Discrete Flavor Symmetries and Models of Neutrino Mixing

Abstract

We review the application of non abelian discrete groups to the theory of neutrino masses and mixing, which is strongly suggested by the agreement of the Tri-Bimaximal mixing pattern with experiment. After summarizing the motivation and the formalism, we discuss specific models, based on A4, S4 and other finite groups, and their phenomenological implications, including lepton flavor violating processes, leptogenesis and the extension to quarks. In alternative to Tri-Bimaximal mixing the application of discrete flavor symmetries to quark-lepton complementarity and Bimaximal Mixing is also considered.

54 pages, 3 figures, minor changes in the text and references added

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• Lepton Mixing Predictions from Infinite Group Series $D_{9n,3n}^{(1)}$ with Generalized CP
• A Bayesian comparison of U(1) lepton flavour models
• Quark and lepton hierarchies from $S_4^{\prime }$ modular flavor symmetry
• An $A_4$ realization of inverse seesaw: neutrino masses, ${\theta }_{13}$ and leptonic non-unitarity
• Inverse seesaw in $A_5^{\prime }$ modular symmetry
• Predictions from scoto-seesaw with $A_4$ modular symmetry
• Revisiting Minimal Lepton Flavour Violation in the Light of Leptonic CP Violation
• Discrete symmetries and models of flavor mixing
• Leptogenesis in flavor models with type I and II seesaws
• Discrete Symmetries and Neutrino Mass Perturbations for θ_{13}
• Broken $S_3$ Symmetry in the Neutrino Mass Matrix
• Lepton Mixing in $A_5$ Family Symmetry and Generalized CP
• Neutrino mu-tau reflection symmetry and its breaking in the minimal seesaw
• Neutrino Mixing and Leptonic CP Violation from $S_4$ Flavour and Generalised CP Symmetries
• Physics with Reactor Neutrinos
• A direct link between neutrinoless double beta decay and leptogenesis in a seesaw model with $S_4$ symmetry
• Flavor-Nonuniversal Dark Gauge Bosons and the Muon g-2
• Tri-Bimaximal Neutrino Mixing and the $T_{13}$ Flavor Symmetry
• Quark hierarchical structures in modular symmetric flavor models at level 6
• Fermion masses and mixing in $\Delta (27)$ flavour model
• Mu-tau reflection symmetry with a texture-zero
• A Shift from Democratic to Tri-bimaximal Neutrino Mixing with Relatively Large theta_{13}
• Modulus $\tau$ linking leptonic CP violation to baryon asymmetry in $A_4$ modular invariant flavor model
• Trimaximal mixing with a texture zero
• Flavor origin of dark matter and its relation with leptonic nonzero ${\theta }_{13}$ and Dirac CP phase $\delta$
• Non-Abelian discrete R symmetries
• The $\mu$-$\tau$ mixed symmetry and neutrino mass matrix
• Quark and lepton flavors with common modulus $\tau$ in $A_4$ modular symmetry
• Non-invertible flavor symmetries in magnetized extra dimensions
• Radiative Seesaw-type Mechanism of Fermion Masses and Non-trivial Quark Mixing
• Quark mass hierarchies and CP violation in $A_4\times A_4\times A_4$ modular symmetric flavor models
• Novel signatures of the Higgs sector from S3 flavor symmetry
• SU(3) Gauge Family Symmetry and Prediction for the Lepton-Flavor Mixing and Neutrino Masses with Maximal Spontaneous CP Violation
• Lepton Flavour Violation and Flavour Symmetries
• Relating neutrino masses and mixings by discrete symmetries
• Horizontal symmetries of leptons with a massless neutrino
• A simplest modular $S_3$ model for leptons
• Distinguishing A Higgs-Like Dilaton Scenario With A Complete Bosonic Effective Field Theory Basis
• Baryon Number, Lepton Number, and Operator Dimension in the SMEFT with Flavor Symmetries
• Neutrino phenomenology and scalar Dark Matter with $A_4$ flavor symmetry in Inverse and type II seesaw
• Implications of residual CP symmetry for leptogenesis in a model with two right-handed neutrinos
• CP-odd invariants for multi-Higgs models: applications with discrete symmetry
• Formulae for flavour neutrino masses and its application to texture two zeros
• Moduli inflation from modular flavor symmetries
• An eigenvector based approach to neutrino mixing
• Predictivity of models with spontaneously broken non-Abelian discrete flavor symmetries
• D14 - A Common Origin of the Cabibbo Angle and the Lepton Mixing Angle theta^l_13
• Towards the minimal seesaw model via CP violation of neutrinos
• Discrete flavour symmetries for degenerate solar neutrino pair and their predictions
• Adjoint $SU(5)$ GUT model with $T_7$ flavor symmetry
• Super Flavorsymmetry with Multiple Higgs Doublets
• Mu-tau reflection symmetry with a high scale texture-zero
• Is the tri-bimaximal mixing accidental?
