Non-Abelian Discrete Symmetries in Particle Physics

Abstract

We review pedagogically non-Abelian discrete groups, which play an important role in the particle physics. We show group-theoretical aspects for many concrete groups, such as representations, their tensor products. We explain how to derive, conjugacy classes, characters, representations, and tensor products for these groups (with a finite number). We discussed them explicitly for $S_N$, $A_N$, $T^{\prime }$, $D_N$, $Q_N$, $\Sigma (2N^2)$, $\Delta (3N^2)$, $T_7$, $\Sigma (3N^3)$ and $\Delta (6N^2)$, which have been applied for model building in the particle physics. We also present typical flavor models by using $A_4$, $S_4$, and $\Delta (54)$ groups. Breaking patterns of discrete groups and decompositions of multiplets are important for applications of the non-Abelian discrete symmetry. We discuss these breaking patterns of the non-Abelian discrete group, which are a powerful tool for model buildings. We also review briefly about anomalies of non-Abelian discrete symmetries by using the path integral approach.

179 pages, 8 figures, section 15 is changed, some references are added

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• Assessing the Viability of $A_4$, $S_4$ and $A_5$ Flavour Symmetries for Description of Neutrino Mixing
• Broken S_3 Flavor Symmetry of Leptons and Quarks: Mass Spectra and Flavor Mixing Patterns
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• Repressing Anarchy in Neutrino Mass Textures
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• Testing atmospheric mixing sum rules at precision neutrino facilities
• The eclectic flavor symmetry of the ${\mathbb{Z}}_2$ orbifold
• Principal series of finite subgroups of SU(3)
• The minimal seesaw and leptogenesis models
• Non-zero θ_{13} linking to Dark Matter from Non-Abelian Discrete Flavor Model in Radiative Seesaw
• Relating quarks and leptons with the T7 flavour group
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• $A_4$ symmetry at colliders and in the universe
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• Mixing Patterns from the Groups Sigma (n phi)
• Neutrino Mixings and the S4 Discrete Flavour Symmetry
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• Modular symmetry anomaly in magnetic flux compactification
• Lepton and Quark Mixing Patterns from Finite Flavor Symmetries
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• The $\Delta (27)$ flavor 3-3-1 model with neutral leptons
• Lepton Flavor Mixing and CP Symmetry
• The D_4 flavor symmery in 3-3-1 model with neutral leptons
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• Hybrid Textures of Majorana Neutrino Mass Matrix and Current Experimental Tests
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• On the finite subgroups of U(3) of order smaller than 512
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• Adjoint SU(5) GUT model with Modular $S_4$ Symmetry
• Neutrino mass textures with one vanishing minor and two equal cofactors
• Modular symmetry in the SMEFT
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• SUSY SU(5) with singlet plus adjoint matter and A4 family symmetry
• Generalized CP and $\Delta (3n^2)$ Family Symmetry for Semi-Direct Predictions of the PMNS Matrix
• Modular symmetry at level 6 and a new route towards finite modular groups
• Quasi-Eclectic Modular Flavor Symmetries
• Discrete symmetries for electroweak natural type-I seesaw mechanism
• Charting the flavor landscape of MSSM-like Abelian heterotic orbifolds
• Origin of family symmetries
• Invariant approach to CP in unbroken $\Delta (27)$
• Quark and Lepton Mixing Patterns from a Common Discrete Flavor Symmetry with Generalized CP
• Predicting CP violation in Deviation from Tri-bimaximal mixing of Neutrinos
• CP4 miracle: shaping Yukawa sector with CP symmetry of order four
• A Model for Tri-bimaximal Mixing from a Completely Broken $A_4$
• Lepton Mixing Predictions from Infinite Group Series $D_{9n,3n}^{(1)}$ with Generalized CP
• Quark and lepton hierarchies from $S_4^{\prime }$ modular flavor symmetry
• The symmetry approach to quark and lepton masses and mixing
• An $S_3$ Model for Lepton Mass Matrices with Nearly Minimal Texture
• Comments on the classification of the finite subgroups of SU(3)
