Trimaximal Neutrino Mixing from Modular A4 Invariance with Residual Symmetries

Abstract

We construct phenomenologically viable models of lepton masses and mixing based on modular $A_4$ invariance broken to residual symmetries ${\mathbb{Z}}_3^T$ or ${\mathbb{Z}}_3^{ST}$ and ${\mathbb{Z}}_2^S$ respectively in the charged lepton and neutrino sectors. In these models the neutrino mixing matrix is of trimaximal mixing form. In addition to successfully describing the charged lepton masses, neutrino mass-squared differences and the atmospheric and reactor neutrino mixing angles ${\theta }_{23}$ and ${\theta }_{13}$, these models predict the values of the lightest neutrino mass (i.e., the absolute neutrino mass scale), of the Dirac and Majorana CP violation(CPV) phases, as well as the existence of specific correlations between i) the values of the solar neutrino mixing angle ${\theta }_{12}$ and the angle ${\theta }_{13}$ (which determines ${\theta }_{12}$), ii) the values of the Dirac CPV phase $\delta$ and of the angles ${\theta }_{23}$ and ${\theta }_{13}$, iii) the sum of the neutrino masses and ${\theta }_{23}$, and iv) between the two Majorana phases.

Figure is replaced. Discussions and References are added

References in corpus (21)

• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Non-Abelian Discrete Symmetries in Particle Physics
• Neutrino Mass and Mixing with Discrete Symmetry
• Underlying A_4 Symmetry for the Neutrino Mass Matrix and the Quark Mixing Matrix
• Softly Broken A_4 Symmetry for Nearly Degenerate Neutrino Masses
• Tri-Bimaximal Neutrino Mixing, A4 and the Modular Symmetry
• Tri-Bimaximal Neutrino Mixing from Discrete Symmetry in Extra Dimensions
• Finite Modular Groups and Lepton Mixing
• Neutrino mixing from finite modular groups
• Possible Alternatives to Tri-bimaximal Mixing
• Current unknowns in the three neutrino framework
• Spontaneous CP violation from vacuum alignment in $S_4$ models of leptons
• Discrete Flavour Symmetries, Neutrino Mixing and Leptonic CP Violation
• Breaking Tri-bimaximal Mixing and Large ${\theta }_{13}$
• Predicting the Values of the Leptonic CP Violation Phases
• Leptonic Dirac CP Violation Predictions from Residual Discrete Symmetries
• Assessing the Viability of $A_4$, $S_4$ and $A_5$ Flavour Symmetries for Description of Neutrino Mixing
• Deviation from Bimaximal Mixing and Leptonic CP Phases in $S_4$ Family Symmetry and Generalized CP
• Predictions for the Majorana CP Violation Phases in the Neutrino Mixing Matrix and Neutrinoless Double Beta Decay
• Predicting CP violation in Deviation from Tri-bimaximal mixing of Neutrinos
• Revisiting $A_4$ model for leptons in light of NuFIT 3.2

Cited by in corpus (113)

