Two-component dark matter and a massless neutrino in a new $B-L$ model

We propose a new extension of the Standard Model by a $U(1{)}_{B-L}$ gauge symmetry in which the anomalies are canceled by two right-handed neutrinos plus four chiral fermions with fractional $B-L$ charges. Two scalar fields that break the $B-L$ symmetry and give masses to the new fermions are also required. After symmetry breaking, two neutrinos acquire Majorana masses via the seesaw mechanism leaving a massless neutrino in the spectrum. Additionally, the other new fermions arrange themselves into two Dirac particles, both of which are automatically stable and contribute to the observed dark matter density. This model thus realizes in a natural way, without ad hoc discrete symmetries, a two-component dark matter scenario. We analyze in some detail the dark matter phenomenology of this model. The dependence of the relic densities with the parameters of the model is illustrated, and the regions consistent with the observed dark matter abundance are identified. Finally, we impose the current limits from LHC and direct detection experiments and show that the high mass region of this model remains unconstrained.

Figure 1

Some of the Feynman diagrams that contribute to DM annihilation in this model. Other possible annihilation final states include $Z^{\prime }{Z}^{\prime }$ and $S{Z}^{\prime }$ ($S=H_1,H_2,A$), which proceed through diagrams similar to (c).

Figure 2

The relic densities as a function of the ${\psi }_1$ mass for $M_1=M_2$. The other parameters were taken to be $M_{H_1}=M_{H_2}=M_A=2.5\mathrm{TeV}$, $M_{N_1}=M_{N_2}=1\mathrm{TeV}$, $M_{Z^{\prime }}=3.5\mathrm{TeV}$, $g_{BL}=0.5$, $\tan \beta =2$, and $\sin \theta =0.5$. The solid (green) line shows the total relic density, $({\mathrm{\Omega }}_1+{\mathrm{\Omega }}_2)h^2$, while the dotted (blue) and dashed (red) lines show, respectively, ${\mathrm{\Omega }}_1{h}^2$ and ${\mathrm{\Omega }}_2{h}^2$. The horizontal band is the region consistent with Planck data.

Figure 3

The relic densities as a function of the ${\psi }_1$ mass for $M_2=1.2M_1$ (left) and $M_2=0.8M_1$ (right). The other parameters were taken to be $M_{H_1}=M_{H_2}=M_A=2.5\mathrm{TeV}$, $M_{N_1}=M_{N_2}=1\mathrm{TeV}$, $M_{Z^{\prime }}=3.5\mathrm{TeV}$, $g_{BL}=0.5$, $\tan \beta =2$, and $\sin \theta =0.5$. The solid (green) line shows the total relic density, $({\mathrm{\Omega }}_1+{\mathrm{\Omega }}_2)h^2$, while the dotted (blue) and dashed (red) lines show, respectively, ${\mathrm{\Omega }}_1{h}^2$ and ${\mathrm{\Omega }}_2{h}^2$. The horizontal band is the region consistent with Planck data.

Figure 4

The relic densities as a function of the ${\psi }_1$ mass for $M_2=1.3M_1$ (left), $M_2=M_1$ (center), and $M_2=0.7M_1$ (right). The other parameters were taken to be $M_{H_1}=1.2\mathrm{TeV}$, $M_{H_2}=1.5\mathrm{TeV}$, $M_A=2.5\mathrm{TeV}$, $M_{N_1}=M_{N_2}=0.5\mathrm{TeV}$, $M_{Z^{\prime }}=2.1\mathrm{TeV}$, $g_{BL}=0.3$, $\tan \beta =1$, and $\sin \theta =0.5$. The solid (green) line shows the total relic density, $({\mathrm{\Omega }}_1+{\mathrm{\Omega }}_2)h^2$, while the dotted (blue) and dashed (red) lines show, respectively, ${\mathrm{\Omega }}_1{h}^2$ and ${\mathrm{\Omega }}_2{h}^2$. The horizontal band is the region consistent with Planck data.

Figure 5

The total relic density as a function of the ${\psi }_1$ mass for $M_2=M_1$ and different values of $\tan \beta$ (left) or $\sin \theta$ (right). The rest of parameters are the same as in Fig. 4.

Figure 6

The viable points shown in the planes ($M_1$, $M_Z^{\prime }$) and ($M_2$, $M_Z^{\prime }$).

Figure 7

The viable points shown in the plane ($M_Z^{\prime }$, $M_1/M_2$).

Figure 8

The viable points shown in the plane ($M_Z^{\prime }$, $\tan \beta$).

Figure 9

The viable points projected onto the planes $(M_{Z^{\prime }},a)$ and $(M_{Z^{\prime }},b)$. $a$ and $b$ are the Yukawa couplings related to the DM particles—see Eqs. (1) and (17).

Figure 10

The viable points projected onto the plane $(M_{Z^{\prime }},\frac{{\mathrm{\Omega }}_1}{{\mathrm{\Omega }}_2})$.

Figure 11

The viable models projected onto the plane $(M_{Z^{\prime }},g_{BL})$. For comparison, the region excluded by the LHC at 13 TeV [41, 42] is also displayed.

Figure 12

The viable points projected onto the planes ($M_i$, ${\sigma }_i^{\mathrm{SI}}\times {\mathrm{\Omega }}_i/{\mathrm{\Omega }}_{\mathrm{DM}}$) for $i=1$ (left panel) and $i=2$ (right panel). The current limits from XENON1T are also shown, as are the expected sensitivities of DARWIN and LZ.