Finite Modular Groups and Lepton Mixing

Abstract

We study lepton mixing patterns which are derived from finite modular groups Gamma_N, requiring subgroups G_nu and G_e to be preserved in the neutrino and charged lepton sectors, respectively. We show that only six groups Gamma_N with N=3,4,5,7,8,16 are relevant. A comprehensive analysis is presented for G_e arbitrary and G_nu=Z2 x Z2, as demanded if neutrinos are Majorana particles. We discuss interesting patterns arising from both groups G_e and G_nu being arbitrary. Several of the most promising patterns are specific deviations from tri-bimaximal mixing, all predicting theta_13 non-zero as favoured by the latest experimental data. We also comment on prospects to extend this idea to the quark sector.

27 pages + 8 pages of appendices, 1 figure

References in corpus (17)

• Indication of Electron Neutrino Appearance from an Accelerator-produced Off-axis Muon Neutrino Beam
• 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
• The Horizontal Symmetry for Neutrino Mixing
• Symmetry of Lepton Mixing
• Comparing Trimaximal Mixing and Its Variants with Deviations from Tri-bimaximal Mixing
• The golden ratio prediction for the solar neutrino mixing
• Discrete Flavour Symmetries in Light of T2K
• Z_2 Symmetry Prediction for the Leptonic Dirac CP Phase
• Minimal Modification To The Tri-bimaximal Neutrino Mixing
• A model for trimaximal lepton mixing
• Fermion Masses and Mixings from Dihedral Flavor Symmetries with Preserved Subgroups
• The Flavor Group Delta(6n^2)
• Golden Ratio Neutrino Mixing and $A_5$ Flavor Symmetry
• On the origin of neutrino flavour symmetry
• Group Theory and Dynamics of Neutrino Mixing
• General Lepton Mixing in Holographic Composite Higgs Models

Cited by in corpus (206)

