Neutrino Mass and Mixing with Discrete Symmetry

Abstract

This is a review article about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry. After a pedagogical introduction and overview of the whole of neutrino physics, we focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle. We then describe the simple bimaximal, tri-bimaximal and golden ratio patterns of lepton mixing and the deviations required for a non-zero reactor angle, with solar or atmospheric mixing sum rules resulting from charged lepton corrections or residual trimaximal mixing. The different types of see-saw mechanism are then reviewed as well as the sequential dominance mechanism. We then give a mini-review of finite group theory, which may be used as a discrete family symmetry broken by flavons either completely, or with different subgroups preserved in the neutrino and charged lepton sectors. These two approaches are then reviewed in detail in separate chapters including mechanisms for flavon vacuum alignment and different model building strategies that have been proposed to generate the reactor angle. We then briefly review grand unified theories (GUTs) and how they may be combined with discrete family symmetry to describe all quark and lepton masses and mixing. Finally we discuss three model examples which combine an SU(5) GUT with the discrete family symmetries A4, S4 and Delta(96).

99 pages, 13 figures, review article, updated to include the results from the latest global fits

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• Reply to a Comment of article ``Evidence for Neutrinoless Double Beta Decay''
• Non-vanishing $U_{e3}$ under $S_3$ symmetry
• Heptagonic Symmetry for Quarks and Leptons

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• Lepton Mixing Parameters from $\Delta (48)$ Family Symmetry and Generalised CP
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• Fermion Masses and Mixing from Double Cover and Metaplectic Cover of $A_5$ Modular Group
• Quark sector of S3 models: classification and comparison with experimental data
• $Z^{\prime }$s in neutrino scattering at DUNE
• Generalized $\mu -\tau$ reflection symmetry and leptonic CP violation
• Classification of lepton mixing matrices from finite residual symmetries
• Nonzero |U_e3| from Charged Lepton Corrections and the Atmospheric Neutrino Mixing Angle
• Discrete flavor symmetries in D-brane models
• Cosmology with the Large Synoptic Survey Telescope: an Overview
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• Generalised Geometrical CP Violation in a $T^{\prime }$ Lepton Flavour Model
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• Minimal see-saw model predicting best fit lepton mixing angles
• Quark-Lepton Mass Relation in a Realistic A4 Extension of the Standard Model
• Generalised CP and $\Delta (96)$ Family Symmetry
• Searches for Long-Lived Particles at the Future FCC-ee
• Leptonic Dirac CP Violation Predictions from Residual Discrete Symmetries
• Predicting Lepton Flavor Mixing from $\Delta (48)$ and Generalized CP Symmetries
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• Neutrino Mixing from CP Symmetry
• Phenomenological Study of Residual Z^s_2 and Zbar^s_2 Symmetries
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• Constraining multi-Higgs flavour models
• Mu-tau reflection symmetry with a texture-zero
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• Modular Origin of Mass Hierarchy: Froggatt-Nielsen like Mechanism
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• Predictions for the Dirac CP Violation Phase in the Neutrino Mixing Matrix
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• Testing Lepton Flavor Models at ESSnuSB
• Probing Lepton Flavor Models at Future Neutrino Experiments
• Golden Littlest Seesaw
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• Soft supersymmetry breaking terms and lepton flavor violations in modular flavor models
• Spontaneous Breaking of Gauge Groups to Discrete Symmetries
• Neutrino masses, the $\mu$-term and ${\mathcal{P}\mathcal{SL}}_2(7)$
• Littlest mu-tau seesaw
• Lepton mass matrix from double covering of $A_4$ modular flavor symmetry
