Flavor Symmetry for Quarks and Leptons

TL;DR

This paper explores how certain finite non-abelian groups, including A4 and SL2(F3), can explain neutrino mixing patterns and quark masses, highlighting the potential of flavor symmetries in particle physics.

Contribution

It systematically studies finite groups up to order 31 and shows that both A4 and T' symmetries can produce tribimaximal neutrino mixing and accommodate quark masses.

Findings

T' symmetry can derive tribimaximal mixing.

T' can accommodate heavy top quark.

Finite groups of order ≤31 include A4 and T'.

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 tetrahedral flavor symmetry $T \equiv A_4$, but also by using the binary tetrahedral symmetry $T^{'} \equiv SL_2(F_3)$ which does not contain the tetrahedral group as a subgroup. $T^{'}$ has the further advantage that it can also neatly accommodate the quark masses including a heavy top quark.