• Predicting theta_13 and the Neutrino Mass Scale from Quark Lepton Mass Hierarchies
• Neutrino Masses and Hubble Tension via a Majoron in MFV
• A Unified Model of Quarks and Leptons with a Universal Texture Zero
• Discrete symmetries and models of flavor mixing
• Non-Minimal Flavored ${\mathbf{S}}_3\otimes {\mathbf{Z}}_2$ Left-Right Symmetric Model
• A 3-3-1 model with low scale seesaw mechanisms
• Proton Hexality in Local Grand Unification
• The Double Cover of the Icosahedral Symmetry Group and Quark Mass Textures
• Broken $S_3$ Symmetry in the Neutrino Mass Matrix
• B-L Model with ${\mathbf{S}}_3$ Symmetry: Nearest Neighbor Interaction Textures and Broken $\mu \leftrightarrow \tau$ Symmetry
• An $S_4\times SU(5)$ SUSY GUT of flavour in 6d
• $\mathcal{C}\mathcal{P}$ Violation from String Theory
• Lepton Mixing in $A_5$ Family Symmetry and Generalized CP
• Tri-Bimaximal Neutrino Mixing and the $T_{13}$ Flavor Symmetry
• Neutrino predictions from a left-right symmetric flavored extension of the standard model
• Neutrino Mixing and Leptonic CP Violation from $S_4$ Flavour and Generalised CP Symmetries
• Probing Lepton Flavor Triality with Higgs Boson Decay
• Quark hierarchical structures in modular symmetric flavor models at level 6
• Modulus $\tau$ linking leptonic CP violation to baryon asymmetry in $A_4$ modular invariant flavor model
• Trimaximal mixing with a texture zero
• Phenomenology in the Zee Model with the A_4 Symmetry
• Non-Abelian discrete R symmetries
• Radiative Seesaw-type Mechanism of Fermion Masses and Non-trivial Quark Mixing
• Neutrinoless Double Beta Decay in Type I+II Seesaw Models
• Top-Down Anatomy of Flavor Symmetry Breakdown
• Quark and lepton flavors with common modulus $\tau$ in $A_4$ modular symmetry
• Non-invertible flavor symmetries in magnetized extra dimensions
• Horizontal symmetries of leptons with a massless neutrino
• Baryon Number, Lepton Number, and Operator Dimension in the SMEFT with Flavor Symmetries
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• Fermion masses and mixings and some phenomenological aspects of a 3-3-1 model with linear seesaw mechanism
• Novel signatures of the Higgs sector from S3 flavor symmetry
• Quark mass hierarchies and CP violation in $A_4\times A_4\times A_4$ modular symmetric flavor models
• SU(3) Gauge Family Symmetry and Prediction for the Lepton-Flavor Mixing and Neutrino Masses with Maximal Spontaneous CP Violation
• Implications of residual CP symmetry for leptogenesis in a model with two right-handed neutrinos
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• Littlest Inverse Seesaw Model
• D14 - A Common Origin of the Cabibbo Angle and the Lepton Mixing Angle theta^l_13
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• A novel Randall-Sundrum model with $S_3$ flavor symmetry
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• Explicit Perturbations to the Stabilizer $\tau =\mathrm{i}$ of Modular $A_5^{\prime }$ Symmetry and Leptonic CP Violation
• Schizophrenic active neutrinos and exotic sterile neutrinos
• Common Origin of Non-zero ${\theta }_{13}$ and Baryon Asymmetry of the Universe in a TeV scale Seesaw Model with $A_4$ Flavour Symmetry
• Neutrino Mixing and Discrete Symmetries
• "Heterotic" Discrete Flavor Model
• Classification of Abelian domain walls
• Perturbations to $\mu -\tau$ Symmetry, Leptogenesis and Lepton Flavour Violation with Type II Seesaw
• Flavour and CP predictions from orbifold compactification
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• Searches for lepton-flavour-violating decays of the Higgs boson into $e\tau$ and $\mu \tau$ in $\sqrt{s}=13$ TeV $pp$ collisions with the ATLAS detector
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• The double mass hierarchy pattern: simultaneously understanding quark and lepton mixing
• Littlest Seesaw model from S4 x U(1)
• Natural Flavour Conservation in a three Higg-doublet Model
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• A left-right symmetric flavor symmetry model
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• Search for the lepton-flavor violating decay of the Higgs boson and additional Higgs bosons in the e$\mu$ final state in proton-proton collisions at $\sqrt{s}$ = 13 TeV
