WIMPs

The relic density obtained in Freeze Out of Non-Relativistic Species implies that in order to reproduce the correct relic abundance, dark matter particles must have an annihilation cross-section of the order $⟨\sigma v⟩\approx 3\times 10^{-26}c{m}^3{s}^{-1}$.

We can consider a simple case where the DM particles self-annihilate into SM particles through the exchange of a gauge boson (like in s-channel). Then, the annihilation cross-section is of the order $⟨\sigma v⟩\sim G_F^2{m}_{WIMP}^2$, where $G_F=1.16\times 10^{-5}Ge{V}^{-2}$ and the correct relic density is obtained for masses of the order of GeV.