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Phenomenological Tests of Supersymmetric A_4 Family Symmetry Model of Neutrino Mass

Recently Babu, Ma and Valle proposed a model of quark and lepton mixing based on $A_4$ symmetry. Within this model the lepton and slepton mixings are intimately related. We perform a numerical study in order to derive the slepton masses and mixings in agreement with present data from neutrino physics. We show that, starting from three-fold degeneracy of the neutrino masses at a high energy scale, a viable low energy neutrino mass matrix can indeed be obtained in agreement with constraints on lepton flavour violating $μ$ and $τ$ decays. The resulting slepton spectrum must necessarily include at least one mass below 200 GeV which can be produced at the LHC. The predictions for the absolute Majorana neutrino mass scale $m_0 \geq 0.3$ eV ensure that the model will be tested by future cosmological tests and $ββ_{0ν}$ searches. Rates for lepton flavour violating processes $\ell_j \to \ell_i + γ$ in the range of sensitivity of current experiments are typical in the model, with BR$(μ\to e γ) \gsim 10^{-15}$ and the lower bound BR$(τ\to μγ) > 10^{-9}$. To first approximation, the model leads to maximal leptonic CP violation in neutrino oscillations.