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• Probing flavor models with Ge-76-based experiments on neutrinoless double-beta decay
• Phenomenological study of neutrino mass, dark matter and baryogenesis within the framework of minimal extended seesaw
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• Lepton masses and mixing in a two-Higgs-doublet model
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• An A_5 Model of Four Lepton Generations
• Quark mixing in an $S_3$ symmetric model with two Higgs doublets
• Revisiting $A_4$ model for leptons in light of NuFIT 3.2
• Admixture of quasi-Dirac and Majorana neutrinos with tri-bimaximal mixing
• Intrinsic Deviation from the Tri-bimaximal Neutrino Mixing in a Class of A_4 Flavor Models
• Models of Neutrino Mass, Mixing and CP Violation
• Renormalisation Group Corrections to Neutrino Mixing Sum Rules
• Semidirect Product Groups, Vacuum Alignment and Tribimaximal Neutrino Mixing
• Neutrino masses and mixing in $A_5$ with flavour antisymmetry
• Model of flavor with quaternion symmetry
• Lepton mass textures from non-invertible multiplication rules
• From Flavour to SUSY Flavour Models
• A study on a minimally broken residual TBM-Klein symmetry with its implications on flavoured leptogenesis and ultra high energy neutrino flux ratios
• Texture zeros of quark mass matrices at fixed point $\tau =\omega$ in modular flavor symmetry
• Neutrino CP violation and sign of baryon asymmetry in the minimal seesaw model
• Exploring Partial $\mu$-$\tau$ Reflection Symmetry at DUNE and Hyper-Kamiokande
• Relating large $U_{e3}$ to the ratio of neutrino mass-squared differences
• Common origin of ${\theta }_{13}$ and dark matter within the flavor symmetric scoto-seesaw framework
• Constraining Type I Seesaw with $A_4$ Flavor Symmetry From Neutrino Data and Leptogenesis
• Theory of Neutrino Masses and Mixing
• Lepton flavor violating $Z$-boson couplings from non-standard Higgs interactions
• Collapsing domain walls beyond $Z_2$
• A Model for Large theta13 Constructed using the Eigenvectors of the S4 Rotation Matrices
• CP Symmetries as Guiding Posts: Revamping Tri-Bi-Maximal Mixing-I
• Neutrino mass textures from F-theory
• Perturbing exactly tri-bimaximal neutrino mixings with charged lepton mass matrices
• When $\tan \beta$ meets all the mixing angles
• A low-scale flavon model with a $Z_N$ symmetry
• Generalised $\mu$-$\tau$ symmetries and calculable gauge kinetic and mass mixing in $U(1{)}_{L_{\mu }-L_{\tau }}$ models
• $\Delta \left(27\right)$ flavor singlet-triplet Higgs model for fermion masses and mixings
• Tri-Direct CP in the Littlest Seesaw Playground
• A model of quarks with Delta (6N^2) family symmetry
• Neutrino Predictions from Generalized CP Symmetries of Charged Leptons
• Consequences of minimal seesaw with complex $\mu \tau$ antisymmetry of neutrinos
• On ${\mathbf{Q}}_6$ flavor symmetry and the breaking of $\mu \leftrightarrow \tau$ symmetry
• Majorana neutrino mass structure induced by rigid instatons on toroidal orbifold
• Spontaneous CP violation in multi-Higgs potentials with triplets of $\Delta (3n^2)$ and $\Delta (6n^2)$
• Leptonic Sum Rules from Flavour Models with Modular Symmetries
• Predicting Leptonic CP phase by considering deviations in charged lepton and neutrino sectors
• Golden Littlest Seesaw
• Finite modular axion and radiative moduli stabilization
• Scotogenic Dirac neutrino mass models embedded with leptoquarks: one pathway to address the flavor anomalies and the neutrino masses together
• Non-zero ${\theta }_{13}$ with Unbroken $\mu -\tau$ Symmetry of the Active Neutrino Mass Matrix in the Presence of a Light Sterile Neutrino
• Quasidegeneracy of Majorana Neutrinos and the Origin of Large Leptonic Mixing
• Testing Lepton Flavor Models at ESSnuSB
• Neutrinoless double beta decay and lepton flavour violation in broken $\mu -\tau$ symmetric neutrino mass models
• Predictive Leptogenesis from Minimal Lepton Flavour Violation
• Spontaneous Breaking of Gauge Groups to Discrete Symmetries
• Electron EDM arising from modulus $\tau$ in the supersymmetric modular invariant flavor models
• Soft supersymmetry breaking terms and lepton flavor violations in modular flavor models
• Twenty years after the discovery of $\mu -\tau$ symmetry
• S_4 x Z_2 Flavor Symmetry in Supersymmetric Extra U(1) Model
