There is a direct group-theoretical connection between neutrino mixing and horizontal symmetry that can be established without any dynamical input. Such a connection is reviewed and expanded in this article. For certain symmetry groups $\mathcal{G}$ including $A_4$ and $S_4$, it is shown that a generic $U(1)\times \mathcal{G}$ Higgs potential of a valon yields exactly the alignments dictated by the group-theoretical approach, but energy can now be used to discriminate different alignments. This mechanism possibly explains why starting from an $A_4$ group, the tribimaximal mixing matrix with an enhanced $S_4$ symmetry is more preferable than the one without it.

• Received 31 March 2011

DOI:https://doi.org/10.1103/PhysRevD.83.113002