New Insights on Lepton Number and Dark Matter

Dark matter (DM) is usually assumed to be stabilized by a symmetry, which is mostly considered to be $Z_2$. For example, in supersymmetry it is $R$ parity, i.e. $(-1)^{3B+L+2j}$. However, it may be $Z_n$ or $U(1)_D$, and derivable from generalized lepton number. In this context, neutrinos may be Majorana or Dirac, and owe their masses to dark matter, i.e. they are scotogenic.