• Probing Lepton Flavor Models at Future Neutrino Experiments
• Collider signatures of vector-like fermions from a flavor symmetric model
• Tribimaximal Mixing in the $SU(5)\times {\mathcal{T}}_{13}$ Texture
• Minimal inverse-seesaw mechanism with Abelian flavour symmetries
• Non-Abelian Discrete Flavor Symmetries on Orbifolds
• Cutting the Scotogenic loop: Adding flavor to Dark Matter
• Phenomenology of keV scale sterile neutrino dark matter with $S_4$ flavor symmetry
• Flavor Symmetry Based MSSM (sMSSM): Theoretical Models and Phenomenological Analysis
• Low scale type I seesaw model for lepton masses and mixings
• 4D modular flavor symmetric models inspired by higher dimensional theory
• Muon anomalies and the $SU(5)$ Yukawa relations
• Neutrino masses, the $\mu$-term and ${\mathcal{P}\mathcal{SL}}_2(7)$
• A model for Neutrino Masses and Dark Matter with the Discrete Gauge Symmetry
• Lepton mass matrix from double covering of $A_4$ modular flavor symmetry
• Quasi-Dirac neutrinos in a model with local $B-L$ symmetry
• Breaking classical Lie groups to finite subgroups - an automated approach
• Constraining Lepton Flavor Violating Higgs Couplings at the HL-LHC in the Vector Boson Fusion Channel
• Flavoured leptogenesis and ${\mathrm{CP}}^{\mu \tau }$ symmetry
• Integral solutions to the one-loop renormalization-group equations for lepton flavor mixing parameters and the Jarlskog invariant
• Higgs boson decays with lepton flavor violation in the $B-L$ symmetric SSM
• CP transformed mixed $\mu \tau$ antisymmetry for neutrinos and its consequences
• Renormalization Group Evolution of Neutrino Parameters in Presence of Seesaw Threshold Effects and Majorana Phases
• Minimal Neutrino Texture with Neutrino Mass Ratio and Cabibbo Angle
• Consistency of perturbed Tribimaximal, Bimaximal and Democratic mixing with Neutrino mixing data
• The CKM matrix with maximal CP violation from Z(12) symmetry
• On the characterization of the SU(3)-subgroups of type C and D
• Lepton and Quark Mixing from Stepwise Breaking of Flavor and CP
• Flavour and CP symmetries in the inverse seesaw
• Renormalisation Group Corrections to the Littlest Seesaw Model and Maximal Atmospheric Mixing
• Texture zeros of low-energy Majorana neutrino mass matrix in 3+1 scheme
• Revisiting Leptogenesis in a SUSY SU(5) x T' Model of Flavour
• Flavored axion in the UV-complete Froggatt-Nielsen models
• New Interpretation of the Recent Result of AMS-02 and Multi-component Decaying Dark Matters with non-Abelian Discrete Flavor Symmetry
• Flavor structure in D-brane models: Majorana neutrino masses
• Towards Minimal S4 Lepton Flavor Model
• Moduli trapping mechanism in modular flavor symmetric models
• Viability of exact tri-bimaximal, golden-ratio and bimaximal mixing patterns and renormalization-group running effects
• Impact of RGE-induced $\mu -\tau$ Reflection Symmetry Breaking on the Effective Majorana Neutrino Mass in $0\nu \beta \beta$ Decay
• Neutrino masses and mixing from flavour antisymmetry
• Complex $S_3$-symmetric 3HDM
• Realization of the minimal extended seesaw mechanism and the $T{M}_2$ type neutrino mixing
• Residual $Z_2$ symmetries and leptonic mixing patterns from finite discrete subgroups of $U(3)$
• Fermion masses and mixings and $g-2$ muon anomaly in a 3-3-1 model with $D_4$ family symmetry
• Controlled fermion mixing and FCNCs in a $\Delta (27)$ 3+1 Higgs Doublet Model
• Common Origin of Non-zero ${\theta }_{13}$ and Dark Matter in an $S_4$ Flavour Symmetric Model with Inverse Seesaw
• Implications of Fermionic Dark Matter on recent neutrino oscillation data
• Neutrino masses and lepton mixing from $A_5\times \mathrm{CP}$
• Remark on modular weights in low-energy effective field theory from type II string theory
• Deviations in Tribimaximal Mixing From Sterile Neutrino Sector
• Target Space Duality of Non-Supersymmetric String Theory
• GAP listing of the finite subgroups of U(3) of order smaller than 2000
• A Further Study of the Frampton-Glashow-Yanagida Model for Neutrino Masses, Flavor Mixing and Baryon Number Asymmetry
• $\mu -\tau$ Reflection Symmetry and Its Explicit Breaking for Leptogenesis in a Minimal Seesaw Model
• Importance of generalized $\mu \tau$ symmetry and its CP extension on neutrino mixing and leptogenesis
• Effective Theories of Flavor and the Non-Universal MSSM
