Asymmetric tri-bi-maximal mixing and residual symmetries

TL;DR

This paper explores how residual flavor and CP symmetries can determine the free phase in asymmetric tri-bi-maximal mixing, leading to precise predictions for lepton mixing and neutrinoless double beta decay.

Contribution

It identifies the smallest unified flavor symmetries that fix the free phase in asymmetric tri-bi-maximal mixing within a GUT framework.

Findings

Residual symmetries fix the free phase in neutrino mixing.

Predictions for lepton mixing angles and CP phases.

Constraints on neutrinoless double beta decay.

Abstract

Asymmetric tri-bi-maximal mixing is a recently proposed, grand unified theory (GUT) based, flavor mixing scheme. In it, the charged lepton mixing is fixed by the GUT connection to down-type quarks and a $\mathcal{T}_{13}$ flavor symmetry, while neutrino mixing is assumed to be tri-bi-maximal (TBM) with one additional free phase. Here we show that this additional free phase can be fixed by the residual flavor and CP symmetries of the effective neutrino mass matrix. We discuss how those residual symmetries can be unified with $\mathcal{T}_{13}$ and identify the smallest possible unified flavor symmetries, namely $(\mathbb{Z}_{13}\times\mathbb{Z}_{13})\rtimes \mathrm{D}_{12}$ and $(\mathbb{Z}_{13}\times\mathbb{Z}_{13})\rtimes \mathrm{S}_4$. Sharp predictions are obtained for lepton mixing angles, CP violating phases and neutrinoless double beta decay.