Constraining {\it CP} violation in a softly broken $A_4$ symmetric Model

Abstract

To understand the mass spectra of charged lepton and neutrino $A_4$ symmetry has been proposed in addition with the Standard $SU(2{)}_L\times U(1{)}_Y$ model. We break $A_4$ symmetry softly and the deviation from the tri-bimaximal mixing arises due to Zee mechanism. In the present work, we express two mixing angles ${\theta }_{13}$ and ${\theta }_{23}$ in terms of a single model parameter and experimental observables, such as, mixing angle ${\theta }_{12}$, mass squared differences $\Delta m_{21}^2$ and $\Delta m_{32}^2$. Using the experimental values of ${\theta }_{23}$, ${\theta }_{12}$, $\Delta m_{21}^2$ and $\Delta m_{32}^2$ we restrict the model parameter and we predict ${\theta }_{13}$. This model gives rise to ${\theta }_{13}\simeq 11^{\circ }$ if we allow $1\sigma$ deviation of ${\theta }_{23}$ and $2^{\circ }$ deviation of ${\theta }_{12}$ from their best fit values. Utilizing all those constraints, we explore the extent of CP violation parameter $J_{\mathrm{CP}}$ in the present model and found a value of $J_{\mathrm{CP}}\approx 2.65\times 10^{-3}$ (for $1\sigma$ deviation of ${\theta }_{23}$ and $2^{\circ }$ deviation of ${\theta }_{12}$) consistent with the other neutrino experimental results. We have studied the mass pattern of neutrino and neutrinoless double beta decay $(\beta {\beta }_{0\nu })$ parameter $|(M_{\nu }{)}_{ee}|$ in this model.

16 pages, 6 eps figures,revised materials and figures, version to appear in Phys.Rev. D

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