Alexander S. Blum

Fermion Masses and Mixings from Dihedral Flavor Symmetries with Preserved Subgroups

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 (nontrivial) 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 nonvanishing 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. Furthermore, we comment on possible forms of Majorana mass matrices. As a first application we find a way to express the Cabibbo angle, i.e. the Cabibbo-Kobayashi-Maskawa matrix element

Golden ratio prediction for solar neutrino mixing

|{V}_{us}|

θ C from the Dihedral Flavor Symmetries D7 and D14

, in terms of group theory quantities only, the group index

The Cabibbo Angle in a Supersymmetric D(14) Model

n

A Supersymmetric D4 Model for mu-tau Symmetry

, the representation index j and the index

Non-Abelian discrete flavor symmetries from T-2/Z(N) orbifolds

{m}_{u,d}

The reinvention of general relativity : a historiographical framework for assessing one hundred years of curved space-time

of the different preserved subgroups in the up and down quark sector:

A supersymmetricD4model for μ−τ symmetry

|{V}_{us}|=|\mathrm{cos}(\frac{\ensuremath{\pi}({m}_{u}\ensuremath{-}{m}_{d})\mathrm{j}}{n})|

General Conditions for Lepton Flavour Violation at Tree- and 1-Loop Level

which is

A Supersymmetric D4 model for μ-τ symmetry

|\mathrm{cos}(\frac{3\ensuremath{\pi}}{7})|\ensuremath{\approx}0.2225