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Left-right symmetric model with $μ\leftrightarrowτ$ symmetry

We analyze the leptonic sector in the left-right symmetric model dressed with a $(Z_{2})^{3}$ discrete symmetry which realizes, after weak spontaneous breaking, a small broken $μ\lraτ$ symmetry that is suggested to explain observable neutrino oscillation data. $μ\lraτ$ symmetry is broken at tree level in the effective neutrino mass matrix due to the mass difference $\widetilde{m}_τ\neq \widetilde{m}_μ$ in the diagonal Dirac mass terms, whereas all lepton mixings arise from a Majorana mass matrix. In the limit of a small breaking we determined $θ_{13}$, and the deviation from the maximal value of $θ_{ATM}$, in terms of the light neutrino hierarchy scale, $m_{3}$, and a single free parameter $h_{s}$ of the model.