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mu-tau Symmetry and Charged Lepton Mass Hierarchy in a Supersymmetric D4 Model

In this note we discuss a supersymmetric (SUSY) D4 x Z5 model which leads to vanishing reactor mixing angle theta_13=0 and maximal atmospheric mixing theta_23=pi/4 in the lepton sector at leading order (LO), due to the preservation of non-trivial distinct D4 subgroups in the charged lepton and neutrino sectors, respectively. The solar mixing angle theta_12 remains undetermined and is expected to be of order one. Since right-handed charged leptons transform as singlets under D4, the charged lepton mass hierarchy can be naturally accounted for. The model predicts inverted mass hierarchy for neutrinos. Additionally, we show that, unlike in most of the other models of this type, all vacuum expectation values (VEVs) of gauge singlets (flavons) can be fixed through mass parameters of the superpotential. Next-to-leading order (NLO) corrections to lepton masses and mixings are calculated and shown to be under control, especially the corrections to theta_23=pi/4 and theta_13=0 are of the order of the generic expansion parameter epsilon = 0.04 and arise dominantly from the charged lepton sector.