• Addressing Neutrino Mixing Models with DUNE and T2HK
• Renormalisation Group Corrections to Neutrino Mass Sum Rules
• A massless neutrino and lepton mixing patterns from finite discrete subgroups of U(3)
• Corrections for tribimaximal, bimaximal and democratic neutrino mixing matrices
• More about quark Yukawa textures from selection rules without group actions
• Leptonic mixing, family symmetries, and neutrino phenomenology
• Accidental stability of dark matter
• Lepton flavor models with discrete prediction of theta_{13}
• Flavour physics without flavour symmetries
• Maximal atmospheric neutrino mixing from texture zeros and quasi-degenerate neutrino masses
• Toward a unified interpretation of quark and lepton mixing from flavor and CP symmetries
• Discrete Family Symmetry from F-Theory GUTs
• Modular Origin of Mass Hierarchy: Froggatt-Nielsen like Mechanism
• Non-Abelian discrete flavor symmetries of 10D SYM theory with magnetized extra dimensions
• Tri-Permuting Mixing Matrix and predictions for theta_13
• Neutrino Mixing Angles in Sequential Dominance to NLO and NNLO
• Lepton mixing patterns from the group $\Sigma (36\times 3)$ with a generalized CP transformation
• Vacuum misalignment corrections to tri-bimaximal mixing and form dominance
• A novel Randall-Sundrum model with $S_3$ flavor symmetry
• Discrete symmetries, roots of unity, and lepton mixing
• Viability of the exact tri-bimaximal mixing at M_{GUT} in SO(10)
• "Heterotic" Discrete Flavor Model
• Neutrino phenomenology, W mass anomaly & muon $(g-2)$ in minimal type-III seesaw using $T^{\prime }$ modular symmetry
• Perturbations to $\mu -\tau$ Symmetry, Leptogenesis and Lepton Flavour Violation with Type II Seesaw
• The Frobenius group T13 and the canonical see-saw mechanism applied to neutrino mixing
• The Impact of Different Parameterizations on the Interpretation of CP Violation in Neutrino Oscillations
• Fermions with cubic and quartic spectrum
• ${\theta }_{13}^{}$ and The Flavor Ring
• Perturbed Yukawa Textures in the Minimal Seesaw Model
• Explicit Perturbations to the Stabilizer $\tau =\mathrm{i}$ of Modular $A_5^{\prime }$ Symmetry and Leptonic CP Violation
• Common Origin of Non-zero ${\theta }_{13}$ and Baryon Asymmetry of the Universe in a TeV scale Seesaw Model with $A_4$ Flavour Symmetry
• Status of Neutrino Mass and Mixing
• Quark mixing from Delta(6N^2) family symmetry
• Delta(54) flavor phenomenology and strings
• Predictivity of Neutrino Mass Sum Rules
• Phenomenological Implications of an SU(5) x S4 x U(1) SUSY GUT of Flavour
• Leptonic Unitarity Triangles and Effective Mass Triangles of the Majorana Neutrinos
• Renormalisation group improved leptogenesis in family symmetry models
• Finite Family Groups for Fermionic and Leptoquark Mixing Patterns
• Surveying the SO(10) Model Landscape: The Left-Right Symmetric Case
• Consequences of $\mu -\tau$ Reflection Symmetry at DUNE
• A new and trivial CP symmetry for extended $A_4$ flavor
• Probing flavor models with Ge-76-based experiments on neutrinoless double-beta decay
• A left-right symmetric flavor symmetry model
• Deviations from Tribimaximal Neutrino Mixing using a Model with $\Delta (27)$ Symmetry
• Minimal seesaw and leptogenesis with the smallest modular finite group
• Approaching Minimal Flavour Violation from an SU(5) x S4 x U(1) SUSY GUT
• Revisiting $A_4$ model for leptons in light of NuFIT 3.2
• Lepton masses and mixing in a two-Higgs-doublet model
• Quark mixing in an $S_3$ symmetric model with two Higgs doublets
• Model of flavor with quaternion symmetry
• From Flavour to SUSY Flavour Models
• Neutrino CP violation and sign of baryon asymmetry in the minimal seesaw model
• A study on a minimally broken residual TBM-Klein symmetry with its implications on flavoured leptogenesis and ultra high energy neutrino flux ratios
• Modifications to the neutrino mixing from the mu-tau reflection symmetry
• Neutrino masses and mixing in $A_5$ with flavour antisymmetry
• Semidirect Product Groups, Vacuum Alignment and Tribimaximal Neutrino Mixing
• Common origin of ${\theta }_{13}$ and dark matter within the flavor symmetric scoto-seesaw framework
