Tri-Bi-Maximal Mixing in Asymmetric Textures

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 $G_2$.