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We provide a complete systematic classification of all two-loop realizationsof the dimension four operator for Dirac neutrino masses. Our classification ismulti-layered, starting first with a classification in terms of all possibledistinct two-loop topologies. Then we discuss the possible diagrams for eachtopology. Model-diagrams originating from each diagram are then considered. Thecriterion for genuineness is also defined and discussed at length. Finally, asexamples, we construct two explicit models which also serve to highlight theintimate connection between the Dirac nature of neutrinos and dark matterstability.

Systematic classification of two loop d = 4 Dirac neutrino mass models and the Diracness-dark matter stability connection