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

The generalized mu-tau interchange symmetry in the leptonic mixing matrix U corresponds to the relations: vertical bar U-mu i vertical bar=vertical bar U-tau i vertical bar with i = 1, 2, 3. It predicts maximal atmospheric mixing and maximal Dirac CP violation given theta(13) not equal 0. We show that the generalized mu-tau 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 A(4), S-4 and A(5) 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 theta(13) in case of (a) while only A(5) can provide theta(13) close to its experimental value in the case (b). We provide an explicit model based on A(5) and discuss a class of perturbations which can generate fully realistic neutrino masses and mixing maintaining the generalized mu-tau symmetry in U. Our approach provides generalization of some of the ideas proposed earlier in order to obtain the predictions,theta(23)=pi/4 and delta(CP)=+/-pi/2. (C) 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license