Sterile neutrinos for warm dark matter and the reactor anomaly in flavor symmetry models

We construct a flavor symmetry model based on the tetrahedral group A4 in which the right-handed neutrinos from the seesaw mechanism can be both keV warm dark matter particles and eV-scale sterile neutrinos. This is achieved by giving the right-handed neutrinos appropriate charges under the same Froggatt-Nielsen symmetry responsible for the hierarchy of the charged lepton masses. We discuss the effect of next-to-leading order corrections to deviate the zeroth order tri-bimaximal mixing. Those corrections have two sources: (i) higher order seesaw terms, which are important when the seesaw particles are eV-scale, and (ii) higher-dimensional effective operators suppressed by additional powers of the cut-off scale of the theory. Whereas the mixing angles of the active neutrinos typically receive corrections of the same order, the mixing of the sterile neutrinos with the active ones is rather stable as it is connected with a hierarchy of mass scales. We also modify an effective A4 model to incorporate keV-scale sterile neutrinos