TeV Scale B-L model with a flat Higgs potential at the Planck scale -- in view of the hierarchy problem

TL;DR

This work proposes that the Higgs potential is flat at a UV scale, motivated by the 126 GeV Higgs and Planck-scale considerations, and explores a minimal, classically conformal $U(1)_{B-L}$ extension of the SM. The $B-L$ sector undergoes Coleman–Weinberg radiative breaking at the TeV scale, and a radiatively generated Higgs–Φ mixing triggers electroweak symmetry breaking, dynamically tying the EW and $B-L$ breaking scales. RG analyses show a lowered Higgs vacuum-stability bound relative to the SM and yield a predictive relation between the TeV-scale $Z'$ mass and the $B-L$ breaking scale, with distinctive collider signatures. The approach provides a simple, UV-insensitive path to the hierarchy problem and vacuum stability, with concrete phenomenological predictions for near-future experiments.

Abstract

The recent discovery of the Higgs-like particle at around 126 GeV has given us a big hint towards the origin of the Higgs potential. Especially the running quartic coupling vanishes near the Planck scale, which indicates a possible link between the physics in the electroweak and the Planck scales. Motivated by this and the hierarchy problem, we investigate a possibility that the Higgs has a flat potential at the Planck scale. In particular, we study the RG analysis of the B-L extension of the standard model with a classical conformality. The B-L symmetry is radiatively broken at the TeV scale via the Coleman-Weinberg mechanism. The electroweak symmetry breaking is triggered by a radiatively generated scalar mixing so that its scale 246 GeV is dynamically related with the B-L breaking scale at TeV. The Higgs boson mass is given at the border of the stability bound,which is lowered by a few GeV from the SM by the effect of the B-L gauge interaction.

Figures (4)

• Figure 1: RG evolution of the self-coupling $\lambda_\phi$ of a SM singlet scalar $\phi$. Since the $\beta$ function is positive, the running coupling crosses zero at a lower energy scale.
• Figure 2: RG evolution of scalar mixing between a SM singlet $\Phi$ and the Higgs $H$. Starting from zero mixing at $M_{UV}=10^{17}GeV$, a small negative mixing is radiatively generated at a lower energy scale. The mixing triggers the EWSB.
• Figure 3: Model prediction is drawn in the black line (from top left to down right). The $B-L$ gauge coupling $\alpha_{B-L}$ and the gauge boson mass $m_{Z'}$ are related because of the flat potential assumption at the Planck scale. The left side of the most left solid line in blue has been already excluded by the LEP experiment. The left of the dashed line can be explored in the 5-$\sigma$ significance at the LHC with $\sqrt{s}$=14 TeV and an integrated luminosity 100 fb$^{-1}$. The left of the most right solid line (in red) can be explored at the ILC with $\sqrt{s}$=1 TeV, assuming 1% accuracy.
• Figure 4: Higgs stability bound up to $M_{UV}=10^{17}$ GeV as a function of the $B-L$ gauge coupling. We set $M_t=173.1$ GeV and $\alpha_s(M_Z)=0.1184.$