• Flavour effects in gravitational leptogenesis
• Highly predictive and testable $A_4$ flavor model within type-I and II seesaw framework and associated phenomenology
• Mass Limit for Light Flavon with Residual $Z_3$ Symmetry
• Flavor structure in $SO(32)$ heterotic string theory
• Low energy phenomena of the lepton sector in an $A_4$ symmetry model with heavy inverse seesaw neutrinos
• Direct and Indirect Detection of Dark Matter in D6 Flavor Symmetric Model
• Bounded-from-below conditions for $A_4$-symmetric 3HDM
• $B-L$ model with $A_4\times Z_3\times Z_4$ symmetry for $3+1$ active$-$sterile neutrino mixing
• Reducing θ_13 to 9 degrees
• Perturbative Bottom-up Approach for Neutrino Mass Matrix in Light of Large θ_{13} and Role of Lightest Neutrino Mass
• Finite quantum corrections to the tribimaximal neutrino mixing
• Exploring the flavor structure of quarks and leptons with reinforcement learning
• Effect of Degenerate Particles on Internal Bremsstrahlung of Majorana Dark Matter
• New approach to neutrino masses and leptogenesis with Occam's razor
• Anomaly of non-Abelian discrete symmetries
• Linear seesaw model with a modular $S_4$ flavor symmetry
• Search for lepton-flavour-violating decays of Higgs-like bosons
• Anomalous Discrete Flavor Symmetry and Domain Wall Problem
• Predicting neutrino oscillations with "bi-large" lepton mixing matrices
• Cosmological Consequences of Domain Walls Biased by Quantum Gravity
• Measuring Oscillations with A Million Atmospheric Neutrinos
• $A_4$-based model with linear seesaw scheme for lepton mass and mixing
• R-parity from string compactification
• Lepton flavor violation by two units
• An explicit SU(12) family and flavor unification model with natural fermion masses and mixings
• Seesaw mirroring between light and heavy Majorana neutrinos with the help of the $S_3^{}$ reflection symmetry
• Revisiting the Dirac Nature of Neutrinos in the Light of $\Delta (27)$ and Cyclic Symmetries
• Modular symmetry anomaly and non-perturbative neutrino mass terms in magnetized orbifold models
• Supersymmetric models on magnetized orbifolds with flux-induced Fayet-Iliopoulos terms
• Simple Theory of Chiral Fermion Dark Matter
• Non-linearly realized discrete symmetries
• Hierarchy spectrum of SM fermions: from top quark to electron neutrino
• $A_4\times U(1{)}_{PQ}$ Model for the Lepton Flavor Structure and the Strong $CP$ Problem
• Like-sign dimuon asymmetry of B0 meson and LFV in SU(5) SUSY GUT with S4 flavor symmetry
• Copositivity for a class of fourth order symmetric tensors given by scalar dark matter
• Deviation from Tribimaximal mixing using $A_4$ flavour model with five extra scalars
• Prediction of $h\to \gamma Z$ from $h\to \gamma \gamma$ at LHC for the IMDS${}_3$ Model
• Flavon Stabilization in Models with Discrete Flavor Symmetry
• Phenomenology of two texture zero neutrino mass in left-right symmetric model with $Z_8\times Z_2$
• Squark flavor mixing and CP asymmetry of neutral $B$ mesons at LHCb
• Hierarchical majorana neutrinos from democratic mass matrices
• Classical and Quantum Discrete Dynamical Systems
• Minimally modified $A_4$ Altarelli-Feruglio model for neutrino masses and mixings and its experimental consequences
• CP and other Symmetries of Symmetries
• Discrete symmetries and Efficient Counting of Operators
• Higgs portal dark matter and neutrino mass and mixing with a doubly charged scalar
• Consequences of $\mu$-$\tau$ reflection symmetry for $3+1$ neutrino mixing
• Taub-NUT Crystal
• Z_4 flavor model in Randall-Sundrum model 1
• Predictions of $m_{ee}$ and neutrino mass from a consistent Froggatt-Nielsen model
• Compatible abelian symmetries in N-Higgs-Doublet Models
• Revisiting Discrete Dark Matter Model:θ_{13}\neq0 and ν_{R} Dark Matter
• Low-scale leptogenesis with flavour and CP symmetries
• Checking Flavour Models at Neutrino Facilities
• Relating the Cabibbo angle to $\tan \beta$ in a two Higgs-doublet model
• Froggatt-Nielsen models with a residual Z_4^R symmetry
• Lepton Mixing, Residual Symmetries, and Trigonometric Diophantine Equations
• Predictive neutrino mass textures with origin of flavor symmetries
• Neutrino masses and mixing in Minimal Inverse Seesaw using $A_4$ modular symmetry
• Phenomenology of S_4 Flavor Symmetric extra U(1) model
