Neutrino mass without lepton number violation, dark matter; and a strongly first-order phase transition

We propose a model to explain the tiny masses of neutrinos with lepton number conservation, where neither too heavy particles beyond the TeV-scale nor tiny coupling constants are required. Assignments of conserving lepton numbers to new fields result in an unbroken $Z_2$ symmetry that stabilizes the dark matter candidate (the lightest $Z_2$-odd particle). In this model, $Z_2$-odd particles play an important role in generating the masses of neutrinos. The scalar dark matter in our model can satisfy constraints on the dark matter abundance and those from direct searches. It is also shown that the strongly first-order phase transition, which is required for electroweak baryogenesis, can be realized in our model. In addition, the scalar potential can in principle contain $CP$-violating phases, which can also be utilized for baryogenesis. Therefore, three problems in the standard model—namely, the absence of neutrino masses, the dark matter candidate, and the mechanism to generate the baryon asymmetry of the Universe—may be simultaneously resolved at the TeV scale. The phenomenology of this model is also discussed briefly.

Figure 1

The diagram for generating Dirac neutrino masses in our model. The arrow shows the flow of the lepton number, which is conserved in our model.

Figure 2

Diagrams of the pair annihilation of ${\mathcal{H}}^0$.

Figure 3

The diagram of the self-annihilation of ${\mathcal{H}}^0$.

Figure 4

The relic abundance of the scalar dark matter ${\mathcal{H}}^0$ in our model. The horizontal dashed line corresponds to $\mathrm{\Omega }{h}^2=0.1186$ [3].

Figure 5

(Left) Contours of ${\phi }_c/T_c$. (Right) In the white region, our model satisfies the condition ${\phi }_c/T_c\gtrsim 1$ for the strongly first-order phase transition, which is required for the electroweak baryogenesis scenario. Solid lines are contours of the deviation $\mathrm{\Delta }{\lambda }_{hhh}/{\lambda }_{hhh}^{\mathrm{SM}}$ of ${\lambda }_{hhh}$ from the SM value ${\lambda }_{hhh}^{\mathrm{SM}}$. Dashed lines show contours of the deviation $\mathrm{\Delta }{\kappa }_{\gamma }$ of $\mathrm{\Gamma }(h\to \gamma \gamma )$ from the SM value.

Figure 6

Mass spectrum of $h$ and new particles for the benchmark values in Eqs. (22) and (25) with $m_A=200\mathrm{GeV}$. Red bold bars show masses of $Z_2$-odd particles.