Quark and lepton mixing angles with a dodeca-symmetry

Abstract

The discrete symmetry D_12 at the electroweak scale is used to fix the quark and lepton mixing angles. At the leading order, the Cabbibo angle theta_C is 15^o, and the PMNS matrix is of a bi-dodeca-mixing form giving the Solar-neutrino angle theta_sol=30^o. Thus, there results the relation theta_sol+theta_C ~ 45^o. Out of discrete vacua, a certain vacuum is chosen for this assignment to be consistent with the dodeca-symmetry. A shift of theta_C from 15^o to 13.14^o might arise from a small breaking of the dodeca-symmetry. The spontaneous breaking leading to the required electroweak vacuum is made possible by introducing an additional parity in an effective field approach or by realizing the electroweak dodeca-symmetry explicitly at a high energy scale. At the vacuum we chose Arg.Det.M_q is nonzero, and hence a solution of the strong CP problem invites a very light axion at a high energy scale. We also comment how the next level corrections can fit the mixing angles to the observed values.

15 pages, 2 figures

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• Discrete Flavour Symmetries, Neutrino Mixing and Leptonic CP Violation
• Determining the Dirac CP Violation Phase in the Neutrino Mixing Matrix from Sum Rules
• Assessing the Viability of $A_4$, $S_4$ and $A_5$ Flavour Symmetries for Description of Neutrino Mixing
• Predictions for the Leptonic Dirac CP Violation Phase: a Systematic Phenomenological Analysis
• Systematic search for successful lepton mixing patterns with nonzero theta_13
• Radiative seesaw-type mechanism of quark masses in SU(3\)_{C}\otimes SU(3\)_{L}\otimes U\(1\)_{X}$
• Light scalar dark matter at neutrino oscillation experiments
• The symmetry approach to quark and lepton masses and mixing
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• Standard and Non-Standard Aspects of Neutrino Physics