On the origin of neutrino flavour symmetry

TL;DR

This paper explores models where discrete family symmetries are completely broken, leading to an accidental neutrino flavor symmetry that explains observed mixing patterns, with specific focus on D-term flavon vacuum alignments and symmetry groups.

Contribution

It introduces a framework for indirect neutrino flavor symmetry models based on discrete groups like Δ(3n^2) and Δ(6n^2), detailing vacuum alignments and implications for neutrino mixing.

Findings

Identification of suitable discrete symmetry groups for indirect models

Analysis of D-term flavon vacuum alignments

Discussion on stability of tri-bimaximal mixing predictions

Abstract

We study classes of models which are based on some discrete family symmetry which is completely broken such that the observed neutrino flavour symmetry emerges indirectly as an accidental symmetry. For such "indirect" models we discuss the D-term flavon vacuum alignments which are required for such an accidental flavour symmetry consistent with tri-bimaximal lepton mixing to emerge. We identify large classes of suitable discrete family symmetries, namely the $\Delta(3n^2)$ and $\Delta(6n^2)$ groups, together with other examples such as $Z_7\rtimes Z_3$. In such indirect models the implementation of the type I see-saw mechanism is straightforward using constrained sequential dominance. However the accidental neutrino flavour symmetry may be easily violated, for example leading to a large reactor angle, while maintaining accurately the tri-bimaximal solar and atmospheric predictions.