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• Collider signatures of vector-like fermions from a flavor symmetric model
• A New bound on CP Violation in the $\tau$ Lepton Yukawa Coupling and electroweak baryogenesis
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• Majorana Physics Through the Cabibbo Haze
• Breaking classical Lie groups to finite subgroups - an automated approach
• Lepton and Quark Mixing from Stepwise Breaking of Flavor and CP
• A Comprehensive Renormalisation Group Analysis of the Littlest Seesaw Model
• Moduli trapping mechanism in modular flavor symmetric models
• Flavor structure in D-brane models: Majorana neutrino masses
• Flavour and CP symmetries in the inverse seesaw
• Integral solutions to the one-loop renormalization-group equations for lepton flavor mixing parameters and the Jarlskog invariant
• Effective alignments as building blocks of flavour models
• Top Quark as a Dark Portal and Neutrino Mass Generation
• Viability of exact tri-bimaximal, golden-ratio and bimaximal mixing patterns and renormalization-group running effects
• Neutrino masses and mixing from flavour antisymmetry
• Common Origin of Non-zero ${\theta }_{13}$ and Dark Matter in an $S_4$ Flavour Symmetric Model with Inverse Seesaw
• Residual $Z_2$ symmetries and leptonic mixing patterns from finite discrete subgroups of $U(3)$
• Predictions for the Dirac CP-Violating Phase from Sum Rules
• Impact of RGE-induced $\mu -\tau$ Reflection Symmetry Breaking on the Effective Majorana Neutrino Mass in $0\nu \beta \beta$ Decay
• Lepton mass and mixing in a Neutrino Mass Model based on $S_4$ flavor symmetry
• Fermion masses and mixings and $g-2$ muon anomaly in a 3-3-1 model with $D_4$ family symmetry
• Realization of the minimal extended seesaw mechanism and the $T{M}_2$ type neutrino mixing
• Muon-to-Electron Conversion in Mirror Fermion Model with Electroweak Scale Non-Sterile Right-handed Neutrinos
• Generalized perturbations in neutrino mixing
• Flavon-induced connections between lepton flavour mixing and charged lepton flavour violation processes
• A Further Study of the Frampton-Glashow-Yanagida Model for Neutrino Masses, Flavor Mixing and Baryon Number Asymmetry
• Target Space Duality of Non-Supersymmetric String Theory
• Effective Theories of Flavor and the Non-Universal MSSM
• Precise predictions for Dirac neutrino mixing
• Highly predictive and testable $A_4$ flavor model within type-I and II seesaw framework and associated phenomenology
• Deviations in Tribimaximal Mixing From Sterile Neutrino Sector
• Remark on modular weights in low-energy effective field theory from type II string theory
• FCNC-free multi-Higgs-doublet models from broken family symmetries
• Flavor structure in $SO(32)$ heterotic string theory
• $\mu -\tau$ Reflection Symmetry and Its Explicit Breaking for Leptogenesis in a Minimal Seesaw Model
• Reducing θ_13 to 9 degrees
• Predicting neutrino oscillations with "bi-large" lepton mixing matrices
• Anomaly of non-Abelian discrete symmetries
• Radiative Corrections to the Solar Lepton Mixing Sum Rule
• Perturbative Bottom-up Approach for Neutrino Mass Matrix in Light of Large θ_{13} and Role of Lightest Neutrino Mass
• Exploring the flavor structure of quarks and leptons with reinforcement learning
• A modified Friedberg-Lee symmetry for the TM1 neutrino mixing
• Cosmological Consequences of Domain Walls Biased by Quantum Gravity
• Linear seesaw model with a modular $S_4$ flavor symmetry
• The role of flavon cross couplings in leptonic flavour mixing
• Hierarchy spectrum of SM fermions: from top quark to electron neutrino
• Clockwork origin of neutrino mixings
• Leptonic CP Violation from a New Perspective
• Stability and symmetry breaking in a three Higgs-boson doublet model with lepton family symmetry O(2)xZ2
• Neutrino non-standard interactions as a portal to test flavour symmetries
• Renormalization group evolution induced leptogenesis in the minimal seesaw model with the trimaximal mixing and mu-tau reflection symmetry
• Modular symmetry anomaly and non-perturbative neutrino mass terms in magnetized orbifold models
• Neutrino Mass Sum Rules and Symmetries of the Mass Matrix
