T(13) Flavor Symmetry and Decaying Dark Matter

We study a new flavor symmetric model with non-Abelian discrete symmetry T_{13}. The T_{13} group is isomorphic to Z_{13} \rtimes Z_3, and it is the minimal group having two complex triplets as the irreducible representations. We show that the T_{13} symmetry can derive lepton masses and mixings consistently. Moreover, if we assume a gauge-singlet fermionic decaying dark matter, its decay operators are also constrained by the T_{13} symmetry so that only dimension six operators of leptonic decay are allowed. We find that the cosmic-ray anomalies reported by PAMELA and Fermi-LAT are explained by decaying dark matter controlled by the T_{13} flavor symmetry.

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