• Neutrino Mass and Mixing with Discrete Symmetry
• Flavor structures of charged fermions and massive neutrinos
• Neutrino mixing from finite modular groups
• Unification of Flavor, CP, and Modular Symmetries
• Trimaximal Neutrino Mixing from Modular A4 Invariance with Residual Symmetries
• Modular $A_4$ invariance and neutrino mixing
• A review of mu-tau flavor symmetry in neutrino physics
• Modular $A_5$ Symmetry for Flavour Model Building
• CP violation of quarks in $A_4$ modular invariance
• Generalised CP Symmetry in Modular-Invariant Models of Flavour
• Modular $S_4$ Models of Lepton Masses and Mixing
• Neutrino Masses and Mixing from Double Covering of Finite Modular Groups
• Finite modular subgroups for fermion mass matrices and baryon/lepton number violation
• Neutrino Mass and Mixing with $A_5$ Modular Symmetry
• A Realistic Pattern of Lepton Mixing and Masses from S4 and CP
• Discrete Flavour Symmetries, Neutrino Mixing and Leptonic CP Violation
• A String Theory of Flavor and CP
• $SU(5)$ Grand Unified Theory with $A_4$ Modular Symmetry
• Double Cover of Modular $S_4$ for Flavour Model Building
• Modular $A_4$ Symmetry Models of Neutrinos and Charged Leptons
• Trimaximal TM${}_1$ mixing with two modular $S_4$ groups
• Multiple modular symmetries as the origin of flavour
• Generalised CP and $A_4$ Family Symmetry
• A modular $A_4$ symmetric model of dark matter and neutrino
• Modular forms of finite modular subgroups from magnetized D-brane models
• Modular $S_3$ symmetric radiative seesaw model
• Discrete Flavour Groups, θ_13 and Lepton Flavour Violation
• New $A_4$ lepton flavor model from $S_4$ modular symmetry
• θ_{13} and Proton Decay in a Minimal SO(10) x S_4 model of Flavor
• Modular $A_4$ invariance and leptogenesis
• A modular $A_4$ symmetric scotogenic model
• Lepton Mixing Predictions from Delta(6n^2) Family Symmetry
• $A_4$ lepton flavor model and modulus stabilization from $S_4$ modular symmetry
• Eclectic Flavor Groups
• Lepton Mixing Patterns from a Scan of Finite Discrete Groups
• Lessons from eclectic flavor symmetries
• Trimaximal TM1 neutrino mixing in S4 with spontaneous CP violation
• Modular Flavor Symmetry on Magnetized Torus
• Modular $S_3$ invariant flavor model in SU(5) GUT
• Modular Invariant Quark and Lepton Models in Double Covering of $S_4$ Modular Group
• Revisiting modular symmetry in magnetized torus and orbifold compactifications
• Modular symmetry origin of texture zeros and quark lepton unification
• Type II seesaw models with modular $A_4$ symmetry
• A Grand Delta(96) x SU(5) Flavour Model
• Tri-bimaximal-Cabibbo Mixing
• Fermion Mass Hierarchies, Large Lepton Mixing and Residual Modular Symmetries
• Modular symmetry by orbifolding magnetized $T^2\times T^2$: realization of double cover of ${\Gamma }_N$
• Discrete symmetries and model-independent patterns of lepton mixing
• Pieces of the Flavour Puzzle
• Modular invariant flavor model of ${\mathrm{A}}_4$ and hierarchical structures at nearby fixed points
• Double Covering of the Modular $A_5^{}$ Group and Lepton Flavor Mixing in the Minimal Seesaw Model
• A4 models of tri-bimaximal-reactor mixing
• Lepton Mixing from Delta (3 n^2) and Delta (6 n^2) and CP
• $CP$ violation in modular invariant flavor models
• Tri-Bimaximal Neutrino Mixing and Discrete Flavour Symmetries
• Lepton mixing from the interplay of the alternating group A5 and CP
• Mixing angle and phase correlations from A5 with generalised CP and their prospects for discovery
• Generalised CP and Trimaximal TM${}_1$ Lepton Mixing in $S_4$ Family Symmetry
• Generalised CP and $\Delta (6n^2)$ Family Symmetry in Semi-Direct Models of Leptons
• Lepton Mixing Predictions including Majorana Phases from $\Delta (6n^2)$ Flavour Symmetry and Generalised CP
• Lepton Mixing Parameters from $\Delta (48)$ Family Symmetry and Generalised CP
• Generalized CP symmetries in Delta(27) flavor models
• Fermion Masses and Mixing from Double Cover and Metaplectic Cover of $A_5$ Modular Group
• Classification of lepton mixing matrices from finite residual symmetries
• Quark and Leptonic Mixing Patterns from the Breakdown of a Common Discrete Flavor Symmetry
• Generalized $\mu$-$\tau$ symmetry and discrete subgroups of O(3)
• A radiative seesaw model with three Higgs doublets in modular $A_4$ symmetry
• Finite Symmetry of Leptonic Mass Matrices
• TFH Mixing Patterns, Large ${\theta }_{13}$ and $\Delta (96)$ Flavor Symmetry
• Generalised CP and $\Delta (96)$ Family Symmetry
