Derivation of Dark Matter Parity from Lepton Parity

It is shown that in extensions of the standard model of quarks and leptons where the additive lepton number $L$ is broken by two units, so that $Z_2$ lepton parity, i.e., $(-1{)}^L$ which is either even or odd, remains exactly conserved, there is the possibility of stable dark matter without additional symmetry. This applies to many existing simple models of Majorana neutrino mass with dark matter, including some radiative models. Several well-known examples are discussed. This new insight leads to the construction of a radiative type II seesaw model of neutrino mass with dark matter where the dominant decay of the doubly charged Higgs boson ${\xi }^{++}$ is into $W^{+}{W}^{+}$ instead of the expected $l_i^{+}{l}_j^{+}$ lepton pairs for the well-known tree-level model.

Figure 1

One-loop $Z_2$ scotogenic neutrino mass.

Figure 2

Three-loop neutrino mass.

Figure 3

Another three-loop neutrino mass.

Figure 4

Two-loop neutrino mass.

Figure 5

One-loop $U(1{)}_D$ scotogenic neutrino mass.

Figure 6

One-loop neutrino mass from $L=0$ Higgs triplet.