Figure 1: Examples of running quartic coupling $\lambda_\Phi$ (Blue), the minimization condition (\ref{['Vmin']}) (Red), and $\lambda_{H\Phi}$(Green) (multiplied by $-0.1$ to fit in the plot) for the instability scale $M_I=2\times10^{11}\,{\rm GeV}$ on the left and $M_I=10^{18}\,{\rm GeV}$ on the right. Successful electroweak symmetry breaking occurs in both examples with the charge mixing parameter, $x=4/5$.
• Figure 2: The values of the gauge coupling $g_{X}$vs. the right-handed neutrino Yukawa coupling $y_N$ (Left), the quartic coupling $\lambda_\Phi$ (Middle), and the $U(1)_X$ breaking scale $v_\phi$ (Right) realizing successful electroweak symmetry breaking. We have chosen the charge mixing parameter to $x=4/5$, the Higgs mass at $126\,{\rm GeV}$ and the instability scale, $M_I=2\times 10^{11}\,{\rm GeV}$ and $10^{18}\,{\rm GeV}$, in the upper and lower panels, respectively. We get $M_X>3$TeV in the region left to the vertical dashed line.
• Figure 3: The values of the $U(1)_X$ gauge boson mass vs. the kinetic mixing, $g_{\rm mix}={\widetilde{g}}$ (Left). The values of the gauge coupling $g_X$vs. singlet scalar mass $M_\phi$ (Middle) and Higgs mixing parameter $\sin\theta$ (Right). We have chosen the charge mixing parameter to $x=4/5$, the Higgs mass at $126\,{\rm GeV}$ and the instability scale, $M_I=2\times 10^{11}\,{\rm GeV}$ and $10^{18}\,{\rm GeV}$, in the upper and lower panels, respectively. The vertical dashed line corresponds to $M_X=3\,{\rm TeV}$.