Dark matter stability and Dirac neutrinos using only standard model symmetries

Abstract

We provide a generic framework to obtain stable dark matter along with naturally small Dirac neutrino masses generated at the loop level. This is achieved through the spontaneous breaking of the global $U(1{)}_{B\ensuremath{-}L}$ symmetry already present in the standard model. The $U(1{)}_{B\ensuremath{-}L}$ symmetry is broken down to a residual even ${\mathcal{Z}}_{n}$ ($n\ensuremath{\ge}4$) subgroup. The residual ${\mathcal{Z}}_{n}$ symmetry simultaneously guarantees dark matter stability and protects the Dirac nature of neutrinos. The $U(1{)}_{B\ensuremath{-}L}$ symmetry in our setup is anomaly free and can also be gauged in a straightforward way. Finally, we present an explicit example using our framework to show the idea in action.