Complex scalar dark matter in a $B$-$L$ model

In this work, we implement a complex scalar dark matter (DM) candidate in a ${U(1)}_{B-L}$ gauge extension of the Standard Model. The model contains three right-handed neutrinos with different quantum numbers and a rich scalar sector, with extra doublets and singlets. In principle, these extra scalars can have vacuum expectation values ($V_{\mathrm{\Phi }}$ and $V_{\varphi }$ for the extra doublets and singlets, respectively) belonging to different energy scales. In the context of $\zeta \equiv \frac{V_{\mathrm{\Phi }}}{V_{\varphi }}\ll 1$, which allows one to obtain naturally light active neutrino masses and mixing compatible with neutrino experiments, the DM candidate arises by imposing a $Z_2$ symmetry on a given complex singlet, ${\varphi }_2$, in order to make it stable. After doing a study of the scalar potential and the gauge sector, we obtain all the DM-dominant processes concerning the relic abundance and direct detection. Then, for a representative set of parameters, we find that a complex DM with mass around 200 GeV, for example, is compatible with the current experimental constraints without resorting to resonances. However, additional compatible solutions with heavier masses can be found in vicinities of resonances. Finally, we address the issue of having a light $CP$-odd scalar in the model showing that it is safe concerning the Higgs and the $Z_{\mu }$-boson invisible decay widths, and also astrophysical constraints regarding energy loss in stars.

Figure 1

Main annihilation processes that contribute to ${⟨\sigma v_{\text{Moller}}⟩}_{\mathrm{ann}}$.

Figure 2

The total thermal relic density of $I_{\mathrm{DM}}$ and $R_{\mathrm{DM}}$ as a function of $M_{\mathrm{DM}}$. We have used three different parameters for ${\mathrm{\Lambda }}_{Hs2}=3\times 10^{-5},1\times 10^{-4},5\times 10^{-4}$.

Figure 3

The spin-independent elastic scattering cross section, ${\sigma }_{\chi ,p}^{\mathrm{SI}}$, off a proton $p$ as a function of $M_{\mathrm{DM}}$ for the same parameters as in Fig. 2, appropriately scaled to the relic density. We also show the XENON100 and LUX exclusion limits [17, 19].