Tri-Bi-Maximal Mixing in Asymmetric Textures

TL;DR

This paper explores the role of asymmetry in Yukawa matrices within a phenomenological framework based on Tri-Bi-Maximal mixing, proposing a model extending from $SU_5$ to $E_6$ with finite family groups.

Contribution

It introduces a novel approach linking asymmetry in Yukawa matrices to Tri-Bi-Maximal mixing, extending grand unified theories with finite family groups for naturalness.

Findings

Tri-Bi-Maximal mixing predicts CP-violating angle accurately.

The model extends from $SU_5$ to $E_6$ with finite family groups.

Asymmetry in Yukawa matrices is crucial for phenomenological consistency.

Abstract

At the occasion of his eighty fifth birthday, I wish to to recognize the crucial role that my advisor, Professor Ayalam Balachandran, played in enabling me to evolve from engineering to physics. So many years later, this student presents his latest efforts: the importance of asymmetry in the Yukawa matrices. We start with a purely phenomenological approach with Tri-Bi-Maximal mixing as input: it predicts the value of the CP-violating angle with the three mixing angles within one sigma of their pdf values. To ensure as much naturalness as possible, a model which starts from $SU_5$ and extends to $E_6$ is discussed, in the context of finite family groups which are subgroups $G_2$.