Neutrino Mixing and the Double Tetrahedral Group

TL;DR

This paper explores how the double tetrahedral group T' can be used to derive the neutrino mixing matrix, introducing new representations and complex coefficients that may explain CP violation geometrically.

Contribution

It presents a minimalist scheme utilizing the double tetrahedral group T' for neutrino mixing, highlighting new representations and complex Clebsch-Gordan coefficients.

Findings

Introduction of three distinct 2D representations.

Complex Clebsch-Gordan coefficients enable geometric CP violation.

Explicit derivation of group theory for T and T'.

Abstract

In the spirit of a previous study of the tetrahedral group $T \simeq A_4$, we discuss a minimalist scheme to derive the neutrino mixing matrix using the double tetrahedral group $T'$, the double cover of $T$. The new features are three distinct 2-dimensional representations and complex Clebsch-Gordan coefficients, which can result in a geometric source of CP violation in the neutrino mass matrix. In an appendix, we derive explicitly the relevant group theory for the tetrahedral group $T$ and its double cover $T'$.