Radiative symmetry breaking in a gauged Zee-Babu model and its gravitational wave imprints

Abstract

We construct a classically scale invariant version of the Zee-Babu model governed by an $U(1)_{B-L}$ gauge symmetry wherein three right handed neutrinos with identical gauge charges are present. A $\mathbb{Z}_2$ symmetry is additionally imposed such that the lightest right handed neutrino becomes a dark matter candidate. A spontaneous breakdown of the $U(1)_{B-L}$ gauge group is triggered radiatively through renormalisation group effects and the dimensionful parameters thus emerging are proportional to the corresponding breaking scale $v_{BL}$. We demonstrate in this study how the same $v_{BL}$ controls the dynamics of neutrino mass generation, lepton flavour violation and dark matter phenomenology. It is revealed that the scenario can simultaneously accommodate the observed neutrino masses and mixings, an appropriately low lepton flavour violation and the observed dark matter relic density for 10 TeV $\lesssim v_{BL} \lesssim$ 55 TeV. In addition, the very radiative nature of the set-up signals a strong first order phase transition in the presence of a non-zero temperature. Stochastic gravitational waves stemming from this phase transition are within the reach of detectors such as LISA and BBO. The scenario therefore emerges as a concrete platform to test classical scale invariance that is tied to neutrino masses and dark matter, through gravitational waves.

Figures (6)

• Figure 1: Variation of $V_{\text{RG}}(\phi)$ versus $\phi$ for $v_{BL} = 10^4$ GeV and for the choices of $\lambda_5(0), g_{BL}(0)$ and $y_{1}(0)$ mentioned in the legends. We have further taken $y_{S2}(0)=y_{S3}(0)=2y_{S1}(0)$ in this case.
• Figure 2: Lepton flavour violation constraints in terms of the dimensionless parameter $V_{e\gamma}$ (see Eq. \ref{['eq:Vegam']}).
• Figure 3: The DM annihilation channels in this model.
• Figure 4: (Left) Variation of $\Omega h^2$ with $M_{N_1}$ for different values of $v_{BL}$. The values of the other model parameters are mentioned in the text. The horizontal line denotes the Planck central value. (Right) Dependence of spin-independent direct detection cross section on the $M_{N_1}$ for different values of $v_{BL}$. The black solid curve represents the bound from LUX-ZEPPELIN experiment.
• Figure 5: The shape of $V_{\text{tot}}(\phi,T)$ at $T=T_c,T_n$ for the four chosen benchamrks.