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We study the renormalization group effects on neutrino masses and mixing inMinimal 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 givingrise to the desired neutrino mass matrix at high energy scale. We take thethree neutrino mass eigenvalues at high energy scale as input parameters andcompute the neutrino parameters at low energy by taking into account ofrenormalization group effects. We observe that the correct output values ofneutrino parameters at low energy are obtained only when the input masseigenvalues are large $|m_{1,2,3}| = 0.08-0.12$ eV with a very mild hierarchyof either inverted or normal type. A large inverted or normal hierarchicalpattern of neutrino masses is disfavored within our framework. We also find apreference towards higher values of $\tan{\beta}$, the ratio of vacuumexpectation values (vev) of two Higgs doublets in MSSM in order to arrive atthe correct low energy output. Such a model predicting large neutrino masseigenvalues with very mild hierarchy and large $\tan{\beta}$ could havetantalizing signatures at oscillation, neutrino-less double beta decay as wellas collider experiments.

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