Neutrino Mixing and the Double Tetrahedral Group

Abstract

In the spirit of a previous study of the tetrahedral group $T\simeq A_4$, we discuss a minimalist scheme to derive the neutrino mixing matrix using the double tetrahedral group $T^{\prime }$, the double cover of $T$. The new features are three distinct 2-dimensional representations and complex Clebsch-Gordan coefficients, which can result in a geometric source of CP violation in the neutrino mass matrix. In an appendix, we derive explicitly the relevant group theory for the tetrahedral group $T$ and its double cover $T^{\prime }$.

18 pages. v2: Added references. v3: Fixed factor of 1/2 for Majorana mass term. Conclusions unaffected. v4: Some clarifications, equation numbers, formatting changes. Conclusions unaffected

References in corpus (7)

• Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry
• CKM and Tri-bimaximal MNS Matrices in a SU(5) x (d)T Model
• A recursive parameterisation of unitary matrices
• Neutrino Tribimaximal Mixing from A_4 Alone
• Parametrizing the Neutrino Mixing Matrix
• Routines for the diagonalization of complex matrices
• Geometrical Origin of CP Violation and CKM and MNS Matrices in SU(5) x T'

Cited by in corpus (1)

• Tri-Bimaximal Neutrino Mixing and the $T_{13}$ Flavor Symmetry