• Revisiting the Dirac Nature of Neutrinos in the Light of $\Delta (27)$ and Cyclic Symmetries
• Low-scale leptogenesis with flavour and CP symmetries
• Data Driven Flavour Model
• Revisiting Discrete Dark Matter Model:θ_{13}\neq0 and ν_{R} Dark Matter
• Compatible abelian symmetries in N-Higgs-Doublet Models
• Lepton Mixing, Residual Symmetries, and Trigonometric Diophantine Equations
• Froggatt-Nielsen models with a residual Z_4^R symmetry
• Checking Flavour Models at Neutrino Facilities
• Higgs portal dark matter and neutrino mass and mixing with a doubly charged scalar
• Testable constraint on near-tribimaximal neutrino mixing
• Leptons and Quarks from a Discrete Flavor Symmetry
• CP and other Symmetries of Symmetries
• A Realistic Neutrino mixing scheme arising from $A_4$ symmetry
• A minimal inverse seesaw model with $S_4$ flavour symmetry
• Predictive neutrino mass textures with origin of flavor symmetries
• Predictions of $m_{ee}$ and neutrino mass from a consistent Froggatt-Nielsen model
• Neutrino mixing sum rules and the Littlest Seesaw
• Predicting ${\delta }^{\text{PMNS}}$, ${\theta }_{23}^{\text{PMNS}}$ and fermion mass ratios from flavour GUTs with CSD2
• Consequences of $\mu$-$\tau$ reflection symmetry for $3+1$ neutrino mixing
• High scale mixing relations as a natural explanation for large neutrino mixing
• Neutrino Phenomenology and Dark matter in an $A_4$ flavour extended B-L model
• Mass hierarchy from the flavor symmetry in supersymmetric multi-Higgs doublet model
• Relativistic Impulse Approximation in the Atomic Ionization Process induced by Millicharged Particles
• Simiplified textures of the seesaw model for the trimaximal neutrino mixings
• Stable lepton mass matrices
• A close look on 2-3 mixing angle with DUNE in light of current neutrino oscillation data
• Representing seesaw neutrino models and their motion in lepton flavour space
• Fully constrained mass matrix: Can symmetries alone determine the flavon vacuum alignments?
• Trimaximal Mixing and Extended Magic Symmetry in a Model of Neutrino Mass Matrix
• Phenomenology of extended multiHiggs doublet models with $S_4$ family symmetry
• Leptogenesis and $CP$ violation in $SU(5)$ models with lepton flavor mixing originating from the right-handed sector
• A hybrid seesaw model and hierarchical neutrino flavor structures based on $A_4$ symmetry
• Radiative Origin of Fermion Mass Hierarchy in Left-Right Symmetric Theory
• Radiative Generation of Non-zero ${\theta }_{13}$ in MSSM with broken $A_4$ Flavor Symmetry
• Five texture zeros in the lepton sector and neutrino oscillations at DUNE
• Minimal eclectic flavor group $Q_8⋊S_3$ and neutrino mixing
• Model independent Analysis of Dirac CP Violating Phase for some well known mixing scenarios
• On the textures of neutrino mass matrix for maximal atmospheric mixing angle and Dirac CP phase
• Type II seesaw supersymmetric neutrino model for ${\theta }_{13}\ne 0$
• Confronting Tri-direct CP-symmetry models to neutrino oscillation experiments
• Viability of $A_4$, $S_4$ and $A_5$ Flavour Symmetries in Light of the First JUNO Result
• Pocket Formulae for Non-Abelian Discrete Anomaly Freedom
• Constraining $A_4$ Leptonic Flavour Model Parameters at Colliders and Beyond
• Lepton-flavour violation in a Pati-Salam model with gauged flavour symmetry
• Flavored Leptogenesis and Neutrino Mass with $A_4$ Symmetry
• Further study on the textures of neutrino mass matrix for maximal atmospherical mixing angle and Dirac CP phase
• Neutrino mass from M Theory SO(10)
• No-go limitations on UV completions of the Neutrino Option
• Reconstructing Effective Lagrangians Embedding Residual Family Symmetries
• Identifying a minimal flavor symmetry of the seesaw mechanism behind neutrino oscillations
• Neutrino masses and mixing angles in a model with six Higgs triplets and $A_4$ symmetry
• Non-zero ${\theta }_{13}$, CP-violation and Neutrinoless Double Beta Decay for Neutrino Mixing in the $A_4\times Z_2\times Z_3$ Flavor Symmetry Model
• Ameliorating the popular lepton mixings with A4 symmetry: A see-saw model for realistic neutrino masses and mixing
• Theory Review of Neutrino Models and CP Violation
• Predictions for the Leptonic Dirac CP-Violating Phase