• Renormalisation Group Corrections to Neutrino Mixing Sum Rules
• Theory of Neutrino Masses and Mixing
• Exploring Partial $\mu$-$\tau$ Reflection Symmetry at DUNE and Hyper-Kamiokande
• Texture zeros of quark mass matrices at fixed point $\tau =\omega$ in modular flavor symmetry
• Lepton mass textures from non-invertible multiplication rules
• Relating large $U_{e3}$ to the ratio of neutrino mass-squared differences
• Models of Neutrino Mass, Mixing and CP Violation
• Predictions for the Dirac CP Violation Phase in the Neutrino Mixing Matrix
• Majorana neutrino mass structure induced by rigid instatons on toroidal orbifold
• Neutrino Predictions from Generalized CP Symmetries of Charged Leptons
• Predicting Leptonic CP phase by considering deviations in charged lepton and neutrino sectors
• $\Delta \left(27\right)$ flavor singlet-triplet Higgs model for fermion masses and mixings
• A model of quarks with Delta (6N^2) family symmetry
• Consequences of minimal seesaw with complex $\mu \tau$ antisymmetry of neutrinos
• Tri-Direct CP in the Littlest Seesaw Playground
• Correlation of normal neutrino mass ordering with upper octant of ${\theta }_{23}^{}$ and third quadrant of $\delta$ via RGE-induced $\mu$-$\tau$ symmetry breaking
• Neutrino mass textures from F-theory
• Perturbing exactly tri-bimaximal neutrino mixings with charged lepton mass matrices
• Spontaneous CP violation in multi-Higgs potentials with triplets of $\Delta (3n^2)$ and $\Delta (6n^2)$
• Generalised $\mu$-$\tau$ symmetries and calculable gauge kinetic and mass mixing in $U(1{)}_{L_{\mu }-L_{\tau }}$ models
• Neutrino and $Z^{\prime }$ phenomenology in an anomaly-free $\mathbf{U}(1)$ extension: role of higher-dimensional operators
• Leptonic Sum Rules from Flavour Models with Modular Symmetries
• A low-scale flavon model with a $Z_N$ symmetry
• Neutrino oscillations from warped flavor symmetry: predictions for long baseline experiments T2K, NOvA and DUNE
• Realizing Tri-bimaximal Mixing in Minimal Seesaw Model with S4 Family Symmetry
• Quasidegeneracy of Majorana Neutrinos and the Origin of Large Leptonic Mixing
• Golden Littlest Seesaw
• Finite modular axion and radiative moduli stabilization
• Phase broken $\mu -\tau$ symmetry and the neutrino mass hierarchy
• Electron EDM arising from modulus $\tau$ in the supersymmetric modular invariant flavor models
• Discrete symmetries and mixing of Dirac neutrinos
• Testing Lepton Flavor Models at ESSnuSB
• Quark mixing in the discrete dark matter model
• Probing Lepton Flavor Models at Future Neutrino Experiments
• Compact model for Quarks and Leptons via flavored-Axions
• Predictive Leptogenesis from Minimal Lepton Flavour Violation
• Spontaneous Breaking of Gauge Groups to Discrete Symmetries
• Soft supersymmetry breaking terms and lepton flavor violations in modular flavor models
• Tomography of flavoured leptogenesis with primordial blue gravitational waves
• A New bound on CP Violation in the $\tau$ Lepton Yukawa Coupling and electroweak baryogenesis
• Phenomenology of keV scale sterile neutrino dark matter with $S_4$ flavor symmetry
• Collider signatures of vector-like fermions from a flavor symmetric model
• Non-Abelian Discrete Flavor Symmetries on Orbifolds
• Flavor Symmetry Based MSSM (sMSSM): Theoretical Models and Phenomenological Analysis
• Neutrino masses, the $\mu$-term and ${\mathcal{P}\mathcal{SL}}_2(7)$
• Lepton mass matrix from double covering of $A_4$ modular flavor symmetry
• Low scale type I seesaw model for lepton masses and mixings
• Flavor Mixing Democracy and Minimal CP Violation
• Muon anomalies and the $SU(5)$ Yukawa relations
• 4D modular flavor symmetric models inspired by higher dimensional theory
• Rare muon and tau decays in A4 Models
• Majorana Physics Through the Cabibbo Haze
• Breaking classical Lie groups to finite subgroups - an automated approach
• On the characterization of the SU(3)-subgroups of type C and D
• Probing the predictions of an orbifold theory of flavor
• Integral solutions to the one-loop renormalization-group equations for lepton flavor mixing parameters and the Jarlskog invariant
• Lepton and Quark Mixing from Stepwise Breaking of Flavor and CP
