In particle physics, Dirac fermions are protected by conserved quantum numbers (electric charges, color charges, etc.). As a result, Dirac fermions can only annihilate with their antiparticles, and massive Dirac fermions (muons, top quarks, etc.) can only decay into their lighter counterparts. Majorana particles OTOH can annihilate with themselves, which prohibits them from carrying any conserved quantum numbers. As a result, the stability of majorana fermions are protected by quantum number conservation which prohibits their decay into Dirac fermions (e.g., $\chi \rightarrow e^{-}\gamma$), and conservation of angular momentum which prohibits single majorana fermions from decaying into bosons or fermion pairs (e.g., $\chi \rightarrow \gamma\gamma$ or $\chi \rightarrow e^{-}e^{+}$). And because majorana fermions don’t interact via electromagnetic or strong interaction, their chance of annihilating with each other is extremely low. This may explain the virtually unchanged abundance of dark matters (which are suspected as majorana weakly interacting massive particles (WIMP)) since the early universe.
However, if neutrinos are majorana fermions, things are totally different. Because majorana neutrinos don’t carry any conserved quantum numbers, decay into neutrinos (e.g., $\chi \rightarrow \nu\gamma$) are not prohibited by conservation laws. And because WIMP experience weak interaction, the decay kinetics should be fast enough to eliminate all majorana WIMP in today’s universe. Does that mean if neutrinos are majorana fermions, there can’t be stable majorana WIMP, and the dark matter must be made of something else (sterile neutrinos etc.)?
