T13T13 flavor symmetry and decaying dark matter

We study a new flavor symmetric model with non-Abelian discrete symmetry T13T13. The T13T13 group is isomorphic to Z13⋊Z3Z13⋊Z3, and it is the minimal group having two complex triplets in the irreducible representations. We show that the T13T13 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 T13T13 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 well explained by decaying dark matter controlled by the T13T13 flavor symmetry.