Criticality and Inflation of the Gauged B-L Model

TL;DR

This paper explores the multiple point principle in a gauged B-L extension of the Standard Model, predicting the B-L gauge boson mass and proposing a new inflation scenario with a scalar field, using two-loop RGEs and minimal assumptions.

Contribution

It demonstrates the realization of the multiple point principle in the gauged B-L model and proposes a novel inflation scenario involving the scalar field with minimal breaking of the principle.

Findings

The B-L gauge boson mass is predicted to be around 696 GeV.

The model achieves electroweak symmetry breaking with very small scalar coupling at the MPP.

A new inflation scenario with the scalar field as the inflaton is proposed.

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 ${\cal{O}}(100)$GeV electroweak symmetry breaking can be achieved even if this breaking is very small; $\lambda_{\Psi}(\Lambda_{\text{MPP}})\leq10^{-10}$. 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{\lambda(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 $\xi\Psi^{2} {\cal{R}}$ based on the two-loop RGEs.