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Dihedral Flavor Symmetries


Blum,  Alexander Simon
Division Prof. Dr. Manfred Lindner, MPI for Nuclear Physics, Max Planck Society;

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Blum, A. S. (2009). Dihedral Flavor Symmetries. PhD Thesis, Ruprecht-Karls Universität, Heidelberg, Germany.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0011-7557-6
This thesis deals with the possibility of describing the flavor sector of the Standard Model of Particle Physics (with neutrino masses), that is the fermion masses and mixing matrices, with a discrete, non-abelian flavor symmetry. In particular, mass independent textures are considered, where one or several of the mixing angles are determined by group theory alone and are independent of the fermion masses. To this end a systematic analysis of a large class of discrete symmetries, the dihedral groups, is analyzed. Mass independent textures originating from such symmetries are described and it is shown that such structures arise naturally from the minimization of scalar potentials, where the scalars are gauge singlet flavons transforming non-trivially only under the flavor group. Two models are constructed from this input, one describing leptons, based on the group D_4, the other describing quarks and employing the symmetry D_{14}. In the latter model it is the quark mixing matrix element V_{ud} - basically the Cabibbo angle - which is at leading order predicted from group theory. Finally, discrete flavor groups are discussed as subgroups of a continuous gauge symmetry and it is shown that this implies that the original gauge symmetry is broken by fairly large representations.