Tri-Bimaximal Neutrino Mixing and Discrete Flavour Symmetries

Abstract

We review the application of non-Abelian discrete groups to Tri-Bimaximal (TB) neutrino mixing, which is supported by experiment as a possible good first approximation to the data. After summarizing the motivation and the formalism, we discuss specific models, mainly those based on A4 but also on other finite groups, and their phenomenological implications, including the extension to quarks. The recent measurements of θ_13 favour versions of these models where a suitable mechanism leads to corrections to θ_13 that can naturally be larger than those to θ_12 and θ_23. The virtues and the problems of TB mixing models are discussed, also in connection with lepton flavour violating processes, and the different approaches are compared.

26 pages, 5 figures, 4 tables. V3 submitted to add an acknowledgment to a network. Review written for the special issue on "Flavor Symmetries and Neutrino Oscillations", published in Fortschritte der Physik - Progress of Physics

References in corpus (84)

• Indication of Electron Neutrino Appearance from an Accelerator-produced Off-axis Muon Neutrino Beam
• Phenomenology with Massive Neutrinos
• Improved search for muon-neutrino to electron-neutrino oscillations in MINOS
• Finite Modular Groups and Lepton Mixing
• Stringy origin of non-Abelian discrete flavor symmetries
• Neutrino tri-bi-maximal mixing from a non-Abelian discrete family symmetry
• Where we are on ${\theta }_{13}$: addendum to "Global neutrino data and recent reactor fluxes: status of three-flavour oscillation parameters"
• The Unique Horizontal Symmetry of Leptons
• Residual Symmetries for Neutrino Mixing with a Large theta_13 and Nearly Maximal delta_D
• Tri-Bimaximal Neutrino Mixing and the Family Symmetry Z_7 x Z_3
• Two-zero Textures of the Majorana Neutrino Mass Matrix and Current Experimental Tests
• The golden ratio prediction for the solar neutrino mixing
• A Simplest A4 Model for Tri-Bimaximal Neutrino Mixing
• Discrete Flavour Symmetries in Light of T2K
• Z_2 Symmetry Prediction for the Leptonic Dirac CP Phase
• Non-Abelian Discrete Flavor Symmetries from Magnetized/Intersecting Brane Models
• A model for fermion masses and lepton mixing in SO(10) x A4
• Trimaximal mixing with predicted θ_13 from a new type of constrained sequential dominance
• A predictive A4 model, Charged Lepton Hierarchy and Tri-bimaximal Sum Rule
• Parametrizing the lepton mixing matrix in terms of deviations from tri-bimaximal mixing
• Fermion Masses in SO(10) Models
• The Flavor Group Delta(3n^2)
• A model for trimaximal lepton mixing
• Lepton Flavour Violation in Models with A4 Flavour Symmetry
• Near Tribimaximal Neutrino Mixing with Delta(27) Symmetry
• Suitability of A_4 as a Family Symmetry in Grand Unification
• Sizeable θ_13 from the Charged Lepton Sector in SU(5), (Tri-)Bimaximal Neutrino Mixing and Dirac CP Violation
• Fermion masses and mixing in models with SO(10) x A_4 symmetry
• Is S4 the horizontal symmetry of tri-bimaximal lepton mixing?
• Golden Ratio Neutrino Mixing and $A_5$ Flavor Symmetry
• Quark-Lepton Complementarity in Unified Theories
• Minimal extension of tri-bimaximal mixing and generalized Z_2 X Z_2 symmetries
• The reactor mixing angle and CP violation with two texture zeros in the light of T2K
• Flavor Symmetry for Quarks and Leptons
• Golden Ratio Prediction for Solar Neutrino Mixing
• Towards a Complete Theory of Fermion Masses and Mixings with SO(3) Family Symmetry and 5d SO(10) Unification
