Freiburg 2008 – wissenschaftliches Programm

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T: Fachverband Teilchenphysik

T 18: Neutrinophysik (Theorie)

T 18.2: Vortrag

Freitag, 7. März 2008, 14:15–14:30, Peterhof-HS 4

Dihedral Flavour Symmetries with conserved subgroups — •Alexander Blum, Claudia Hagedorn, Andreas Hohenegger, and Manfred Lindner — Max-Planck-Institut für Kernphysik, Heidelberg

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. 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 CKM matrix element | V_us |, in terms of group theory quantities only, the group index n, the representation index j and the index m_u,d of the different preserved subgroups in the up and down quark sector: | V_us | = | cos(π(m_u−m_d)j/n) | which is | cos(3 π/7)| = 0.2225 for n=7, j=1, m_u=3 and m_d=0. We prove that two successful models which lead to maximal atmospheric mixing and vanishing θ₁₃ 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.