Group Theoretic Bases for Tribimaximal Mixing

TL;DR

This paper explores finite non-abelian groups as flavor symmetries to derive tribimaximal neutrino mixing, highlighting an alternative group X(24) that extends understanding beyond the well-known A4 symmetry.

Contribution

It systematically studies finite groups of order up to 31 and identifies X(24) as a novel flavor symmetry capable of explaining neutrino mixing and quark mass hierarchy.

Findings

Tribimaximal mixing can be derived from groups other than A4.

X(24) can underwrite neutrino mixing and quark mass hierarchy.

X(24) does not contain A4 as a subgroup.

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 $g \leq 31$ 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) $\equiv SL_2(F_3) \equiv Q_4 \tilde{\times} Z_3$. 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.