TeV-scale B − L model with a flat Higgs potential at the Planck scale: In view of the hierarchy problem

Abstract

The recent discovery of a Higgs-like particle at around 126 GeV has provided a big hint towards the origin of the Higgs potential. In particular, the running quartic coupling vanishes near the Planck scale, which indicates a possible link between the physics in the electroweak and 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 renormalization group analysis of the B − L (baryon number minus lepton number) extension of the standard model [1,2] with 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 to the B − L breaking scale at the TeV level. The Higgs boson mass is given at the border of the stability bound, which is lowered by a few GeV from the standard model by the effect of the B − L gauge interaction.