Light Dark Matter from Forbidden Channels

Dark matter (DM) may be a thermal relic that annihilates into heavier states in the early universe. This forbidden DM framework accommodates a wide range of DM masses from keV to weak scales. An exponential hierarchy between the DM mass and the weak scale follows from the exponential suppression of the thermally averaged cross section. Stringent constraints from the cosmic microwave background are evaded because annihilations turn off at late times. We provide an example where DM annihilates into dark photons, which is testable through large DM self-interactions and direct detection.

Figure 1

The left panel contains Feynman diagrams relevant for (1) the relic density, (2) self-interactions, (3) indirect detection, and (4) direct detection. The right panel shows the relic density ${\mathrm{\Omega }}_{\psi }{h}^2$ as a function of the mass splitting, $\mathrm{\Delta }\equiv (m_{{\gamma }_d}-m_{\psi })/m_{\psi }$. The red (blue) curves correspond to $m_{\psi }=1\mathrm{GeV}$ (MeV) and the solid (dashed) curves correspond to ${\alpha }_d=0.1({10}^{-3})$.

Figure 2

The left side shows the splitting $\mathrm{\Delta }$, versus $m_{\psi }$, with ${\mathrm{\Omega }}_{\psi }{h}^2$ fixed to the observed abundance. Different curves correspond to different values of ${\alpha }_d$. For $m_{\psi }>1\mathrm{MeV}$, the dark sector temperature equals the SM temperature, while for $m_{\psi }<1\mathrm{MeV}$ the dark sector is cooler than the SM as described in the thermally decoupled dark sector section. The right side shows the freeze-out temperature, $x_f\equiv m_{\psi }/T_f$, as a function of $m_{\psi }$, with $\mathrm{\Delta }$ fixed to the value shown to the left.

Figure 3

The left side shows constraints on the kinetic mixing parameter $\epsilon$, versus $m_{\psi }$, with $\mathrm{\Delta }$ chosen to match the observed relic density and ${\alpha }_d=0.1$. Annihilation to SM states dominates over forbidden channels in the upper gray region, and the dark sector is thermally decoupled from the SM in the lower gray region. Limits are shown from beam dump experiments (orange) [46, 47, 48, 49, 50], supernovae cooling (blue) [46, 51], Planck (purple) [15, 52], and direct detection (pink) [53, 54, 55]. The dashed brown (black) curves show the projected reach of SuperCDMS SNOLAB [2] (electron scattering [56]). The red shaded area (dashed curve) shows the approximate sensitivity of current observations to DM self-interactions, ${\sigma }_{\mathrm{SI}}/m_{\psi }\gtrsim 1(0.1){\mathrm{cm}}^2/\mathrm{g}$ [19, 20, 35, 36, 37, 38]. The right side shows constraints on the dark sector when it is thermally decoupled from the SMİn the upper gray area $4\psi \to 2\psi$ dominates over forbidden annihilations. In the lower gray area DM is overabundant. The red shading and dashed curve represent the same values for the self-interaction cross section as in the left panel. In the purple shaded area the DM mass is too small to be simultaneously consistent with the Pauli exclusion principle and the densities observed in dwarf spheroidal galaxies [57, 58, 59].