Simplified Dirac dark matter models and gamma-ray lines

We investigate simplified dark matter models where the dark matter candidate is a Dirac fermion charged only under a new gauge symmetry. In this context one can understand dynamically the stability of the dark matter candidate and the annihilation through the new gauge boson is not velocity suppressed. We present the simplest Dirac dark matter model charged under the local $B-L$ gauge symmetry. We discuss in great detail the theoretical predictions for the annihilation into two photons, into the standard model Higgs and a photon, and into the $Z$ gauge boson and a photon. Our analytical results can be used for any Dirac dark matter model charged under an Abelian gauge symmetry. The numerical results are shown in the $B-L$ dark matter model. We discuss the correlation between the constraints on the model from collider searches and dark matter experiments.

Figure 1

Dark matter relic density ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2$ vs the dark matter mass $M_{\chi }$ for different choices of the dark matter $B-L$ quantum number $n$. In the left panel we use $n=1/3$, while in the right panel we use $n=3$, and we give the relic density for two choices of the mass of the $Z_{BL}$ and the gauge coupling $g_{BL}$ that fulfil $M_{Z_{BL}}/g_{BL}=7\mathrm{TeV}$. The thin blue band corresponds to the currently allowed relic dark matter density measured by the Planck collaboration, ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2=0.1199\pm 0.0027$ [15].

Figure 2

Direct detection cross section ${\sigma }_{\chi N}^{\mathrm{SI}}$ vs the dark matter mass $M_{\chi }$ compatible with the relic density constraints for $n=1/3$ (left panel) and $n=3$ (right panel). The colored dashed lines show ${\sigma }_{\chi N}^{\mathrm{SI}}$ for different choices of $M_{Z_{BL}}/g_{BL}$ compatible with current collider limits. The black dash-dotted line shows the minimal direct detection cross section. We show the LUX [16] and XENON100 [17] constraints, as well as the prospects for XENON1T [18]. The orange dash-dotted line shows the coherent neutrino scattering background [19].

Figure 3

Coupling $Z^{\prime }\gamma \gamma$ generated by a loop of fermions $f$ charged under $U(1{)}^{\prime }$ and carrying electric charge. In the calculation, the crossed diagram has to be taken into account.

Figure 4

Coupling $Z^{\prime }h\gamma$ generated by a top loop. In the calculation, the crossed diagram has to be taken into account.

Figure 5

Coupling $Z^{\prime }Z\gamma$ generated by a loop of fermions charged under $U(1{)}^{\prime }$ and carrying electric charge. In the calculation, the crossed diagram has to be taken into account.

Figure 6

Allowed parameter space for the indirect detection for the channels $\overline{\chi }\chi \to h\gamma$ (left panel) and $\overline{\chi }\chi \to Z\gamma$ (right panel) compatible with the relic density constraint. The limits of Fermi-LAT [26] and H.E.S.S. [27] are shown by the blue and red lines, respectively. See Table 1 in Appendix pp1 for the values of the cross section limits. Note that the highest cross section in the indirect detection experiments corresponds to the parameters leading to the lowest cross sections in the direct searches.

Figure 7

Allowed parameter space for the dark matter annihilation into two bottom quarks compatible with the relic density constraint. The experimental bounds from Fermi-LAT [28] are given.