Group Theory and Dynamics of Neutrino Mixing

TL;DR

This paper explores the group-theoretical basis of neutrino mixing, showing how certain symmetry groups determine mixing patterns and how energy considerations can select specific alignments, potentially explaining observed neutrino behaviors.

Contribution

It establishes a direct connection between neutrino mixing and horizontal symmetry groups, and demonstrates how Higgs potentials can produce specific group-theoretic alignments.

Findings

Group-theoretical connection between neutrino mixing and symmetry groups.

Higgs potential yields group-aligned configurations.

Energy considerations can discriminate between different alignments.

Abstract

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 $\G$ including $A_4$ and $S_4$, it is shown that a generic $U(1)\x\G$ Higgs potential of a valon yields exactly the alignments dictated by the group-theoretic 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.