• Fractionalized time reversal, parity and charge conjugation symmetry in topological superconductor: a possible origin of three generations of neutrinos and mass mixing
• Proton decay and $\mu \to e+\gamma$ Connection in a Renormalizable SO(10) GUT for Neutrinos
• Study of a tri-direct littlest seesaw model at MOMENT
• Pseudo-Dirac neutrinos from flavour dependent CP symmetry
• On neutrino and charged lepton masses and mixings: A view from the electroweak-scale right-handed neutrino model
• Testing constrained sequential dominance models of neutrinos
• Lepton Mixing Predictions from (Generalised) CP and Discrete Flavour Symmetry
• Spontaneously stabilised dark matter from a fermiophobic $U(1{)}^{\prime }$ gauge symmetry
• A translational flavor symmetry in the mass terms of Dirac and Majorana fermions
• Neutrino Mass Matrices from Two Zero 3x2 Yukawa Textures and Minimal d=5 Entries
• Lepton and Quark Masses and Mixing in a SUSY Model with Delta(384) and CP
• Combining Pati-Salam and Flavour Symmetries
• Planck Scale Origin of Non-zero ${\theta }_{13}$ and Super-WIMP Dark Matter
• Neutrino Physics Now and in the Near Future
• Next-to-tribimaximal mixing against CP violation and baryon asymmetry signs
• Unification of gauge, family, and flavor symmetries illustrated in gauged SU(12) models
• The translational $\mu$-$\tau$ reflection symmetry of Majorana neutrinos
• On Building superpotentials in F- GUTs
• An extended 3-3-1 model with two scalar triplets and linear seesaw mechanism
• Quasi-degenerate Neutrino mass models and their significance: A model independent investigation
• Non-Abelian Domain Walls and Gravitational Waves
• Low scale leptogenesis under neutrino $\mu$-$\tau$ reflection symmetry
• Modulated bimaximal neutrino mixing
• Coxeter groups and the PMNS matrix
• Non-maximal θ_{23}, large θ_{13} and tri-bimaximal θ_{12} via quark-lepton complementarity at next-to-leading order
• SUSY SU(5) $\times S_4$ GUT Flavor Model for Fermion Masses and Mixings with Adjoint, Large ${\theta }_{13}^{PMNS}$
• Unveiling Neutrino Mysteries with $\Delta (27)$ Symmetry
• Revisiting the Universal Texture Zero of Flavour: a Markov Chain Monte Carlo Analysis
• A Systematic Analysis of Perturbations for Hexagonal Mixing Matrix
• Novel Flavon Stabilization with Trimaximal Neutrino Mixing
• Majorana phases in high-scale mixings unification hypotheses
• Masses and Mixing of Neutral Leptons in a Grand Unified E_6 Model with Intermediate Pati-Salam Symmetry
• Leptogenesis, Fermion Masses and Mixings in a SUSY $SU(5)$ GUT with $D_4$ Flavor Symmetry
• A non-renormalizable neutrino mass model with ${\mathbf{S}}_3\otimes {\mathbf{Z}}_2$ symmetry
• MSSM-like from $S{U}_5\times D_4$ Models
• Improving heavy Dirac neutrino prospects at future hadron colliders using machine learning
• Flavor symmetric origin of texture zeros in minimal inverse seesaw and impacts on leptogenesis
• A split seesaw model with hidden neutrinoless double beta decay but successful leptogenesis
• Generalized Matter Parities from Finite Modular Symmetries
• Connecting dark matter, baryogenesis and neutrinoless double beta decay in a $A_4\otimes Z_8$ based $\nu$2HDM
• The problem of flavour
• Fermion Masses and Mixing in Pati-Salam Unification with $S_3$ Modular Symmetry
• Phenomenological implications of a minimal F-theory GUT with discrete symmetry
• Residual Symmetries and Scalar Multiplet Vacuum Alignment in Non-Abelian Flavour Models
• A new texture of neutrino mass matrix with three constraints
• Particular textures of the minimal seesaw model
• A Radiative Model of Quark Masses with Binary Tetrahedral Symmetry
• A neutrino mixing model based on an $A_4\times Z_3\times Z_4$ flavour symmetry
• Minimal lepton flavour structures lead to non-maximal 2-3 mixing
• Neutrinos Meet Supersymmetry: Quantum Aspects of of Neutrinophysics in Supersymmetric Theories
• Resonant leptogenesis in inverse see-saw framework with modular $S_4$ symmetry
• The Minimal Flavor Structure from Decomposition of the Fermion Mass Matrix
• Flavour anomalies meet flavour symmetry
• A mechanism relating the fermionic mass hierarchy to the flavor mixing
• Gauge-flavon unification
• Neutrino mass generation from the perspective of presymmetry
