Quaternion Family Symmetry of Quarks and Leptons

Details Quaternion Family Symmetry of Quarks and Leptons Quaternion Family Symmetry of Quarks and Leptons

2004-09-15

arxiv.org/abs/hep-ph/0409187v2

Phys.Rev. D71 (2005) 011901

Physics

High Energy Physics

High Energy Physics - Phenomenology

latex, 10 pages, 2 eps figures, notations revised, classification of $D_4$ models corrected

Scientific paper

10.1103/PhysRevD.71.011901

To a first approximation, the quark mixing matrix has $\theta^q_{13} = \theta^q_{23} = 0$, whereas the lepton mixing matrix has $\theta^l_{23} = \pi/4$. We show how this structure may be understood if the family symmetry is $Q_8$, the quaternion group of eight elements. We find three viable scenarios for the Majorana neutrino mass matrix, each depending on 4 parameters and predicting a specific mass spectrum. The phenomenology of the two Higgs doublets which generate the Yukawa sector is analyzed and testable predictions are derived. We discuss also the closely related model based on $D_4$, the symmetry group of the square.

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