The Golden Ratio Prediction for the Solar Angle from a Natural Model with A5 Flavour Symmetry

Abstract

We formulate a consistent model predicting, in the leading order approximation, maximal atmospheric mixing angle, vanishing reactor angle and tan θ_12 = 1/ϕ where ϕ is the Golden Ratio. The model is based on the flavour symmetry A5 \times Z5 \times Z3, spontaneously broken by a set of flavon fields. By minimizing the scalar potential of the theory up to the next-to-leading order in the symmetry breaking parameter, we demonstrate that this mixing pattern is naturally achieved in a finite portion of the parameter space, through the vacuum alignment of the flavon fields. The leading order approximation is stable against higher-order corrections. We also compare our construction to other models based on discrete symmetry groups.

28 pages, 2 figures. Minor changes, references added. Corrected typos in Appendix A. Version appeared on JHEP

References in corpus (13)

• Phenomenology with Massive Neutrinos
• A Simplest A4 Model for Tri-Bimaximal Neutrino Mixing
• Deviation from tri-bimaximal neutrino mixing in A4 flavor symmetry
• Lepton Flavour Violation in Models with A4 Flavour Symmetry
• Predictive flavour symmetries of the neutrino mass matrix
• Embedding A4 into left-right flavor symmetry: Tribimaximal neutrino mixing and fermion hierarchy
• Golden Ratio Prediction for Solar Neutrino Mixing
• Simple Finite Non-Abelian Flavor Groups
• Deviation from tri-bimaximal mixing and flavor symmetry breaking in a seesaw type A4 model
• A_4 Symmetry and Lepton Masses and Mixing
• The flavor problem and discrete symmetries
• Rare muon and tau decays in A4 Models
• Quintics with Finite Simple Symmetries

Cited by in corpus (64)

• Neutrino Mass and Mixing: from Theory to Experiment
• Finite Modular Groups and Lepton Mixing
• Lepton mixing and discrete symmetries
• Unified Models of Neutrinos, Flavour and CP Violation
• Modular $A_5$ Symmetry for Flavour Model Building
• Discrete Flavour Symmetries in Light of T2K
• Discrete Flavour Symmetries, Neutrino Mixing and Leptonic CP Violation
• Discrete Flavour Groups, θ_13 and Lepton Flavour Violation
• Golden Ratio Neutrino Mixing and $A_5$ Flavor Symmetry
• Tri-bimaximal-Cabibbo Mixing
• Discrete symmetries and model-independent patterns of lepton mixing
• Tri-Bimaximal Neutrino Mixing and Discrete Flavour Symmetries
• Mixing angle and phase correlations from A5 with generalised CP and their prospects for discovery
• Lepton mixing from the interplay of the alternating group A5 and CP
• Generalized $\mu$-$\tau$ symmetry and discrete subgroups of O(3)
• Predictions for Leptonic Mixing Angle Correlations and Non-trivial Dirac CP Violation from $A_5$ with Generalised CP Symmetry
• Repressing Anarchy in Neutrino Mass Textures
• Neutrino Mixings and the S4 Discrete Flavour Symmetry
• A Bottom-Up Approach to Lepton Flavor and CP Symmetries
• Testing solar lepton mixing sum rules in neutrino oscillation experiments
• Group Theory and Dynamics of Neutrino Mixing
• An SU(5) x A5 Golden Ratio Flavour Model
• Systematic search for successful lepton mixing patterns with nonzero theta_13
• The T7 flavor symmetry in 3-3-1 model with neutral leptons
• A Golden A_5 Model of Leptons with a Minimal NLO Correction
• A4 Flavor Models in Split Seesaw Mechanism
• Near Maximal Atmospheric Neutrino Mixing in Neutrino Mass Models with Two Texture Zeros
• Neutrino Mixing with Non-Zero ${\theta }_{13}$ and CP Violation in the 3-3-1 Model Based on $S_4$ Flavor Symmetry
• A highly predictive $A_4$ flavour 3-3-1 model with radiative inverse seesaw mechanism
• Flavour violation in a supersymmetric T' model
• Parametrizing the Lepton Mixing Matrix in terms of Charged Lepton Corrections
• The symmetry approach to quark and lepton masses and mixing
• Golden ratio lepton mixing and nonzero reactor angle with $A_5$
• Discrete Symmetries and Neutrino Mass Perturbations for θ_{13}
• General Lepton Mixing in Holographic Composite Higgs Models
• Tri-Bimaximal Neutrino Mixing and the $T_{13}$ Flavor Symmetry
• Leptogenesis in an SU(5) x A5 Golden Ratio Flavour Model
• Relating neutrino masses and mixings by discrete symmetries
• Lepton Sector Phases and Their Roles in Flavor and Generalized CP Symmetries
• Perturbations to $\mu -\tau$ Symmetry, Leptogenesis and Lepton Flavour Violation with Type II Seesaw
• Neutrino Mixing and Discrete Symmetries
• Flavored Non-Minimal Left-Right Symmetric Model Fermion Masses and Mixings
• Neutrino masses and mixing in $A_5$ with flavour antisymmetry
• Spontaneous Breaking of Gauge Groups to Discrete Symmetries
• Muon anomalies and the $SU(5)$ Yukawa relations
• Renormalization Group Evolution of Neutrino Parameters in Presence of Seesaw Threshold Effects and Majorana Phases
• Neutrino masses and lepton mixing from $A_5\times \mathrm{CP}$
• Predictions for the Dirac CP-Violating Phase from Sum Rules
• Flavon-induced connections between lepton flavour mixing and charged lepton flavour violation processes
• Lepton Flavor Violation and Neutrino Masses from $A_5$ and CP in the Non-Universal MSSM
• Neutrino masses and mixing in Minimal Inverse Seesaw using $A_4$ modular symmetry
• The neutrino mixing matrix could (almost) be diagonal with entries {\pm}1
• An Overview of Neutrino Mixing
• Deviations from Tribimaximal and Golden Ratio mixings under radiative corrections of neutrino masses and mixings
• Constraining $A_4$ Leptonic Flavour Model Parameters at Colliders and Beyond
• Fractionalized time reversal, parity and charge conjugation symmetry in topological superconductor: a possible origin of three generations of neutrinos and mass mixing
• Constraining Low-Scale Flavor Models with $(\mathbf{g}-2{)}_{\mathbf{\mu }}$ and Lepton Flavor Violation
• An $A_5$ inverse seesaw model with perturbed golden ratio mixing
• Phases of Flavor Neutrino Masses and CP Violation
• A Modern Look at the Oscillation Physics Case for a Neutrino Factory
• $A_5$ symmetry and deviation from Golden Ratio mixing with charged lepton flavor violation
• Predicting Neutrino Mixing Angles Using Group Presentations
• Discrete Flavour Symmetries from the Heisenberg Group
• A universal form for quark and neutrino mass matrices