Golden Ratio Prediction for Solar Neutrino Mixing

Abstract

It has recently been speculated that the solar neutrino mixing angle is connected to the golden ratio phi. Two such proposals have been made, cot theta_{12} = phi and cos theta_{12} = phi/2. We compare these Ansatze and discuss a model leading to cos theta_{12} = phi/2 based on the dihedral group D_{10}. This symmetry is a natural candidate because the angle in the expression cos theta_{12} = phi/2 is simply pi/5, or 36 degrees. This is the exterior angle of a decagon and D_{10} is its rotational symmetry group. We also estimate radiative corrections to the golden ratio predictions.

arXiv comment15 pages, 1 figure. Matches published version

References in corpus (18)

• Tri-Bimaximal Mixing and the Neutrino Oscillation Data
• Tri-Bimaximal Neutrino Mixing, A4 and the Modular Symmetry
• Symmetries and Generalisations of Tri-Bimaximal Neutrino Mixing
• Three-flavour neutrino oscillation update
• Nearly Tri-Bimaximal Neutrino Mixing and CP Violation
• Running Neutrino Masses, Mixings and CP Phases: Analytical Results and Phenomenological Consequences
• Some Simple Mixing and Mass Matrices for Neutrinos
• Hints of theta_13>0 from global neutrino data analysis
• Icosahedral (A5) Family Symmetry and the Golden Ratio Prediction for Solar Neutrino Mixing
• The golden ratio prediction for the solar neutrino mixing
• Fermion Masses and Mixings from Dihedral Flavor Symmetries with Preserved Subgroups
• Correlated Hierarchy, Dirac Masses and Large Mixing Angles
• Unified Parametrization for Quark and Lepton Mixing Angles
• Corrections to Tri-bimaximal Neutrino Mixing: Renormalization and Planck Scale Effects
• Radiatively broken symmetries of nonhierarchical neutrinos
• theta_C from the Dihedral Flavor Symmetries D_7 and D_14
• The Cabibbo Angle in a Supersymmetric D14 Model
• Lectures on Models of Neutrino Masses and Mixings

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