• Geometrical Model for Non-Zero theta_13
• The centers of discrete groups as stabilizers of Dark Matter
• The Higgs decay rate to two photons in a model with two fermiophobic-Higgs doublets
• Data Driven Flavour Model
• Neutrino phenomenology in a left-right $D_4$ symmetric model
• Hierarchical structure of physical Yukawa couplings from matter field Kähler metric
• Phenomenological implications of the Friedberg-Lee transformation in a neutrino mass model with $\mu \tau$-flavored CP symmetry
• Phenomenology of extended multiHiggs doublet models with $S_4$ family symmetry
• Stable lepton mass matrices
• Flavor origin of R-parity
• Mass hierarchy from the flavor symmetry in supersymmetric multi-Higgs doublet model
• CP violations in a predictive $A_4$ symmetry model
• On the lepton CP violation in a $\nu$2HDM with flavor
• Symmetries for the 4HDM: extensions of cyclic groups
• High scale mixing relations as a natural explanation for large neutrino mixing
• Symmetryless Dark Matter
• $\mathcal{C}\mathcal{P}$ violation with an unbroken $\mathcal{C}\mathcal{P}$ transformation
• Simiplified textures of the seesaw model for the trimaximal neutrino mixings
• Lepton Private Higgs and the discrete group Σ(81)
• Trimaximal Mixing and Extended Magic Symmetry in a Model of Neutrino Mass Matrix
• Lepton masses and mixing in a scotogenic model
• Scotogenic majorana neutrino masses in a predictive orbifold theory of flavour
• Yukawa interactions, flavor symmetry, and non-canonical Kähler potential
• Relative scale separation in orbifolds of $S^2$ and $S^5$
• Phenomenology of an Extended $1+2$ Higgs Doublet Model with $S_3$ Family Symmetry
• Muon g-2 through a flavor structure on soft SUSY terms
• Cancellation Mechanism of FCNCs in S_4 x Z_2 Flavor Symmetric Extra U(1) Model
• Radiative Generation of Non-zero ${\theta }_{13}$ in MSSM with broken $A_4$ Flavor Symmetry
• Co-positivity of tensors and bounded from below conditions of CP conserving two-Higgs-doublet potential
• A hybrid seesaw model and hierarchical neutrino flavor structures based on $A_4$ symmetry
• Texture of Two Vanishing Subtraces in Neutrino Mass Matrix and Current Experimental Tests
• Discrete remnants of orbifolding
• Confronting Tri-direct CP-symmetry models to neutrino oscillation experiments
• 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
• Pocket Formulae for Non-Abelian Discrete Anomaly Freedom
• Viability of $A_4$, $S_4$ and $A_5$ Flavour Symmetries in Light of the First JUNO Result
• Type II seesaw supersymmetric neutrino model for ${\theta }_{13}\ne 0$
• Building SO${}_{10}$- models with ${\mathbb{D}}_4$ symmetry
• Neutrino mixing and Leptogenesis with modular $S_3$ symmetry in the framework of type III seesaw
• A modular $A_4$ symmetric Scotogenic model for Neutrino mass and Dark Matter
• Discrete Gauge Symmetry and Aharonov-Bohm Radiation in String Theory
• Broken $S_{3\mathrm{L}}^{}\times S_{3\mathrm{R}}^{}$ Flavor Symmetry and Leptonic CP Violation
• A Supersymmetric Grand Unified Model with Noncompact Horizontal Symmetry
• "Hidden" O(2) and SO(2) Symmetry in Lepton Mixing
• Binary Icosahedral Flavor Symmetry for Four Generations of Quarks and Leptons
• Parametrization of PMNS matrix based on dodeca-symmetry
• Introduction to Sporadic Groups
• Discrete Goldstone Bosons
• Testing the minimal $S_4$ model of neutrinos with the Dirac and Majorana phases
• Study of a tri-direct littlest seesaw model at MOMENT
• Light flavon signals at electron - photon colliders
• Theory Review of Neutrino Models and CP Violation
• Robustness of Neutrino Mass Matrix Predictions
• Ameliorating the popular lepton mixings with A4 symmetry: A see-saw model for realistic neutrino masses and mixing
• Froggatt-Nielsen Meets the SMEFT
• Systematic analysis of 3HDM symmetries
• Texture zeros and hierarchical masses from flavour (mis)alignment
• On neutrino and charged lepton masses and mixings: A view from the electroweak-scale right-handed neutrino model
• Seesaw mechanism in magnetic compactifications
• Lepton Mixing Predictions from (Generalised) CP and Discrete Flavour Symmetry
• Pseudo-Dirac neutrinos from flavour dependent CP symmetry
• Fermion mass and mixing pattern in a minimal T7 flavor 331 model
• Lepton masses and mixings, and muon anomalous magnetic moment in an extended $B-L$ model with type I seesaw mechanism