• An SO(10) GUT Model with $S4$ Flavor Symmetry
• Fermion Mass Hierarchies and Flavor Mixing from $T^{\prime }$ Symmetry
• Simple Finite Non-Abelian Flavor Groups
• A new family symmetry for SO(10) GUTs
• Neutrino mixing from the double tetrahedral group T^{\prime}
• Different SO(10) Paths to Fermion Masses and Mixings
• Quark lepton complementarity and renormalization group effects
• Ultraviolet Completion of Flavour Models
• Tribimaximal Mixing From Small Groups
• An SO(10)XS4 Model of Quark-Lepton Complementarity
• Implications of a class of neutrino mass matrices with texture zeros for non-zero ${\theta }_{13}$
• Q_6 flavor symmetry model for the extension of the minimal standard model by three right-handed sterile neutrinos
• Embedding the Zee-Wolfenstein neutrino mass matrix in an SO(10) x A4 GUT scenario
• A_4 model for the quark mass matrices
• Neutrino masses and tribimaximal mixing in the minimal renormalizable supersymmetric SU(5) grand unified model with A4 flavor symmetry
• The Seesaw Mechanism in Quark-Lepton Complementarity
• Embedding A4 into SU(3)xU(1) flavor symmetry: Large neutrino mixing and fermion mass hierarchy in SO(10) GUT
• Near Maximal Atmospheric Mixing in Neutrino Mass Matrices with Two Vanishing Minors
• Fermion Mass Hierarchies and Flavour Mixing from a Minimal Discrete Symmetry
• $T^{{}^{\prime }}$ Predictions of PMNS and CKM Angles
• Quark-lepton complementarity and tribimaximal neutrino mixing from discrete symmetry
• Getting at large theta_13 with almost maximal theta_23 from tri-bimaximal mixing
• Low and High Energy Phenomenology of Quark-Lepton Complementarity Scenarios
• Quark-lepton complementarity with quasidegenerate Majorana neutrinos
• Broken S3 Symmetry in the Neutrino Mass Matrix and Non-Zero theta_{13}
• Radiatively broken symmetries of nonhierarchical neutrinos
• Non-Abelian Discrete Flavor Symmetries from T^2/Z_N Orbifolds
• On the finite subgroups of U(3) of order smaller than 512
• Non-Abelian Discrete Groups from the Breaking of Continuous Flavor Symmetries
• Adjoint SUSY $SU(5)$ Grand Unified Model with $S_4$ Flavor Symmetry
• Quark-lepton complementarity, neutrino and standard model data predict $({\theta }_{13}^{PMNS}=9_{-2}^{+1}{)}^{\circ }$
• Systematic Parameter Space Search of Extended Quark-Lepton Complementarity
• Flavour violation in a supersymmetric T' model
• Neutrino mixing matrices with relatively large ${\theta }_{13}$ and with texture one-zero
• Measurable Neutrino Mass Scale in A4 x SU(5)
• Tri-bi-maximal mixing in viable family symmetry unified model with extended seesaw
• Non-Abelian family symmetries in Pati-Salam unification
• Predicting theta_13 and the Neutrino Mass Scale from Quark Lepton Mass Hierarchies
• Non-zero ${\theta }_{13}$ and CP-violation in inverse neutrino mass matrix
• General Lepton Mixing in Holographic Composite Higgs Models
• The charged lepton mass matrix and non-zero ${\theta }_{13}$ with TeV scale New Physics
• Soft supersymmetry breaking terms from A4 lepton flavor symmetry
• Large theta_13 from a model with broken L_e-L_mu-L_tau symmetry
• Deviations from Tri-Bimaximality and Quark-Lepton Complementarity
• Tri-bimaximal Mixing and Cabibbo Angle in S4 Flavor Model with SUSY
• Renormalisation group improved leptogenesis in family symmetry models
• Large θ_13 from finite quantum corrections in quasi-degenerate neutrino mass spectrum
• Fermion masses and mixing with tri-bimaximal in SO(10) with type-I seesaw