• Flavor structure in D-brane models: Majorana neutrino masses
• Expanding neutrino oscillation parameter measurements in NOvA using a Bayesian approach
• The other variants of mixed $\mu$-$\tau$ symmetry
• A full parametrization of the $9\times 9$ active-sterile flavor mixing matrix in the inverse or linear seesaw scenario of massive neutrinos
• Moduli trapping mechanism in modular flavor symmetric models
• CP transformed mixed $\mu \tau$ antisymmetry for neutrinos and its consequences
• Flavoured leptogenesis and ${\mathrm{CP}}^{\mu \tau }$ symmetry
• Renormalization Group Evolution of Neutrino Parameters in Presence of Seesaw Threshold Effects and Majorana Phases
• Radiative neutrino masses from order-4 CP symmetry
• Consistency of perturbed Tribimaximal, Bimaximal and Democratic mixing with Neutrino mixing data
• Charged lepton contributions to bipair neutrino mixing
• Realization of the minimal extended seesaw mechanism and the $T{M}_2$ type neutrino mixing
• Neutrino masses and lepton mixing from $A_5\times \mathrm{CP}$
• Impact of RGE-induced $\mu -\tau$ Reflection Symmetry Breaking on the Effective Majorana Neutrino Mass in $0\nu \beta \beta$ Decay
• Effective alignments as building blocks of flavour models
• Fermion masses and mixings and $g-2$ muon anomaly in a 3-3-1 model with $D_4$ family symmetry
• 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 $U(3)$
• Viability of exact tri-bimaximal, golden-ratio and bimaximal mixing patterns and renormalization-group running effects
• Implications of Fermionic Dark Matter on recent neutrino oscillation data
• Lepton mass and mixing in a Neutrino Mass Model based on $S_4$ flavor symmetry
• Neutrino masses and mixing from flavour antisymmetry
• Top Quark as a Dark Portal and Neutrino Mass Generation
• Freeze-in Dirac neutrinogenesis: thermal leptonic CP asymmetry
• $\mu -\tau$ Reflection Symmetry and Its Explicit Breaking for Leptogenesis in a Minimal Seesaw Model
• A Further Study of the Frampton-Glashow-Yanagida Model for Neutrino Masses, Flavor Mixing and Baryon Number Asymmetry
• Flavour effects in gravitational leptogenesis
• Precise predictions for Dirac neutrino mixing
• Remark on modular weights in low-energy effective field theory from type II string theory
• Neutrino Mass from a d=7 Effective Operator in a SUSY-GUT Framework
• Hidden flavor symmetries of SO(10) GUT
• Radiative charged-lepton mass generation in multi-Higgs doublet models
• Flavor structure in $SO(32)$ heterotic string theory
• Effective Theories of Flavor and the Non-Universal MSSM
• Reducing θ_13 to 9 degrees
• FCNC-free multi-Higgs-doublet models from broken family symmetries
• Deviations in Tribimaximal Mixing From Sterile Neutrino Sector
• Flavon-induced connections between lepton flavour mixing and charged lepton flavour violation processes
• Importance of generalized $\mu \tau$ symmetry and its CP extension on neutrino mixing and leptogenesis
• Highly predictive and testable $A_4$ flavor model within type-I and II seesaw framework and associated phenomenology
• Low energy phenomena of the lepton sector in an $A_4$ symmetry model with heavy inverse seesaw neutrinos
• Target Space Duality of Non-Supersymmetric String Theory
• Topology of quantum vacuum
• An expansion for Neutrino Phenomenology
• Anomaly of non-Abelian discrete symmetries
• Slepton Non-Universality in the Flavor-Effective MSSM
• Seesaw mirroring between light and heavy Majorana neutrinos with the help of the $S_3^{}$ reflection symmetry
• Cosmological Consequences of Domain Walls Biased by Quantum Gravity
• Measuring Oscillations with A Million Atmospheric Neutrinos
• Linear seesaw model with a modular $S_4$ flavor symmetry
• Anomalous Discrete Flavor Symmetry and Domain Wall Problem
• Predicting neutrino oscillations with "bi-large" lepton mixing matrices
• The role of flavon cross couplings in leptonic flavour mixing
• Inverse see-saw neutrino masses in the Littlest Higgs model with T-parity
• Exploring the flavor structure of quarks and leptons with reinforcement learning
• An explicit SU(12) family and flavor unification model with natural fermion masses and mixings
