Radiative Generation of Non-zero $\theta_{13}$ in MSSM with broken $A_4$ Flavor Symmetry

TL;DR

This paper explores how renormalization group effects in MSSM with broken $A_4$ flavor symmetry can generate the observed non-zero $ heta_{13}$ neutrino mixing angle, emphasizing the importance of large neutrino masses and high $ an{eta}$ values.

Contribution

It presents a flavor symmetry model based on $A_4$ that explains the origin of neutrino mixing angles and masses, incorporating RG effects to match low-energy observations.

Findings

Large neutrino mass eigenvalues (~0.1 eV) are necessary for correct low-energy parameters.

High $ an{eta}$ values are favored to achieve the observed neutrino mixing.

Disfavoring of strongly hierarchical neutrino mass patterns within the model.

Abstract

We study the renormalization group effects on neutrino masses and mixing in Minimal Supersymmetric Standard Model (MSSM) by considering a $\mu-\tau$ symmetric mass matrix at high energy scale giving rise to Tri-Bi-Maximal (TBM) type mixing. We outline a flavor symmetry model based on $A_4$ symmetry giving rise to the desired neutrino mass matrix at high energy scale. We take the three neutrino mass eigenvalues at high energy scale as input parameters and compute the neutrino parameters at low energy by taking into account of renormalization group effects. We observe that the correct output values of neutrino parameters at low energy are obtained only when the input mass eigenvalues are large $|m_{1,2,3}| = 0.08-0.12$ eV with a very mild hierarchy of either inverted or normal type. A large inverted or normal hierarchical pattern of neutrino masses is disfavored within our framework. We also find a preference towards higher values of $\tan{\beta}$, the ratio of vacuum expectation values (vev) of two Higgs doublets in MSSM in order to arrive at the correct low energy output. Such a model predicting large neutrino mass eigenvalues with very mild hierarchy and large $\tan{\beta}$ could have tantalizing signatures at oscillation, neutrino-less double beta decay as well as collider experiments.