Abstract
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. In this model context, we investigate the electroweak vacuum instability problem in the SM. It is well known that in the classically conformal U(1)_{B-L} extension of the SM, the electroweak vacuum remains unstable in the renormalization group analysis at the one-loop level. In this paper, we extend the analysis to the two-loop level, and perform parameter scans. We identify a parameter region which not only solve the vacuum instability problem, but also satisfy the recent ATLAS and CMS bounds from search for Z^prime boson resonance at the LHC Run-2. Considering self-energy corrections to the SM Higgs doublet through the right-handed neutrinos and the Z^prime boson, we derive the naturalness bound on the model parameters to realize the electroweak scale without fine-tunings.
Highlights
According to the argument by Bardeen [1] once the classical conformal invariance and its minimal violation by quantum anomalies are imposed on the standard model (SM), the model can be logarithmically sensitive to the ultraviolet cutoff
The massless U(1) Higgs model discussed by Coleman and Weinberg [3] nicely fits this picture, where the model is defined as a massless, conformal invariant theory, and the U(1) gauge symmetry is radiatively broken by the Coleman–Weinberg (CW) mechanism, generating a mass scale through the dimensional transmutation
We have considered the minimal B − L extension of the Standard Model, where the anomaly-free global B − L symmetry in the Standard Model is gauged and three right-hand neutrinos and a B − L Higgs field are introduced
Summary
According to the argument by Bardeen [1] once the classical conformal invariance and its minimal violation by quantum anomalies are imposed on the SM (or the general Higgs model), the model can be logarithmically sensitive to the ultraviolet cutoff. The simplest possibility is to introduce three right-handed neutrinos, which are nothing but the particles that we need to incorporate the neutrino mass in the SM In this conformal symmetric model, the B − L gauge symmetry is broken by the vacuum expectation value (VEV) of the B − L Higgs field developed by the CW mechanism, and the masses for Z boson and three right-handed neutrinos are generated. We evaluate self-energy corrections to the SM Higgs doublet from the heavy states, the Z boson and the right-handed neutrinos associated with the B − L symmetry breaking, and find naturalness bounds to reproduce the electroweak scale without any fine-tunings of model parameters. The electroweak symmetry breaking is driven by the radiative B − L symmetry breaking
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