• A modified Friedberg-Lee symmetry for the TM1 neutrino mixing
• Stability and symmetry breaking in a three Higgs-boson doublet model with lepton family symmetry O(2)xZ2
• Leptonic CP Violation from a New Perspective
• Clockwork origin of neutrino mixings
• Non-linearly realized discrete symmetries
• Modular symmetry anomaly and non-perturbative neutrino mass terms in magnetized orbifold models
• Revisiting the Dirac Nature of Neutrinos in the Light of $\Delta (27)$ and Cyclic Symmetries
• Particle Physics at the LHC Start
• Deviation from Tribimaximal mixing using $A_4$ flavour model with five extra scalars
• Lepton mixing from the hidden sector
• Neutrino Mass Sum Rules and Symmetries of the Mass Matrix
• SO(10) models with flavour symmetries: Classification and examples
• Strong coupling, discrete symmetry and flavour
• Flavon Stabilization in Models with Discrete Flavor Symmetry
• Neutrino non-standard interactions as a portal to test flavour symmetries
• Revisiting Discrete Dark Matter Model:θ_{13}\neq0 and ν_{R} Dark Matter
• CP and other Symmetries of Symmetries
• Consequences of $\mu$-$\tau$ reflection symmetry for $3+1$ neutrino mixing
• Phenomenology of S_4 Flavor Symmetric extra U(1) model
• Axion and Neutrino physics in a $U(1)$-enhanced supersymmetric model
• Magic square and Dirac flavor neutrino mass matrix
• Neutrino phenomenology in a left-right $D_4$ symmetric model
• Higgs portal dark matter and neutrino mass and mixing with a doubly charged scalar
• Classical and Quantum Discrete Dynamical Systems
• Minimally modified $A_4$ Altarelli-Feruglio model for neutrino masses and mixings and its experimental consequences
• Froggatt-Nielsen models with a residual Z_4^R symmetry
• Compatible abelian symmetries in N-Higgs-Doublet Models
• Discrete symmetries and Efficient Counting of Operators
• Predictions of $m_{ee}$ and neutrino mass from a consistent Froggatt-Nielsen model
• Z_4 flavor model in Randall-Sundrum model 1
• Lepton Mixing, Residual Symmetries, and Trigonometric Diophantine Equations
• Checking Flavour Models at Neutrino Facilities
• Predictive neutrino mass textures with origin of flavor symmetries
• A Realistic Neutrino mixing scheme arising from $A_4$ symmetry
• A minimal inverse seesaw model with $S_4$ flavour symmetry
• Data Driven Flavour Model
• Fully constrained mass matrix: Can symmetries alone determine the flavon vacuum alignments?
• Symmetry Finder applied to the 1-3 mass eigenstate exchange symmetry
• Symmetryless Dark Matter
• Scotogenic majorana neutrino masses in a predictive orbifold theory of flavour
• Stable lepton mass matrices
• Yukawa interactions, flavor symmetry, and non-canonical Kähler potential
• Phenomenological implications of the Friedberg-Lee transformation in a neutrino mass model with $\mu \tau$-flavored CP symmetry
• The role of lepton flavor symmetries in leptogenesis
• Trimaximal Mixing and Extended Magic Symmetry in a Model of Neutrino Mass Matrix
• Theoretical Overview on the Flavor Issues of Massive Neutrinos
• Relative scale separation in orbifolds of $S^2$ and $S^5$
• An Overview of Neutrino Mixing
• Representing seesaw neutrino models and their motion in lepton flavour space
• High scale mixing relations as a natural explanation for large neutrino mixing
• Phenomenology of extended multiHiggs doublet models with $S_4$ family symmetry
• Implications of the Muon g-2 result on the flavour structure of the lepton mass matrix
• Determination of the ${\theta }_{23}$ octant in long baseline neutrino experiments within and beyond the standard model
• Diagonal reflection symmetries, four-zero texture, and trimaximal mixing with predicted ${\theta }_{13}$ in an $A_4$ symmeric model
• Texture of Two Vanishing Subtraces in Neutrino Mass Matrix and Current Experimental Tests
• Constraining $A_4$ Leptonic Flavour Model Parameters at Colliders and Beyond
• Further study on the textures of neutrino mass matrix for maximal atmospherical mixing angle and Dirac CP phase
• Neutrino mixing and Leptogenesis with modular $S_3$ symmetry in the framework of type III seesaw
• Knitting neutrino mass textures with or without Tri-Bi maximal mixing
• A modular $A_4$ symmetric Scotogenic model for Neutrino mass and Dark Matter
