Small Neutrino Masses from a Decoupled Singlet Scalar Field

We propose a unified solution with $Z_4$ discrete symmetry for small neutrino masses and stability of dark matter. The Standard Model is extended with an inert doublet scalar, a dark singlet scalar, a spurion scalar and right-handed neutrinos, which all transform nontrivially under $Z_4$. After the $Z_4$ symmetry is broken to $Z_2$ by the VEV of the spurion, much below the mass scale of the dark singlet scalar, a small lepton number violating coupling for the inert doublet is generated at tree level, so small neutrino masses are obtained at one-loops for relatively light new fields. We discuss the important roles of the $Z_4$ symmetry for neutrino masses, dark matter physics and thermal leptogenesis.