Criticality and Inflation of the Gauged B-L Model

Abstract

We consider the multiple point principle (MPP) and the inflation of the gauged B-L extension of the Standard Model (SM) with a classical conformality. We examine whether the scalar couplings and their beta functions can become simultaneously zero at ${\Lambda }_{\text{MPP}}:=10^{17}$ GeV by using the two-loop renormalization group equations (RGEs). We find that we can actually realize such a situation and that the parameters of the model are uniquely determined by the MPP. However, as discussed in \cite{Iso:2012jn}, if we want to realize the electroweak symmetry breaking by the radiative B-L symmetry breaking, the self coupling ${\lambda }_{\Psi }$ of a newly introduced SM singlet complex scalar $\Psi$ must have a non-zero value at ${\Lambda }_{\text{MPP}}$, which means the breaking of the MPP. We find that the $\mathcal{O}(100)$GeV electroweak symmetry breaking can be achieved even if this breaking is very small; ${\lambda }_{\Psi }({\Lambda }_{\text{MPP}})\le 10^{-10}$. Within this situation, the mass of the B-L gauge boson is predicted to be \begin{equation} M_{B-L}=2\sqrt{2}\times\sqrt{\frac{λ(v_{h})}{0.10}}\times v_{h}\simeq 696\hspace{1mm}\text{GeV},\nonumber\end{equation} where $\lambda$ is the Higgs self coupling and $v_h$ is the Higgs expectation value. This is a remarkable prediction of the (slightly broken) MPP. Furthermore, such a small ${\lambda }_{\Psi }$ opens a new possibility: $\Psi$ plays a roll of the inflaton \cite{Okada:2011en}. Another purpose of this paper is to investigate the ${\lambda }_{\Psi }{\Psi }^4$ inflation scenario with the non-minimal gravitational coupling $\xi {\Psi }^2\mathcal{R}$ based on the two-loop RGEs.

arXiv comment28 pages, 8 figures; some typos are corrected, Eq.(11) is corrected, the predicted mass of M_{B-L} has changed, RGEs are corrected, footnotes added, references added (v2); some typos are corrected, Eq.(26) is added, references added, version to appear in PTEP(v3)

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