• Non-zero ${\theta }_{13}$ and CP violation in a model with $A_4$ flavor symmetry
• Modular Invariant $A_4$ Models for Quarks and Leptons with Generalized CP Symmetry
• The Minimal Flavour Violating Axion
• A4xSU(5) SUSY GUT of Flavour with Trimaximal Neutrino Mixing
• Modular flavor symmetries of three-generation modes on magnetized toroidal orbifolds
• Dirac Neutrinos with $S_4$ Flavor Symmetry in Warped Extra Dimensions
• Simple two Parameter Description of Lepton Mixing
• Twin Modular $S_4$ with $SU(5)$ GUT
• SUSY Breaking Constraints on Modular flavor $S_3$ Invariant $SU(5)$ GUT Model
• Mixing Patterns from the Groups Sigma (n phi)
• Neutrino Mixings and the S4 Discrete Flavour Symmetry
• Classification of discrete modular symmetries in Type IIB flux vacua
• Modular symmetry anomaly in magnetic flux compactification
• Flavor and CP symmetries for leptogenesis and 0nubb decay
• Lepton and Quark Mixing Patterns from Finite Flavor Symmetries
• CP Violation in the Lepton Sector and Implications for Leptogenesis
• Testing solar lepton mixing sum rules in neutrino oscillation experiments
• Symplectic modular symmetry in heterotic string vacua: flavor, CP, and $R$-symmetries
• Implications of the Daya Bay observation of θ_{13} on the leptonic flavor mixing structure and CP violation
• Simplified Models of Flavourful Leptoquarks
• Fermion masses and mixing in modular A4 Symmetry
• Symmetries and stabilisers in modular invariant flavour models
• Lepton flavor at the electroweak scale: A complete A4 model
• Solving the Strong CP Problem with Discrete Symmetries and the Right Unitarity Triangle
• CP Symmetry and Lepton Mixing from a Scan of Finite Discrete Groups
• Residual flavor symmetry breaking in the landscape of modular flavor models
• $A_4$ Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point $\tau =\omega$
• Modular symmetry at level 6 and a new route towards finite modular groups
• Compatibility of theta13 and the Type I Seesaw Model with A4 Symmetry
• [Re]constructing Finite Flavour Groups: Horizontal Symmetry Scans from the Bottom-Up
• Modular symmetry in the SMEFT
• How good is μ-τsymmetry after results on non-zero θ_{13}?
• Quark and Lepton Mixing Patterns from a Common Discrete Flavor Symmetry with Generalized CP
• The symmetry approach to quark and lepton masses and mixing
• Quark and lepton hierarchies from $S_4^{\prime }$ modular flavor symmetry
• Residual Z2 x Z2 symmetries and lepton mixing
• Predictions from scoto-seesaw with $A_4$ modular symmetry
• Inverse seesaw in $A_5^{\prime }$ modular symmetry
• Revisiting Minimal Lepton Flavour Violation in the Light of Leptonic CP Violation
• Golden ratio lepton mixing and nonzero reactor angle with $A_5$
• A Unified Model of Quarks and Leptons with a Universal Texture Zero
• 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
• Bottom-Up Discrete Symmetries for Cabibbo Mixing
• Spontaneous breaking of $SO(3)$ to finite family symmetries with supersymmetry - an $A_4$ model
• Relating neutrino masses and mixings by discrete symmetries
• Horizontal symmetries of leptons with a massless neutrino
• Quark mass hierarchies and CP violation in $A_4\times A_4\times A_4$ modular symmetric flavor models
• Discrete flavour symmetries for degenerate solar neutrino pair and their predictions
• D14 - A Common Origin of the Cabibbo Angle and the Lepton Mixing Angle theta^l_13
• Moduli inflation from modular flavor symmetries
• Implications of residual CP symmetry for leptogenesis in a model with two right-handed neutrinos
• Neutrino Mass and Mixing Models with Eclectic Flavor Symmetry $\Delta (27)⋊T^{\prime }$
• Toward a unified interpretation of quark and lepton mixing from flavor and CP symmetries
• A massless neutrino and lepton mixing patterns from finite discrete subgroups of U(3)
• Lepton flavor models with discrete prediction of theta_{13}
• Classification of three generation models by orbifolding magnetized $T^2\times T^2$
• Modular Origin of Mass Hierarchy: Froggatt-Nielsen like Mechanism
• Flavor mixing and CP violation from the interplay of $S_4$ modular group and gCP
• Discrete symmetries, roots of unity, and lepton mixing
• Texture-zero patterns of lepton mass matrices from modular symmetry
• Neutrino Mixing and Discrete Symmetries
• Bilarge Neutrino Mixing and Abelian Flavor Symmetry
• Quark and lepton flavor structure in magnetized orbifold models at residual modular symmetric points
• Status of Neutrino Mass and Mixing