• Soft breaking of the $\mu \leftrightarrow \tau$ symmetry by ${\mathbf{S}}_4\otimes {\mathbf{Z}}_2$
• Discrete Flavour Symmetries from the Heisenberg Group
• Predicting Neutrino Mixing Angles Using Group Presentations
• CP-like Symmetry with Discrete and Continuous Groups and CP Violation/Restoration
• Subcritical hybrid inflation in a generalized superconformal model
• A Unified Yukawa Interaction for the Standard Model of Quarks and Leptons
• The origin of discrete symmetries in F-theory models
• All one-loop scalar vertices in the effective potential approach
• The common origin of the family mass hierarchy and CP violation from flavour-dependent vacuum for quarks and leptons
• Computation of products of phase space factors and nuclear matrix elements for the Double Beta Decay
• Sum Rules for Leptons
• Deviations of exact neutrino textures using radiative neutrino masses
• The Neutrinos of the Neighboring Brane
• A universal form for quark and neutrino mass matrices
• Standard and Non-Standard Aspects of Neutrino Physics
• Modular flavored dark matter
• A lepton model with nearly Cobimaximal mixing
• Quark and lepton flavor model with leptoquarks in a modular $A_4$ symmetry
• Prediction of Neutrino Mixing based on $C_2\times D_3$
• Leptogenesis in the $\mu \tau$ basis
• Fermion masses and mixings and $g-2$ muon anomaly in a $Q_6$ flavored 2HDM
• Status and Perspectives of Neutrino Physics
• Scalar field dark matter with two components: combined approach from particle physics and cosmology
• $SO(10)$ models with $A_4$ modular symmetry
• Gauge extension of non-Abelian discrete flavor symmetry
• Aspects of Leptonic Flavour Mixing
• PSL(2,7) Representations and their relevance to Neutrino Physics
• Neutrino mass, mixing and discrete symmetries
• Muon $g-2$, dark matter, and neutrino mass explanations in a modular $A_4$ symmetry
• Breaking of the tetra-maximal neutrino mixing pattern
• ${\text{TM}}_1$ neutrino mixing with $\sin {\theta }_{13}=\frac{1}{\sqrt{3}}\sin \frac{\pi }{12}$
• Light neutrino masses from gravitational condensation: the Schwinger-Dyson approach
• On Bimaximal Neutrino Mixing and GUT's
• A comparative study between the modified Fritzsch and nearest neighbor interaction textures
• The Strong CP Problem and Discrete Symmetries
• Leptogenesis via Varying Weinberg Operator: the Closed-Time-Path Approach
• Lepton mixing patterns from $PS{L}_2(7)$ with a generalised CP symmetry
• Rescuing leptogenesis in inverse seesaw models with the help of non-Abelian flavor symmetries
• $TeV$-Scale Resonant Leptogenesis $A_4$ with a scaling texture
• Connecting Tribimaximal and Bitrimaximal Mixings
• $TeV$-Scale Resonant Leptogenesis with New Scaling Ansatz on Neutrino Dirac Mass Matrix from $A_4$ Flavor Symmetry
• Radiative Corrections as Origin of Tiny Fermion Masses
• Scalar and gauge sectors in the 3-Higgs Doublet Model under the S3-symmetry
• Neutrino Oscillations in the Three Flavor Paradigm
• Fermion masses and mixings and charged lepton flavor violation in a 3-3-1 model with inverse seesaw
• Neutrino flavor mixing with approximate $\mu$-$\tau$ symmetry within the low-scale minimal linear seesaw model
• Tri-bimaximal-Cabibbo Mixing: Flavour violations in the charged lepton sector
• CKM matrix and flavor symmetries
• Non-SUSY Lepton Flavor Model with 3HDM
• $A_4$ flavor symmetric model in SUSY SU(5) GUT
• A discrete anatomy of the neutrino mass matrix
• Flavour Symmetry Embedded -- GLoBES (FaSE-GLoBES)
• Neutrino Masses and Mixings from Continuous Symmetries
• Exploring the flavor structure of leptons via diffusion models
• New partial symmetries from group algebras for lepton mixing
• Theory and phenomenology of Dirac neutrinos
• Diffusion-model approach to flavor models: A case study for $S_4^{\prime }$ modular flavor model
• Exploring mixed lepton-quark interactions in non-resonant leptoquark production at the LHC
• Flavor Moonshine
• Yukawa textures in modular symmetric vacuum of magnetized orbifold models
• Revisiting Flavor Model and Leptogenesis
• Cosmic Collider Gravitational Waves sourced by Right-handed Neutrino production from Bubbles: Testing Seesaw, Leptogenesis and Dark Matter