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

Abstract

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