• Flavor structures of charged fermions and massive neutrinos
• Unification of Flavor, CP, and Modular Symmetries
• CP violation of quarks in $A_4$ modular invariance
• Generalised CP Symmetry in Modular-Invariant Models of Flavour
• Neutrino Masses and Mixing from Double Covering of Finite Modular Groups
• Finite modular subgroups for fermion mass matrices and baryon/lepton number violation
• Modular $S_4$ and $A_4$ Symmetries and Their Fixed Points: New Predictive Examples of Lepton Mixing
• Neutrino Mass and Mixing with $A_5$ Modular Symmetry
• A String Theory of Flavor and CP
• 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
• A modular $A_4$ symmetry realization of two-zero textures of the Majorana neutrino mass matrix
• Multiple modular symmetries as the origin of flavour
• Modular $S_3$ symmetric radiative seesaw model
• New $A_4$ lepton flavor model from $S_4$ modular symmetry
• Modular $A_4$ invariance and leptogenesis
• $A_4$ lepton flavor model and modulus stabilization from $S_4$ modular symmetry
• Eclectic Flavor Groups
• Modular Invariant Dynamics and Fermion Mass Hierarchies around $\tau =i$
• Lessons from eclectic flavor symmetries
• Modular Flavor Symmetry on Magnetized Torus
• Modular Invariant Quark and Lepton Models in Double Covering of $S_4$ Modular Group
• Modular $S_3$ invariant flavor model in SU(5) GUT
• 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
• Lepton Flavor Mixing and CP Violation in the Minimal Type-(I+II) Seesaw Model with a Modular $A_4$ Symmetry
• Modular Invariant Models of Lepton Masses at Levels 4 and 5
• Fermion Mass Hierarchies, Large Lepton Mixing and Residual Modular Symmetries
• Landscape of Modular Symmetric Flavor Models
• Modular symmetry by orbifolding magnetized $T^2\times T^2$: realization of double cover of ${\Gamma }_N$
• 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
• $CP$ violation in modular invariant flavor models
• The Minimal Seesaw Model with a Modular $S_4$ Symmetry
• Lepton flavor model with modular $A_4$ symmetry in large volume limit
• Eclectic flavor scheme from ten-dimensional string theory -- II. Detailed technical analysis
• Automorphic Forms and Fermion Masses
• Fermion Masses and Mixing from Double Cover and Metaplectic Cover of $A_5$ Modular Group
• Spontaneous CP violation by modulus $\tau$ in $A_4$ model of lepton flavors
• Modular Invariant $A_4$ Models for Quarks and Leptons with Generalized CP Symmetry
• Half-integral weight modular forms and application to neutrino mass models
• Modular flavor symmetries of three-generation modes on magnetized toroidal orbifolds
• $SU(5)$ GUTs with $A_4$ modular symmetry
• Twin Modular $S_4$ with $SU(5)$ GUT
• Spontaneous CP violation and symplectic modular symmetry in Calabi-Yau compactifications
• CP Symmetry and Symplectic Modular Invariance
• SUSY Breaking Constraints on Modular flavor $S_3$ Invariant $SU(5)$ GUT Model
• Classification of discrete modular symmetries in Type IIB flux vacua
• Modular symmetry anomaly in magnetic flux compactification
• Challenge for spontaneous CP violation in Type IIB orientifolds with fluxes
• Towards unification of quark and lepton flavors in $A_4$ modular invariance
• Dirac neutrino mass models with a modular $S_4^{}$ symmetry
• Symplectic modular symmetry in heterotic string vacua: flavor, CP, and $R$-symmetries
• The first string-derived eclectic flavor model with realistic phenomenology
• Fermion masses and mixing in modular A4 Symmetry
• Symmetries and stabilisers in modular invariant flavour models
• Residual flavor symmetry breaking in the landscape of modular flavor models
• Modular $S_4\times SU(5)$ GUT
• $A_4$ Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point $\tau =\omega$
• Modular symmetry in the SMEFT
• Modular symmetry at level 6 and a new route towards finite modular groups
• Loop Fayet-Iliopoulos terms in $T^2/Z_2$ models: instability and moduli stabilization
• Quark and lepton hierarchies from $S_4^{\prime }$ modular flavor symmetry
• The symmetry approach to quark and lepton masses and mixing
• 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
• Quark mass hierarchies and CP violation in $A_4\times A_4\times A_4$ modular symmetric flavor models
• Flipped SU(5) with modular $A_4$ symmetry
• Leptogenesis in $SO(10)$ Models with $A_4$ Modular Symmetry
• Flavor mixing and CP violation from the interplay of $S_4$ modular group and gCP
• Modular Origin of Mass Hierarchy: Froggatt-Nielsen like Mechanism
• Texture-zero patterns of lepton mass matrices from modular symmetry
• Classification of three generation models by orbifolding magnetized $T^2\times T^2$
• Explicit Perturbations to the Stabilizer $\tau =\mathrm{i}$ of Modular $A_5^{\prime }$ Symmetry and Leptonic CP Violation
• Quark and lepton flavor structure in magnetized orbifold models at residual modular symmetric points
• Two A4 modular symmetries for Tri-Maximal 2 mixing
• Subcritical regime of hybrid inflation with modular $A_4$ symmetry
• A Survey of Neutrino Flavor Models and the Neutrinoless Double Beta Decay Funnel
• Common origin of ${\theta }_{13}$ and dark matter within the flavor symmetric scoto-seesaw framework
• Flavor Structures of Quarks and Leptons from Flipped SU(5) GUT with $A_4$ Modular Flavor Symmetry
• Leptonic Sum Rules from Flavour Models with Modular Symmetries
• Electron EDM arising from modulus $\tau$ in the supersymmetric modular invariant flavor models
• Two A5 modular symmetries for Golden Ratio 2 mixing
• 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
• Remark on modular weights in low-energy effective field theory from type II string theory
• Linear seesaw model with a modular $S_4$ flavor symmetry
• Modular Invariant Models of Leptons at Level 7
• Modular symmetry anomaly and non-perturbative neutrino mass terms in magnetized orbifold models
• CP violations in a predictive $A_4$ symmetry model
• Simiplified textures of the seesaw model for the trimaximal neutrino mixings
• Confronting the prediction of leptonic Dirac CP-violating phase with experiments
• Trimaximal Mixing and Extended Magic Symmetry in a Model of Neutrino Mass Matrix
• A hybrid seesaw model and hierarchical neutrino flavor structures based on $A_4$ symmetry
• Theory Review of Neutrino Models and CP Violation
• Completing the eclectic flavor scheme of the ${\mathbb{Z}}_2$ orbifold
• Algebraic realisation of three fermion generations with $S_3$ family and unbroken gauge symmetry from $\mathbb{C}\ell (8)$
• Majorana neutrino masses by D-brane instanton effects in magnetized orbifold models
• Generalized Matter Parities from Finite Modular Symmetries
• Subcritical hybrid inflation in a generalized superconformal model
• Modular flavored dark matter
• $SO(10)$ models with $A_4$ modular symmetry
• Natural solution of SUSY $\mu$ problem from modulus stabilization in modular flavor model
• Quark and lepton flavor model with leptoquarks in a modular $A_4$ symmetry
• Muon $g-2$, dark matter, and neutrino mass explanations in a modular $A_4$ symmetry
• Yukawa textures in modular symmetric vacuum of magnetized orbifold models
• Quasi two-zero texture in Type-II seesaw at fixed points from modular $A_4$ symmetry
• $TeV$-Scale Resonant Leptogenesis $A_4$ with a scaling texture
• A radiative Type-II seesaw model with broken Symmetry Ansatz
• Modular Flavour Symmetries and Modulus Stabilisation