• Neutrino Mixing and Leptogenesis in a $L_e-L_{\mu }-L_{\tau }$ model
• Confronting Tri-direct CP-symmetry models to neutrino oscillation experiments
• On the textures of neutrino mass matrix for maximal atmospheric mixing angle and Dirac CP phase
• Viability of $A_4$, $S_4$ and $A_5$ Flavour Symmetries in Light of the First JUNO Result
• Model independent Analysis of Dirac CP Violating Phase for some well known mixing scenarios
• Pocket Formulae for Non-Abelian Discrete Anomaly Freedom
• Radiative Generation of Non-zero ${\theta }_{13}$ in MSSM with broken $A_4$ Flavor Symmetry
• "Hidden" O(2) and SO(2) Symmetry in Lepton Mixing
• Minimal eclectic flavor group $Q_8⋊S_3$ and neutrino mixing
• Lepton-flavour violation in a Pati-Salam model with gauged flavour symmetry
• A hybrid seesaw model and hierarchical neutrino flavor structures based on $A_4$ symmetry
• Type II seesaw supersymmetric neutrino model for ${\theta }_{13}\ne 0$
• Seesaw Mechanism Confronting PAMELA in S_4 Flavor Symmetric Extra U(1) Model
• Flavored Leptogenesis and Neutrino Mass with $A_4$ Symmetry
• The Freund-Rubin Coset, Textures and Group Theory
• Identifying a minimal flavor symmetry of the seesaw mechanism behind neutrino oscillations
• Pseudo-Dirac neutrinos from flavour dependent CP symmetry
• Reconstructing Effective Lagrangians Embedding Residual Family Symmetries
• Spontaneously stabilised dark matter from a fermiophobic $U(1{)}^{\prime }$ gauge 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
• Robustness of Neutrino Mass Matrix Predictions
• Testing the minimal $S_4$ model of neutrinos with the Dirac and Majorana phases
• Lepton Mixing Predictions from (Generalised) CP and Discrete Flavour Symmetry
• Testing constrained sequential dominance models of neutrinos
• CP violation in bipair neutrino mixing
• Fractionalized time reversal, parity and charge conjugation symmetry in topological superconductor: a possible origin of three generations of neutrinos and mass mixing
• Recent Progress in Flavor Model Building
• A Model of Four Generation Fermions and Cold Dark Matter and Matter-Antimatter Asymmetry
• Theory Review of Neutrino Models and CP Violation
• Neutrino mass from M Theory SO(10)
• CP violation in modified bipair neutrino mixing and leptogenesis
• Proton decay and $\mu \to e+\gamma$ Connection in a Renormalizable SO(10) GUT for Neutrinos
• Renormalization Group Running of Lepton Mixing Parameters in See-Saw Models with $S_4$ Flavor Symmetry
• Study of a tri-direct littlest seesaw model at MOMENT
• Neutrino mixing and masses in SO(10) GUTs with hidden sector and flavor symmetries
• SUSY SU(5) $\times S_4$ GUT Flavor Model for Fermion Masses and Mixings with Adjoint, Large ${\theta }_{13}^{PMNS}$
• Discrete symmetries from hidden sectors
• Knotted strings and leptonic flavor structure
• Unveiling Neutrino Mysteries with $\Delta (27)$ Symmetry
• Combining Pati-Salam and Flavour Symmetries
• Lepton mixing and the charged-lepton mass ratios
• Neutrino and Charged Lepton Flavour Today
• A translational flavor symmetry in the mass terms of Dirac and Majorana fermions
• Planck Scale Origin of Non-zero ${\theta }_{13}$ and Super-WIMP Dark Matter
• Neutrinos and the matter-antimatter asymmetry in the Universe
• Algebraic realisation of three fermion generations with $S_3$ family and unbroken gauge symmetry from $\mathbb{C}\ell (8)$
• Nonzero ${\theta }_{13}$ in $SO(3)\to A_4$ lepton models
• Neutrino Physics Now and in the Near Future
• The Challenges of Flavour Physics
• Searching exotic Higgs bosons at the LHC
• Electroweak and Majorana Sector Higgs Bosons and Pseudo-Nambu-Goldstone Bosons
• Unification of gauge, family, and flavor symmetries illustrated in gauged SU(12) models
• A see-saw scenario of an $A_4$ flavour symmetric standard model
• Next-to-tribimaximal mixing against CP violation and baryon asymmetry signs
• The translational $\mu$-$\tau$ reflection symmetry of Majorana neutrinos
• A Clifford Algebra Approach to Chiral Symmetry Breaking and Fermion Mass Hierarchies
• A Comprehensive Mechanism Reproducing the Mass and Mixing Parameters of Quarks and Leptons
