Is the tri-bimaximal mixing accidental?

TL;DR

This paper explores whether deviations from tri-bimaximal mixing in neutrino oscillations are accidental or stem from underlying flavor symmetries, analyzing how such deviations affect the neutrino mass matrix structure.

Contribution

It develops a formalism to analyze how deviations from TBM mixing influence the neutrino mass matrix and underlying flavor symmetries, revealing possible structures and symmetries.

Findings

Deviations can cause strong modifications of the mass matrix.

Mass matrices may become 'anarchical' or have different symmetries.

Examples include matrices with texture zeros and hierarchical structures.

Abstract

The Tri-bimaximal (TBM) mixing is not accidental if structures of the corresponding leptonic mass matrices follow immediately from certain (residual or broken) flavor symmetry. We develop a simple formalism which allows one to analyze effects of deviations of the lepton mixing from TBM on structure of the neutrino mass matrix and on underlying flavor symmetry. We show that possible deviations from the TBM mixing can lead to strong modifications of the mass matrix and strong violation of the TBM mass relations. As a result, the mass matrix may have an "anarchical" structure with random values of elements or it may have some symmetry which differs from the TBM symmetry. Interesting examples include matrices with texture zeros, matrices with certain "flavor alignment" as well as hierarchical matrices with a two-component structure, where the dominant and sub-dominant contributions have different symmetries. This opens up new approaches to understand the lepton mixing.