Tri-bimaximal Neutrino Mixing and $θ_{13}$

Abstract

We propose an extension of tri-bimaximal mixing to include a non-zero reactor angle $θ_{13}$ while maintaining the tri-bimaximal predictions for the atmospheric angle $θ_{23}=45^o$ and solar angle $θ_{12}=35^o$. We show how such tri-bimaximal-reactor mixing can arise at leading order from the(type I) see-saw mechanism with partially constrained sequential dominance. Partially constrained sequential dominance can be realized in GUT models with a non-Abelian discrete family symmetry, such as $A_4$, spontaneously broken by flavons with a particular vacuum alignment.