• Testing constrained sequential dominance models of neutrinos
• 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
• Analysis of right-handed Majorana neutrino mass in an $SU(4)\times SU(2{)}_L\times SU(2{)}_R$ Pati--Salam model with democratic texture
• Renormalization Group Running of Lepton Mixing Parameters in See-Saw Models with $S_4$ Flavor Symmetry
• Scotogenic dark matter in an orbifold theory of flavor
• Neutrino and Charged Lepton Flavour Today
• Two-zero textures based on $A_4$ symmetry and unimodular mixing matrix
• On fermion masses and mixing in a model with $A_4$ symmetry
• Hybrid seesaw neutrino model in SUSY $SU(5)\times {\mathbb{A}}_4$
• New Mixing Structures of Chiral Generations in a Model with Noncompact Horizontal Symmetry
• A translational flavor symmetry in the mass terms of Dirac and Majorana fermions
• The translational $\mu$-$\tau$ reflection symmetry of Majorana neutrinos
• Dirac Scoto Inverse-Seesaw from $A_4$ Flavor Symmetry
• An extended 3-3-1 model with two scalar triplets and linear seesaw mechanism
• One-loop Type II Seesaw Neutrino Model with Stable Dark Matter Candidates
• Searching exotic Higgs bosons at the LHC
• On flavor symmetries of phenomenologically viable string compactifications
• Planck Scale Origin of Non-zero ${\theta }_{13}$ and Super-WIMP Dark Matter
• Knotted strings and leptonic flavor structure
• On Building superpotentials in F- GUTs
• Two-Higgs-Doublet Models with a Flavored ${\mathbb{Z}}_2$
• A see-saw scenario of an $A_4$ flavour symmetric standard model
• Unification of gauge, family, and flavor symmetries illustrated in gauged SU(12) models
• Neutrino phenomenology and keV dark matter in 2HDM with $A_4$ symmetry
• SUSY SU(5) $\times S_4$ GUT Flavor Model for Fermion Masses and Mixings with Adjoint, Large ${\theta }_{13}^{PMNS}$
• Lepton and Quark Masses and Mixing in a SUSY Model with Delta(384) and CP
• A neutrino mixing model based on an $A_4\times Z_3\times Z_4$ flavour symmetry
• Phenomenological aspects of the fermion and scalar sectors of a $S_4$ flavored 3-3-1 model
• Continuous and Discrete Symmetries of Renormalization Group Equations for Neutrino Oscillations in Matter
• A non-renormalizable neutrino mass model with ${\mathbf{S}}_3\otimes {\mathbf{Z}}_2$ symmetry
• Deviation to the Tri-Bi-Maximal flavor pattern and equivalent classes
• Telling compositeness at a distance with outer automorphisms and CP
• Flavor symmetric origin of texture zeros in minimal inverse seesaw and impacts on leptogenesis
• Diluting quark flavor hierarchies using dihedral symmetry
• Revisiting the Universal Texture Zero of Flavour: a Markov Chain Monte Carlo Analysis
• Leptogenesis, Fermion Masses and Mixings in a SUSY $SU(5)$ GUT with $D_4$ Flavor Symmetry
• Flavor's Delight
• MSSM-like from $S{U}_5\times D_4$ Models
• Improving heavy Dirac neutrino prospects at future hadron colliders using machine learning
• A new texture of neutrino mass matrix with three constraints
• A Radiative Model of Quark Masses with Binary Tetrahedral Symmetry
• Residual Symmetries and Scalar Multiplet Vacuum Alignment in Non-Abelian Flavour Models
• Modular-symmetry-protected seesaw
• Generalized Matter Parities from Finite Modular Symmetries
• A Systematic Analysis of Perturbations for Hexagonal Mixing Matrix
• Connecting dark matter, baryogenesis and neutrinoless double beta decay in a $A_4\otimes Z_8$ based $\nu$2HDM
• Fermion Masses and Mixing in Pati-Salam Unification with $S_3$ Modular Symmetry
• Chasing after flavor symmetries of quarks from bottom up
• Novel Flavon Stabilization with Trimaximal Neutrino Mixing
• Phenomenological implications of a minimal F-theory GUT with discrete symmetry
• Subcritical hybrid inflation in a generalized superconformal model
• Anomaly-safe discrete groups
• Mathematical Modeling of Finite Quantum Systems
• Flavor Imprints on Novel Low Mass Dark Matter
• Soft breaking of the $\mu \leftrightarrow \tau$ symmetry by ${\mathbf{S}}_4\otimes {\mathbf{Z}}_2$
• Sum Rules for Leptons
• Flavour in $SU(5)$ Finite Grand Unified Models
• A bottom-up approach to fermion mass hierarchy: a case with vector-like fermions
• CP-like Symmetry with Discrete and Continuous Groups and CP Violation/Restoration
• Clebsch-Gordan coefficients of discrete groups in subgroup bases
