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In this work, a flavour theory of a neutrino mass model based on $ A_{4} $symmetry is considered to explain the phenomenology of neutrino mixing. Thespontaneous symmetry breaking of $ A_{4} $ symmetry in this model leads totribimaximal mixing in the neutrino sector at a leading order. We consider theeffect of $ Z_{2} \times Z_{2}$ invariant perturbations in neutrino sector andfind the allowed region of correction terms in the perturbation matrix that isconsistent with 3$ \sigma $ ranges of the experimental values of the mixingangles. We study the entanglement of this formalism on the otherphenomenological observables, such as $ \delta_{CP} $ phase, the neutrinooscillation probability $ P(\nu_{\mu}\rightarrow \nu_{e} )$, the effectiveMajorana mass $ |m_{ee} |$ and $ |m^{eff}_{\nu e} |$. A $ Z_{2} \times Z_{2}$invariant perturbations in this model is introduced in the neutrino sectorwhich leads to testable predictions of $ \theta_{13} $ and CP violation. Bychanging the magnitudes of perturbations in neutrino sector, one can generateviable values of $ \delta_{CP} $ and neutrino oscillation parameters. Next weinvestigate the feasibility of charged lepton flavour violation in type-Iseesaw models with leptonic flavour symmetries at high energy that leads totribimaximal neutrino mixing. We consider an effective theory with an $A_{4}\times Z_{2} \times Z_{2} $ symmetry, which after spontaneous symmetry breakingat high scale which is much higher than the electroweak scale leads to chargedlepton flavour violation processes once the heavy Majorana neutrino massdegeneracy is lifted either by renormalization group effects or by a softbreaking of the $ A_{4} $ symmetry. In this context the implications forcharged lepton flavour violation processes like $ \mu \rightarrow e \gamma $, $\tau \rightarrow e \gamma $, $ \tau \rightarrow \mu \gamma $ are discussed.

nuclear physics b

Non$-$zero $ \theta_{13} $ and $ \delta_{CP} $ phase with $ A_{4} $  Flavor Symmetry and Deviations to Tri$-$Bi$-$Maximal mixing via $ Z_{2}  \times Z_{2}$ invariant perturbations in the Neutrino sector