• Non-Abelian Domain Walls and Gravitational Waves
• Coxeter groups and the PMNS matrix
• Partial $\mu -\tau$ Textures and Leptogenesis
• On Building superpotentials in F- GUTs
• Two-zero textures based on $A_4$ symmetry and unimodular mixing matrix
• An extended 3-3-1 model with two scalar triplets and linear seesaw mechanism
• Lepton and Quark Masses and Mixing in a SUSY Model with Delta(384) and CP
• A Possible Hermitian Neutrino Mixing Ansatz
• Hybrid seesaw neutrino model in SUSY $SU(5)\times {\mathbb{A}}_4$
• Origin of Symmetric PMNS and CKM Matrices
• Chasing after flavor symmetries of quarks from bottom up
• An infrared origin of leptonic mixing and its test at DeepCore
• Particular textures of the minimal seesaw model
• Minimal lepton flavour structures lead to non-maximal 2-3 mixing
• A Systematic Analysis of Perturbations for Hexagonal Mixing Matrix
• Flavor symmetric origin of texture zeros in minimal inverse seesaw and impacts on leptogenesis
• Novel Flavon Stabilization with Trimaximal Neutrino Mixing
• Phenomenological implications of a minimal F-theory GUT with discrete symmetry
• Prediction for the neutrino mass in the KATRIN experiment from lensing by the galaxy cluster A1689
• A neutrino mixing model based on an $A_4\times Z_3\times Z_4$ flavour symmetry
• Fermion Masses and Mixing in Pati-Salam Unification with $S_3$ Modular Symmetry
• Majorana phases in high-scale mixings unification hypotheses
• Generalized Matter Parities from Finite Modular Symmetries
• Residual Symmetries and Scalar Multiplet Vacuum Alignment in Non-Abelian Flavour Models
• Perspectives in Neutrino Physics
• A new texture of neutrino mass matrix with three constraints
• Improving heavy Dirac neutrino prospects at future hadron colliders using machine learning
• The problem of flavour
• Modular-symmetry-protected seesaw
• MSSM-like from $S{U}_5\times D_4$ Models
• Leptogenesis, Fermion Masses and Mixings in a SUSY $SU(5)$ GUT with $D_4$ Flavor Symmetry
• A bottom-up approach to fermion mass hierarchy: a case with vector-like fermions
• Phenomenological Implications of $\mathbf{\Delta }(54)$ Flavor Symmetry with Triple Inverse Seesaw
• CP-like Symmetry with Discrete and Continuous Groups and CP Violation/Restoration
• The Seesaw Evaded Modular Dirac Framework
• The origin of discrete symmetries in F-theory models
• Flavor Imprints on Novel Low Mass Dark Matter
• Comparative study of the 1-2 exchange symmetries in neutrino frameworks with global and local validities
• Discrete Flavour Symmetries from the Heisenberg Group
• Theoretical Results on Neutrinos
• Symmetry in neutrino oscillation in matter with non-unitarity
• Magic square and three-zero textures for Dirac neutrinos
• Octant of ${\theta }_{23}$, MH, $0\nu \beta \beta$ decay and vacuum alignment of $A_4$ flavour symmetry in an inverse seesaw model
• Sum Rules for Leptons
• The Majorana neutrino mass matrix indicated by the current data
• Optical effects of domain walls
• Leptogenesis in the presence of exact flavor symmetries
• Subcritical hybrid inflation in a generalized superconformal model
• Mathematical Modeling of Finite Quantum Systems
• Inflation and Leptogenesis in a $U(1)$-enhanced supersymmetric model
• Parameterization of Pontecorvo-Maki-Nakagawa-Sakata mixing matrix based on CP-violating bipair neutrino mixing
• Particle Physics in the LHC Era and beyond
• Quark-lepton mass relations from modular flavor symmetry
• 50 Years of Neutrino Physics
• Yang-Mills theory for semidirect products $\mathrm{G}⋉{\mathfrak{g}}^{\ast }$ and its instantons
• Partial mass-degeneracy and spontaneous CP violation in the lepton sector
• The discrete charm of flavour and CP violation
• Standard and Non-Standard Aspects of Neutrino Physics
• Gauge extension of non-Abelian discrete flavor symmetry
• A universal form for quark and neutrino mass matrices
• Geometric phases in neutrino mixing
• Modular flavored dark matter
• Status and Perspectives of Neutrino Physics
• Low scale leptogenesis and $T{M}_1$ mixing in neutrinophillic two Higgs doublet model($\nu$2HDM) with S4 flavor symmetry
• Leptogenesis via Varying Weinberg Operator: the Closed-Time-Path Approach
