Generalized μ–τ symmetry and discrete subgroups of O(3)

The generalized μ–τ interchange symmetry in the leptonic mixing matrix U corresponds to the relations: |Uμi|=|Uτi| with i=1,2,3. It predicts maximal atmospheric mixing and maximal Dirac CP violation given θ13≠0. We show that the generalized μ–τ symmetry can arise if the charged lepton and neutrino mass matrices are invariant under specific residual symmetries contained in the finite discrete subgroups of O(3). The groups A4, S4 and A5 are the only such groups which can entirely fix U at the leading order. The neutrinos can be (a) non-degenerate or (b) partially degenerate depending on the choice of their residual symmetries. One obtains either vanishing or very large θ13 in case of (a) while only A5 can provide θ13 close to its experimental value in the case (b). We provide an explicit model based on A5 and discuss a class of perturbations which can generate fully realistic neutrino masses and mixing maintaining the generalized μ–τ symmetry in U. Our approach provides generalization of some of the ideas proposed earlier in order to obtain the predictions, θ23=π/4 and δCP=±π/2.