Cited by in corpus (66)

• Unified Models of Neutrinos, Flavour and CP Violation
• Discrete Flavour Symmetries, Neutrino Mixing and Leptonic CP Violation
• Symmetry breaking patterns in 3HDM
• Determining the Dirac CP Violation Phase in the Neutrino Mixing Matrix from Sum Rules
• Sterile Neutrino portal to Dark Matter II: Exact Dark symmetry
• Generalised Geometrical CP Violation in a $T^{\prime }$ Lepton Flavour Model
• Generalized $\mu$-$\tau$ symmetry and discrete subgroups of O(3)
• Nonzero ${\theta }_{13}$ and Leptogenesis in a Type-I See-saw Model with $A_4$ Symmetry
• The Minimal Flavour Violating Axion
• Predictions for the Leptonic Dirac CP Violation Phase: a Systematic Phenomenological Analysis
• Phenomenological Study of Residual Z^s_2 and Zbar^s_2 Symmetries
• Abelian symmetries of the N-Higgs-doublet model with Yukawa interactions
• Leptonic Dynamical Yukawa Couplings
• Discrete symmetries for electroweak natural type-I seesaw mechanism
• How good is μ-τsymmetry after results on non-zero θ_{13}?
• The symmetry approach to quark and lepton masses and mixing
• A Bayesian comparison of U(1) lepton flavour models
• Neutrino Masses and Hubble Tension via a Majoron in MFV
• Revisiting Minimal Lepton Flavour Violation in the Light of Leptonic CP Violation
• B-L Model with ${\mathbf{S}}_3$ Symmetry: Nearest Neighbor Interaction Textures and Broken $\mu \leftrightarrow \tau$ Symmetry
• Distinguishing A Higgs-Like Dilaton Scenario With A Complete Bosonic Effective Field Theory Basis
• Spontaneous CP Violation in Lepton-sector: a common origin for ${\theta }_{13}$, Dirac CP phase and leptogenesis
• Discrete flavour symmetries for degenerate solar neutrino pair and their predictions
• Matter inflation with A_4 flavour symmetry breaking
• Corrections for tribimaximal, bimaximal and democratic neutrino mixing matrices
• A massless neutrino and lepton mixing patterns from finite discrete subgroups of U(3)
• Discrete symmetries, roots of unity, and lepton mixing
• Consequences of $\mu -\tau$ Reflection Symmetry at DUNE
• Exploring Partial $\mu$-$\tau$ Reflection Symmetry at DUNE and Hyper-Kamiokande
• Neutrino masses and mixing in $A_5$ with flavour antisymmetry
• Understanding for flavor physics in the lepton sector
• Minimal modifications to the Tri-Bimaximal neutrino mixing
• Predictive Leptogenesis from Minimal Lepton Flavour Violation
• A New bound on CP Violation in the $\tau$ Lepton Yukawa Coupling and electroweak baryogenesis
• Breaking classical Lie groups to finite subgroups - an automated approach
• Can an unbroken flavour symmetry provide an approximate description of lepton masses and mixing?
• Stable fermion mass matrices and the charged lepton contribution to neutrino mixing
• Residual $Z_2$ symmetries and leptonic mixing patterns from finite discrete subgroups of $U(3)$
• Neutrino masses and mixing from flavour antisymmetry
• Impact of RGE-induced $\mu -\tau$ Reflection Symmetry Breaking on the Effective Majorana Neutrino Mass in $0\nu \beta \beta$ Decay
• $\mu -\tau$ Reflection Symmetry and Its Explicit Breaking for Leptogenesis in a Minimal Seesaw Model
• Flavon-induced connections between lepton flavour mixing and charged lepton flavour violation processes
• Low energy phenomena of the lepton sector in an $A_4$ symmetry model with heavy inverse seesaw neutrinos
• The role of flavon cross couplings in leptonic flavour mixing
• Consequences of $\mu$-$\tau$ reflection symmetry for $3+1$ neutrino mixing
• Data Driven Flavour Model
• Testable constraint on near-tribimaximal neutrino mixing
• CP violations in a predictive $A_4$ symmetry model
• Pseudo-Dirac neutrinos from flavour dependent CP symmetry
• Testing the minimal $S_4$ model of neutrinos with the Dirac and Majorana phases
• Deviations to Tri-Bi-Maximal mixing in the limit of $\mu -\tau$ symmetry
• Restricting Majorana phases in the Tri-Bi-Maximal limit
• Two-zero textures based on $A_4$ symmetry and unimodular mixing matrix
• Nonzero ${\theta }_{13}$ in $SO(3)\to A_4$ lepton models
• SUSY SU(5) $\times S_4$ GUT Flavor Model for Fermion Masses and Mixings with Adjoint, Large ${\theta }_{13}^{PMNS}$
• A non-renormalizable neutrino mass model with ${\mathbf{S}}_3\otimes {\mathbf{Z}}_2$ symmetry
• A neutrino mixing model based on an $A_4\times Z_3\times Z_4$ flavour symmetry
• Five models for lepton mixing
• Soft breaking of the $\mu \leftrightarrow \tau$ symmetry by ${\mathbf{S}}_4\otimes {\mathbf{Z}}_2$
• The Minimal Flavor Structure from Decomposition of the Fermion Mass Matrix
• Effects on sinθ_{12} from perturbation of the neutrino mixing matrix with the partially degenerated neutrino masses
• A lepton model with nearly Cobimaximal mixing
• The special Two zeros texture based on $A_4$ symmetry and perturbation method
• Breaking of the tetra-maximal neutrino mixing pattern
• $TeV$-Scale Resonant Leptogenesis with New Scaling Ansatz on Neutrino Dirac Mass Matrix from $A_4$ Flavor Symmetry
• A Bottom-Up Approach: The Data Driven Flavour Model