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We discuss the most general necessary and sufficient condition for threemassless light neutrinos in variants of the type I seesaw mechanism in which weintroduce an arbitrary number of fermionic gauge singlets. We find that havingmassless light neutrinos is equivalent to enforcing the conservation of leptonnumber. As a consequence, any symmetry that leads to massless light neutrinoswill contain as an unbroken subgroup a conserved lepton number. This will beimportant for searches for heavy sterile neutrinos since in general the lightneutrino masses will be proportional to small lepton number violatingparameters that will also suppress lepton number violating signatures.

Equivalence between massless neutrinos and lepton number conservation in fermionic singlet extensions of the Standard Model