• Two A4 modular symmetries for Tri-Maximal 2 mixing
• A left-right symmetric flavor symmetry model
• Finite Family Groups for Fermionic and Leptoquark Mixing Patterns
• Subcritical regime of hybrid inflation with modular $A_4$ symmetry
• 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
• Common origin of ${\theta }_{13}$ and dark matter within the flavor symmetric scoto-seesaw framework
• Neutrino mixing in SO(10) GUTs with non-abelian flavor symmetry in the hidden sector
• Golden Littlest Seesaw
• Predictive Leptogenesis from Minimal Lepton Flavour Violation
• Soft supersymmetry breaking terms and lepton flavor violations in modular flavor models
• Models for Neutrino Masses and Mixings
• Electron EDM arising from modulus $\tau$ in the supersymmetric modular invariant flavor models
• Finite modular axion and radiative moduli stabilization
• Cutting the Scotogenic loop: Adding flavor to Dark Matter
• Symmetry based parameterizations of the lepton mixing matrix
• Lepton mass matrix from double covering of $A_4$ modular flavor symmetry
• 4D modular flavor symmetric models inspired by higher dimensional theory
• Moduli trapping mechanism in modular flavor symmetric models
• Lepton and Quark Mixing from Stepwise Breaking of Flavor and CP
• Neutrino Mass Sum Rules from Modular ${\mathcal{A}}_4$ Symmetry
• Residual $Z_2$ symmetries and leptonic mixing patterns from finite discrete subgroups of $U(3)$
• Neutrino masses and mixing from flavour antisymmetry
• Remark on modular weights in low-energy effective field theory from type II string theory
• A Built-in Horizontal Symmetry of $SO(10)$
• Target Space Duality of Non-Supersymmetric String Theory
• FCNC-free multi-Higgs-doublet models from broken family symmetries
• Linear seesaw model with a modular $S_4$ flavor symmetry
• Radiative Corrections to the Solar Lepton Mixing Sum Rule
• Study on perturbation schemes for achieving the real PMNS matrix from various symmetric textures
• Leptonic Mixing and Group Structure Constants
• Trimaximal-Cabibbo neutrino mixing: A parametrization in terms of deviations from tri-bimaximal mixing
• Modular Invariant Models of Leptons at Level 7
• Nonholomorphic $A_4$ modular invariance for fermion masses and mixing in SU(5) GUT
• Modular symmetry anomaly and non-perturbative neutrino mass terms in magnetized orbifold models
• Lepton Mixing, Residual Symmetries, and Trigonometric Diophantine Equations
• New mixing schemes for (3+1) neutrinos
• Data Driven Flavour Model
• Non-holomorphic modular flavor symmetry and odd weight polyharmonic Maaß form
• Neutrino masses and mixing in Minimal Inverse Seesaw using $A_4$ modular symmetry
• New textures for the lepton mass matrices
• Theoretical Overview on the Flavor Issues of Massive Neutrinos
• Confronting the prediction of leptonic Dirac CP-violating phase with experiments
• Double seesaw mechanism and lepton mixing
• Fermion Masses and Mixing in General Warped Extra Dimensional Models
• Minimal eclectic flavor group $Q_8⋊S_3$ and neutrino mixing
• Neutrino mixing and Leptogenesis with modular $S_3$ symmetry in the framework of type III seesaw
• Theory Review of Neutrino Models and CP Violation
• Reconstructing Effective Lagrangians Embedding Residual Family Symmetries
• Coxeter groups and the PMNS matrix
• Origin of Symmetric PMNS and CKM Matrices
• Lepton and Quark Masses and Mixing in a SUSY Model with Delta(384) and CP
• Five models for lepton mixing
• Fermion Masses and Mixing in Pati-Salam Unification with $S_3$ Modular Symmetry
• Generalized Matter Parities from Finite Modular Symmetries
• Group-theoretical search for rows or columns of the lepton mixing matrix
• Flavor's Delight
• Neutrino Mixing from $\Delta (6n^2)$ Groups
• Discrete Flavour Symmetries from the Heisenberg Group
• Flavour anomalies meet flavour symmetry
• Quark-lepton mass relations from modular flavor symmetry
• Minimal Modular Flavor Symmetry and Lepton Textures Near Fixed Points
• Neutrino mass, mixing and discrete symmetries
• Muon $g-2$, dark matter, and neutrino mass explanations in a modular $A_4$ symmetry
• Quark and lepton flavor model with leptoquarks in a modular $A_4$ symmetry
• On Bimaximal Neutrino Mixing and GUT's
• PSL(2,7) Representations and their relevance to Neutrino Physics
• Yukawa textures in modular symmetric vacuum of magnetized orbifold models
• CKM matrix and flavor symmetries
• Modular Flavour Symmetries and Modulus Stabilisation
• Recent developments in Neutrino Physics