Binary Tetrahedral Flavor Symmetry

TL;DR

This paper explores the Binary Tetrahedral flavor symmetry group T' to unify leptons and quarks, accurately predict neutrino and quark mixing angles, and propose a dark matter candidate, demonstrating the potential of finite groups in modeling fundamental particles.

Contribution

It introduces a novel application of the Binary Tetrahedral symmetry group T' to unify fermion sectors and extend neutrino mixing models, with predictions aligning well with experimental data.

Findings

Accurate prediction of atmospheric and reactor neutrino mixing angles

Precise estimation of the Cabibbo angle

Proposal of a dark matter candidate outside current experimental limits

Abstract

A study of the T' Model and its variants utilizing Binary Tetrahedral Flavor Symmetry. We begin with a description of the historical context and motivations for this theory, together with some conceptual background for added clarity, and an account of our theory's inception in previous works. Our model endeavors to bridge two categories of particles, leptons and quarks, a unification made possible by the inclusion of additional Higgs particles, shared between the two fermion sectors and creating a single coherent system. This is achieved through the use of the Binary Tetrahedral symmetry group and an investigation of the Tribimaximal symmetry evidenced by neutrinos. Our work details perturbations and extensions of this T' Model as we apply our framework to neutrino mixing, quark mixing, unification, and dark matter. Where possible, we evaluate model predictions against experimental results and find excellent matching with the atmospheric and reactor neutrino mixing angles, an accurate prediction of the Cabibbo angle, and a dark matter candidate that remains outside the limits of current tests. Additionally, we include mention of a number of unanswered questions and remaining areas of interest for future study. Taken together, we believe these results speak to the promising potential of finite groups and flavor symmetries to act as an approximation of nature.