Group Theoretic Bases for Tribimaximal Mixing

Abstract

Present data on neutrino masses and mixing favor the highly symmetric tribimaximal neutrino mixing matrix which suggests an underlying flavor symmetry. A systematic study of non-abelian finite groups of order $g\le 31$ reveals that tribimaximal mixing can be derived not only from the well known flavor symmetry $T\equiv A_4$, the tetrahedral group, but also by using the alternative flavor symmetry X(24) $\equiv S{L}_2(F_3)\equiv Q_4\tilde{\times }{Z}_3$. X(24) does not contain the tetrahedral group as a subgroup, and has the advantage over it as a flavor symmetry that it can not only underwrite bitrimaximal mixing for neutrinos, equally as well, but also provide a first step to understanding the quark mass hierarchy.

Comments: 9 pages latex. Flavor group renamed X(24), unconnected to tetrahedral group