• Flavored Peccei-Quinn symmetries in the minimal $\nu$DFSZ model
• The mass ratios parametrization
• Theoretical Results on Neutrinos
• The Seesaw Evaded Modular Dirac Framework
• Discrete Flavour Symmetries from the Heisenberg Group
• Flavour anomalies meet flavour symmetry
• Effects on sinθ_{12} from perturbation of the neutrino mixing matrix with the partially degenerated neutrino masses
• Leptogenesis in the $\mu \tau$ basis
• Quark and lepton flavor model with leptoquarks in a modular $A_4$ symmetry
• Neutrino mass, mixing and discrete symmetries
• Note about the implementation of finite symmetries in the lepton sector
• Double Froggatt--Nielsen Mechanism
• Standard and Non-Standard Aspects of Neutrino Physics
• An Explicit SU(12) Family and Flavor Unification Model
• Aspects of Leptonic Flavour Mixing
• Partial mass-degeneracy and spontaneous CP violation in the lepton sector
• PSL(2,7) Representations and their relevance to Neutrino Physics
• Minimal A4 Type-II Seesaw Realization of Testable Neutrino Mass Sum Rules
• Modular flavored dark matter
• Lepton mixing patterns from $PS{L}_2(7)$ with a generalised CP symmetry
• A comparative study between the modified Fritzsch and nearest neighbor interaction textures
• A Classification and Analysis of Higgs-flavor Models
• Gauge extension of non-Abelian discrete flavor symmetry
• ${\text{TM}}_1$ neutrino mixing with $\sin {\theta }_{13}=\frac{1}{\sqrt{3}}\sin \frac{\pi }{12}$
• Breaking of the tetra-maximal neutrino mixing pattern
• On Bimaximal Neutrino Mixing and GUT's
• Dark Matter interactions in an $S_4\times Z_5$ flavor symmetry framework
• Muon $g-2$, dark matter, and neutrino mass explanations in a modular $A_4$ symmetry
• Fermion masses and mixings in a $U(1{)}_X$ model based on the $\Sigma (18)$ discrete symmetry
• R-parity from string compactification
• Status and Perspectives of Neutrino Physics
• Flavon alignments from orbifolding: $SU(5)\times SU(3)$ model with ${\mathbb{T}}^6/\Delta (54)$
• Non-SUSY Lepton Flavor Model with 3HDM
• $TeV$-Scale Resonant Leptogenesis with New Scaling Ansatz on Neutrino Dirac Mass Matrix from $A_4$ Flavor Symmetry
• Computations in Finite Groups and Quantum Physics
• A discrete anatomy of the neutrino mass matrix
• Fermion masses and mixings and charged lepton flavor violation in a 3-3-1 model with inverse seesaw
• Neutrino Oscillations in the Three Flavor Paradigm
• Gravitational wave complementarity and impact of NANOGrav data on gravitational leptogenesis: cosmic strings
• Nearly right unitarity triangle and CP phase in quark and lepton flavor mixings
• Exploring the flavor structure of leptons via diffusion models
• Kinematical Observables in Semi-Invisible Decays
• CKM matrix and flavor symmetries
• Diffusion-model approach to flavor models: A case study for $S_4^{\prime }$ modular flavor model
• Scalar and gauge sectors in the 3-Higgs Doublet Model under the S3-symmetry
• Revisiting Flavor Model and Leptogenesis
• $A_4$ flavor symmetric model in SUSY SU(5) GUT
• Flavor structure from misalignment of inner products in noncommutative geometry
• Fate of ${\theta }_{12}$ under $\mu -\tau$ Reflection Symmetry in Light of the First JUNO Results
• Spontaneous CP breaking in $S_3$ flavored Higgs sector with soft-breaking terms
• Obtaining nonvanishing ${\theta }_{13}$ with constrained neutrino Yukawa matrix and implications for flavor model buildings
• Flavor and CP from String Theory
• Yukawa textures in modular symmetric vacuum of magnetized orbifold models
• Modular Flavour Symmetries and Modulus Stabilisation
• Phenomenological Aspects of Possible Vacua of a Neutrino Flavor Model
• $\mathbf{B}-\mathbf{L}$ model with ${\mathbf{D}}_4\times {\mathbf{Z}}_4\times {\mathbf{Z}}_2$ symmetry for fermion mass hierarchies and mixings
• Flavour Symmetry Embedded -- GLoBES (FaSE-GLoBES)
• One-parameter Neutrino Mass Matrix and Symmetry Realization
• CP Violating Phase Originated from Right-handed Neutrino Mixing
• Chiral perturbative analysis for an almost massless neutrino in the type-I seesaw mechanism
• Charged scalar production at the Compact Linear Collider for the $S_3\otimes {\mathbb{Z}}_2$ model
• Flavor Moonshine
• On a mechanism realizing quark mass hierarchy
• New partial symmetries from group algebras for lepton mixing