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 $Λ_{\text{MPP}}:=10^{17}$ 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 $λ_Ψ$ of a newly introduced SM singlet complex scalar $Ψ$ must have a non-zero value at $Λ_{\text{MPP}}$, which means the breaking of the MPP. We find that the ${\cal{O}}(100)$GeV electroweak symmetry breaking can be achieved even if this breaking is very small; $λ_Ψ(Λ_{\text{MPP}})\leq10^{-10}$. 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 $λ$ 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 $λ_Ψ$ opens a new possibility: $Ψ$ plays a roll of the inflaton \cite{Okada:2011en}. Another purpose of this paper is to investigate the $λ_ΨΨ^{4}$ inflation scenario with the non-minimal gravitational coupling $ξΨ^{2} {\cal{R}}$ based on the two-loop RGEs.