Minimal model of Majoronic dark radiation and dark matter

We extend the singlet Majoron model of dark radiation by adding another singlet scalar of unit lepton charge. The spontaneous breaking of global $U(1{)}_L$ connects dark radiation with neutrino mass generation via the type-I seesaw mechanism. The model naturally has a stable scalar dark matter field. It also predicts the existence of a light scalar of mass less than 1 GeV that mixes with the Standard Model Higgs boson. We perform a numerical analysis of the parameters of the model by imposing constraints from giving correct relic abundance and satisfying bounds from direct dark matter detection, rare decays of the $B$ meson, and invisible width of the Higgs boson. The viability of the model in accommodating the gamma rays from the Galactic center is discussed as well. The model gives rise to new rare Higgs boson decays such as four-muon final states with displaced vertices. Another unique signal is two muons and missing energy recoil against the muon pair. Our result also shows that such a bridge between dark radiation and the seesaw mechanism will put the seesaw scale in the range of 1–100 TeV.

Figure 1

Fermion-antifermion annihilation into a pair of Majorons.

Figure 2

$\rho \rho$ annihilation into SM particles.

Figure 3

$\rho \rho$ to a pair of SM Higgs, light scalars and Majorons.

Figure 4

Leading channel for DM-nucleon scattering via Higgs and light scalar exchange. DM is $\rho$.

Figure 5

The probability distribution of $\theta$ (Left Panel) and $M_S$ (Right Panel) of all viable parameter configurations.

Figure 6

Left panel: The distribution of $\overline{\kappa }$ vs $M_{\rho }$. Right panel: The mass ratio of two $Z_2$-odd particles vs $M_{\rho }$.

Figure 7

${\lambda }_{\varphi H}$ (left panel) and ${\lambda }_{\varphi S}$ (right panel) vs $M_{\rho }$.

Figure 8

The lepton number violating scale $v_S$ vs $M_{\rho }$.

Figure 9

$⟨{\sigma }_{S}v⟩/⟨\sigma v{⟩}_{\text{total}}$ (left panel) and $⟨{\sigma }_{\omega }v⟩/⟨\sigma v{⟩}_{\text{total}}$ (right panel) vs $M_{\rho }$.

Figure 10

Spin-independent elastic $\rho$-nucleon scattering cross section vs $M_{\rho }$. Where the solid line is the current LUX limit and the dashed line is the LUX 300-day projected sensitivity.

Figure 11

Comparison of the diffuse gamma-ray spectrum $E^{2}dN/dE$ with arbitrary unit from the benchmark 35 GeV DM and $⟨{\sigma }_{b}v⟩=1.42\times 10^{-9}(\mathrm{GeV}{)}^{-2}$ (red), $M_{\rho }=37.30\mathrm{GeV}$ and $B\times B{r}_h=0.507$ in our model (black), and $M_{\rho }=36.53\mathrm{GeV}$ and $B\times B{r}_h=0.499$ in our model (blue dash).

Figure 12

The boost factor needed for $m_S>M_K-m_{\pi }$ to get the best-fit benchmark as a function of $\theta$.

Figure 13

SM Higgs invisible decay width ${\mathrm{\Gamma }}_{\text{inv}}^H$ as a function of $m_{\rho }$.

Figure 14

Left panel: light scalar $s$ decay width vs $M_s$, Right panel: invisible decay branching ratio vs $M_s$.

Figure 15

Expected $c\tau$ (in cm) as a function of $m_s$.

Figure 16

Decay width $\mathrm{\Gamma }(h\to ss)$ in MeV (left panel) and $\mathrm{Br}(s\to \mu \mu )$ (right panel).

Figure 17

The branching ratios for $2\mu +\cancel{E}$ (Left panel) and $2\pi +\cancel{E}$ (right panel) in our model.