Model-Independent Analysis of Tri-bimaximal Mixing -- a Softly-Broken Hidden or an Accidental Symmetry?

TL;DR

This paper investigates whether tri-bimaximal mixing (TBM) in neutrinos is a hidden symmetry or an accidental one by analyzing perturbations in a model-independent way and comparing with grand unified theories, focusing on the sensitivity of |U_{e3}| to neutrino mass hierarchy.

Contribution

It provides a model-independent framework to analyze TBM perturbations and links the nature of TBM symmetry to neutrino mass hierarchy and |U_{e3}| measurements.

Findings

|U_{e3}| is highly sensitive to neutrino mass scale and ordering.

Observation of |U_{e3}|^2 > 0.001-0.01 would challenge softly-broken TBM with normal hierarchy.

Inverted and quasi-degenerate hierarchies do not lead to definitive conclusions.

Abstract

To address the issue of whether tri-bimaximal mixing (TBM) is a softly-broken hidden or an accidental symmetry, we adopt a model-independent analysis in which we perturb a neutrino mass matrix leading to TBM in the most general way but leave the three texture zeros of the diagonal charged lepton mass matrix unperturbed. We compare predictions for the perturbed neutrino TBM parameters with those obtained from typical SO(10) grand unified theories with a variety of flavor symmetries. Whereas SO(10) GUTs almost always predict a normal mass hierarchy for the light neutrinos, TBM has a priori no preference for neutrino masses. We find, in particular for the latter, that the value of |U_{e3}| is very sensitive to the neutrino mass scale and ordering. Observation of |U_{e3}|^2 > 0.001 to 0.01 within the next few years would be incompatible with softly-broken TBM and a normal mass hierarchy and would suggest that the apparent TBM symmetry is an accidental symmetry instead. No such conclusions can be drawn for the inverted and quasi-degenerate hierarchy spectra.