Claudia Hagedorn

A SUSY SU(5) Grand Unified Model of Tri-Bimaximal Mixing from A4

We discuss a grand unified model based on SUSY SU(5) in extra dimensions and on the flavour group A4 × U(1) which, besides reproducing tri-bimaximal mixing for neutrinos with the accuracy required by the data, also leads to a natural description of the observed pattern of quark masses and mixings.

S4 flavor symmetry and fermion masses: towards a grand unified theory of flavor

Pursuing a bottom-up approach to explore which flavor symmetry could serve as an explanation of the observed fermion masses and mixings, we discuss an extension of the standard model (SM) where the flavor structure for both quarks and leptons is determined by a spontaneously broken S4 and the requirement that its particle content is embeddable simultaneously into the conventional SO(10) grand unified theory (GUT) and a continuous flavor symmetry Gf like SO(3)f or SU(3)f. We explicitly provide the Yukawa and the Higgs sector of the model and show its viability in two numerical examples which arise as small deviations from rank one matrices. In the first case, the corresponding mass matrix is democratic and in the second one only its 2-3 block is non-vanishing. We demonstrate that the Higgs potential allows for the appropriate vacuum expectation value (VEV) configurations in both cases, if CP is conserved. For the first case, the chosen Yukawa couplings can be made natural by invoking an auxiliary Z2 symmetry. The numerical study we perform shows that the best-fit values for the lepton mixing angles θ12 and θ23 can be accommodated for normal neutrino mass hierarchy. The results for the quark mixing angles turn out to be too small. Furthermore the CP-violating phase δ can only be reproduced correctly in one of the examples. The small mixing angle values are likely to be brought into the experimentally allowed ranges by including radiative corrections. Interestingly, due to the S4 symmetry the mass matrix of the right-handed neutrinos is proportional to the unit matrix.

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

Lepton Flavour Violation in Models with A(4) Flavour Symmetry

|{V}_{us}|

Vacuum alignment in SUSY A4 models

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

Lepton mixing from the interplay of the alternating group A 5 and CP

n

θ C from the Dihedral Flavor Symmetries D7 and D14

, the representation index j and the index

The discrete flavor symmetry D5

{m}_{u,d}

The Cabibbo Angle in a Supersymmetric D(14) Model

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

SUSY S

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