Sterile neutrinos as the warm dark matter in the type II seesaw model

Abstract

In the framework of type II seesaw mechanism we discuss the number of sterile right-handed Majorana neutrinos being the warm dark matter (WDM). When the type II seesaw mass term ${M}_{\ensuremath{\nu}}^{\mathrm{II}}$ is far less than the type I seesaw mass term ${M}_{\ensuremath{\nu}}^{\mathrm{I}}$, only one of three sterile neutrinos may be the WDM particle. On the contrary, the WDM particles may contain all sterile neutrinos. If ${M}_{\ensuremath{\nu}}^{\mathrm{II}}\ensuremath{\sim}{M}_{\ensuremath{\nu}}^{\mathrm{I}}$, the allowed number is not more than $\mathcal{N}\ensuremath{-}1$ for $\mathcal{N}$ sterile neutrinos. It is worthwhile to stress that three different types of neutrino mass spectrum are permitted when ${M}_{\ensuremath{\nu}}^{\mathrm{II}}\ensuremath{\gg}{M}_{\ensuremath{\nu}}^{\mathrm{I}}$ and ${M}_{\ensuremath{\nu}}^{II}\ensuremath{\sim}{M}_{\ensuremath{\nu}}^{I}$.