Electroweak vacuum stability in classically conformal B-L extension of the Standard Model

Understand

We consider the minimal U(1)$_{B-L}$ extension of the Standard Model (SM) with the classically conformal invariance, where an anomaly free U(1)$_{B-L}$ gauge symmetry is introduced along with three generations of right-handed neutrinos and a U(1)$_{B-L}$ Higgs field.

• Because of the classically conformal symmetry, all dimensional parameters are forbidden.
• The $B-L$ gauge symmetry is radiatively broken through the Coleman-Weinberg mechanism, generating the mass for the $U(1)_{B-L}$ gauge boson ($Z^\prime$ boson) and the right-handed neutrinos.
• Through a small negative coupling between the SM Higgs doublet and the $B-L$ Higgs field, the negative mass term for the SM Higgs doublet is generated and the electroweak symmetry is broken.