Symmetry of Lepton Mixing

TL;DR

This paper explores neutrino and quark mixing symmetries, identifying groups capable of reproducing observed patterns and proposing methods to construct models that explain these mixings from symmetry principles.

Contribution

It provides a systematic list of symmetry groups for neutrino mixing and a recipe to determine mixing patterns from finite groups with specific properties.

Findings

List of symmetry groups for neutrino mixing for n=3

Method to derive mixing patterns from finite groups

Potential to predict CKM parameters from symmetry

Abstract

Neutrino mixing is studied from a symmetry perspective, both bottom-up and top-down. In the bottom-up approach, we start from the tri-bimaximal mixing, or one of its three partial patterns, and construct a list of horizontal symmetry groups capable of reproducing the mixng without adjustment of parameters. This list, labeled by an integer $n\ge 3$, is explicitly calculated for $n=3$. In the top-down approach, we start from any finite group possessing a three-dimensional irreducible representation and an order-2 element, give a recipe to determine what mixing pattern it contains, and how to construct a dynamical model to reveal a particular mixing. Finally, we point out that if quark mixing is controlled by symmetry in this way, then there is an exciting possibility to determine most of the CKM mixing parameters by symmetry alone.