Classically conformal U(1)\(^\prime\) extended Standard Model and Higgs vacuum stability

• Published in: arXiv.org 2015-04
• Main Authors: Oda, Satsuki, Okada, Nobuchika, Takahashi, Dai-suke
• Format: Article
• Language: English
• Subjects: Anomalies; Broken symmetry; Mathematical models; Neutrinos; Parameter identification; Stability; Standard model (particle physics); Symmetry; Upper bounds
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1504.06291

We consider the minimal U(1)\(^\prime\) extension of the Standard Model (SM) with conformal invariance at the classical level, where in addition to the SM particle contents, three generations of right-handed neutrinos and a U(1)\(^\prime\) Higgs field are introduced. In the presence of the three right-handed neutrinos, which are responsible for the seesaw mechanism, this model is free from all the gauge and gravitational anomalies. The U(1)\(^\prime\) gauge symmetry is radiatively broken via the Coleman-Weinberg mechanism, by which the U(1)\(^\prime\) gauge boson (\(Z^\prime\) boson) mass as well as the Majorana mass for the right-handed neutrinos are generated. The radiative U(1)\(^\prime\) symmetry breaking also induces a negative mass squared for the SM Higgs doublet to trigger the electroweak symmetry breaking. In this context, we investigate a possibility to solve the SM Higgs vacuum instability problem. The model includes only three free parameters (U(1)\(^\prime\) charge of the SM Higgs doublet, U(1)\(^\prime\) gauge coupling and \(Z^\prime\) boson mass), for which we perform parameter scan, and identify a parameter region resolving the SM Higgs vacuum instability. We also examine naturalness of the model. The heavy states associated with the U(1)\(^\prime\) symmetry breaking contribute to the SM Higgs self-energy. We find an upper bound on \(Z^\prime\) boson mass, \(m_{Z^\prime} \lesssim 6\) TeV, in order to avoid a fine-tuning severer than 10 % level. The \(Z^\prime\) boson in this mass range can be discovered at the LHC Run-2 in the near future.