Fine tuning in an A4-based Tri-Bimaximal neutrino-mixing model

TL;DR

This paper analyzes the A4-based Tri-Bimaximal neutrino mixing model and finds that achieving the observed small mass-squared difference ratio requires significant fine tuning, questioning the model's naturalness.

Contribution

It demonstrates that the Altarelli-Feruglio A4 model needs fine tuning to match experimental neutrino mass differences, highlighting a potential issue in its naturalness.

Findings

The model requires fine tuning to reproduce the observed r_{23} ratio.

Fine tuning is necessary in both basic and seesaw versions of the model.

The study evaluates the naturalness of the A4-based neutrino mixing model.

Abstract

The A4 group stands in the basis of many models that predict Tri-Bimaximal neutrino mixing at leading order. We study the Altarelli-Feruglio A4 symmetry model and show that in order to produce as small value of r_{23} (ratio of mass-squared differences) as measured, it requires fine tuning. This observation is important for an evaluation of the model, since the problem it is trying to solve in the first place is the tuning of the three mixing angles. We get the required level of fine tuning for the model in both its basic form and its seesaw realization.