Fermion masses and mixings from dihedral flavor symmetries with preserved subgroups

Journal Article · Tue Apr 01 04:00:00 EDT 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.77.076004· OSTI ID:21249974

Blum, A; Hagedorn, C; Lindner, M ^[1]

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1. Max-Planck-Institut fuer Kernphysik, Postfach 10 39 80, 69029 Heidelberg (Germany)

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 |V{sub us}|, in terms of group theory quantities only, the group index n, the representation index j and the index m{sub u,d} of the different preserved subgroups in the up and down quark sector: |V{sub us}|=|cos(({pi}(m{sub u}-m{sub d})j/n))| which is |cos((3{pi}/7))|{approx_equal}0.2225 for n=7, j=1, m{sub u}=3 and m{sub d}=0. We prove that two successful models which lead to maximal atmospheric mixing and vanishing {theta}{sub 13} in the lepton sector are based on the fact that the flavor symmetry is broken in the charged lepton, Dirac neutrino and Majorana neutrino sector down to different preserved subgroups whose mismatch results in the prediction of these mixing angles. This also demonstrates the power of preserved subgroups in connection with the prediction of mixing angles in the quark as well as in the lepton sector.

• OSTI ID: 21249974
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 7 Vol. 77; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CABIBBO ANGLE
D QUARKS
FLAVOR MODEL
FORECASTING
GROUP THEORY
KOBAYASHI-MASKAWA MATRIX
MASS
MIXING
NEUTRINOS
SYMMETRY
SYMMETRY BREAKING
TWO-DIMENSIONAL CALCULATIONS
WEINBERG ANGLE