Fermion Masses and Mixings from Dihedral Flavor Symmetries with Preserved Subgroups

Understand

We perform a systematic study of dihedral groups used as flavor symmetry.

• The key feature here is the fact that we do not allow the dihedral groups to be broken in an arbitrary way, but in all cases some (non-trivial) subgroup has to be preserved.
• In this way we arrive at only five possible (Dirac) mass matrix structures which can arise, if we require that the matrix has to have a non-vanishing determinant and that at least two of the three generations of left-handed (conjugate) fermions are placed into an irreducible two-dimensional representation of the flavor group.
• We show that there is no difference between the mass matrix structures for single- and double-valued dihedral groups.