• On Bimaximal Neutrino Mixing and GUT's
• Rescuing leptogenesis in inverse seesaw models with the help of non-Abelian flavor symmetries
• Fermion masses and mixings and $g-2$ muon anomaly in a $Q_6$ flavored 2HDM
• Effects on sinθ_{12} from perturbation of the neutrino mixing matrix with the partially degenerated neutrino masses
• Lepton mixing patterns from $PS{L}_2(7)$ with a generalised CP symmetry
• Advanced One-Parameter CKM Mixing Matrix and Universal Deviation from Exact Quark-Lepton Complementarity
• Aspects of Leptonic Flavour Mixing
• PSL(2,7) Representations and their relevance to Neutrino Physics
• Breaking of the tetra-maximal neutrino mixing pattern
• An Explicit SU(12) Family and Flavor Unification Model
• ${\text{TM}}_1$ neutrino mixing with $\sin {\theta }_{13}=\frac{1}{\sqrt{3}}\sin \frac{\pi }{12}$
• The special Two zeros texture based on $A_4$ symmetry and perturbation method
• Leptogenesis in the $\mu \tau$ basis
• Minimal A4 Type-II Seesaw Realization of Testable Neutrino Mass Sum Rules
• Triplet scalar flavored leptogenesis with spontaneous CP violation
• Muon $g-2$, dark matter, and neutrino mass explanations in a modular $A_4$ symmetry
• Prediction of Neutrino Mixing based on $C_2\times D_3$
• Quark and lepton flavor model with leptoquarks in a modular $A_4$ symmetry
• Is magic texture for Majorana neutrino immanent in Dirac nature?
• Modified TM2 for Reproducing All Best-Fit Values of Neutrino Mixing Angles
• Dark Matter interactions in an $S_4\times Z_5$ flavor symmetry framework
• Note about the implementation of finite symmetries in the lepton sector
• Modular Flavour Symmetries and Modulus Stabilisation
• Non-SUSY Lepton Flavor Model with 3HDM
• $TeV$-Scale Resonant Leptogenesis $A_4$ with a scaling texture
• Yukawa textures in modular symmetric vacuum of magnetized orbifold models
• A Bottom-Up Approach: The Data Driven Flavour Model
• Fermion masses and mixings and charged lepton flavor violation in a 3-3-1 model with inverse seesaw
• Obtaining nonvanishing ${\theta }_{13}$ with constrained neutrino Yukawa matrix and implications for flavor model buildings
• Probing Leptogenesis and Pre-BBN Universe with Gravitational Waves Spectral Shapes
• Seesaw neutrino masses from an $A_4$ model with two equal vacuum expectation values
• Unification based on the mysterious cubic-structure grouping of quarks and leptons
• Neutrino flavor mixing with approximate $\mu$-$\tau$ symmetry within the low-scale minimal linear seesaw model
• A discrete anatomy of the neutrino mass matrix
• One-parameter Neutrino Mass Matrix and Symmetry Realization
• Quantum Spacetime Imprints: The 24-Cell, Standard Model Symmetry and Its Flavor Mixing
• Charged Higgs Decay to Bottom and Charm Quarks from $Z_3$-Flavored Two Higgs Doublet Models
• CKM matrix and flavor symmetries
• Predictions of the neutrino oscillations parameters
• Scalar and gauge sectors in the 3-Higgs Doublet Model under the S3-symmetry
• Gravitational wave complementarity and impact of NANOGrav data on gravitational leptogenesis: cosmic strings
• On a mechanism realizing quark mass hierarchy
• Revisiting Flavor Model and Leptogenesis
• Computations in Finite Groups and Quantum Physics
• Neutrino Masses and Mixings from Continuous Symmetries
• Nearly right unitarity triangle and CP phase in quark and lepton flavor mixings
• Diffusion-model approach to flavor models: A case study for $S_4^{\prime }$ modular flavor model
• On the ambiguities in the tri-bimaximal mixing matrix and corresponding charged lepton corrections
• Probing Long-Range Forces in Neutrino Oscillations at the ESSnuSB Experiment
• Fine tuning in an A4-based Tri-Bimaximal neutrino-mixing model
• Flavor Moonshine
• Exploring the flavor structure of leptons via diffusion models
• Models for neutrino mass with discrete symmetries
• The Physics of Neutrinos
• Flavour Symmetry Embedded -- GLoBES (FaSE-GLoBES)
• $TeV$-Scale Resonant Leptogenesis with New Scaling Ansatz on Neutrino Dirac Mass Matrix from $A_4$ Flavor Symmetry
• $A_4$ flavor symmetric model in SUSY SU(5) GUT
• Recent developments in Neutrino Physics
• New partial symmetries from group algebras for lepton mixing