Flavor mixing and CP violation from the interplay of $S_4$ modular group and gCP

Abstract

We have performed a systematical analysis of lepton and quark masses models based on ${\Gamma }_4\cong S_4$ modular symmetry with gCP symmetry. We have considered both cases that neutrinos are Majorana particles and Dirac particles. All possible nontrivial representation assignments of matter fields are considered, and the most general form of fermion mass matrices are given. The phenomenologically viable models with the lowest number of free parameters together with the results of fit are presented. We find out nine lepton models with seven real free parameters including the real and imaginary parts of modulus for Majorana neutrinos, which can accommodate the lepton masses and neutrino oscillation data. The prediction for leptogenesis is studied in an example lepton model. The observed baryon asymmetry as well as lepton masses and mixing angles can be explained. For Dirac neutrinos, four lepton models with five real free couplings are compatible with experimental data. Ten quark models containing seven couplings are found to be able to accommodate the hierarchical quark masses and mixing angles and CP violation phase. Furthermore, the $S_4$ modular symmetry can provide a unified description of lepton and quark flavor structure, and a benchmark model is presented.

arXiv comment42 pages, 5 figures

References in corpus (88)

• The fate of hints: updated global analysis of three-flavor neutrino oscillations
• Search for Majorana Neutrinos near the Inverted Mass Hierarchy Region with KamLAND-Zen
• Leptogenesis for Pedestrians
• Towards a complete theory of thermal leptogenesis in the SM and MSSM
• CP violating decays in leptogenesis scenarios
• Global analysis of three-flavour neutrino oscillations: synergies and tensions in the determination of theta_23, delta_CP, and the mass ordering
• An improved upper limit on the neutrino mass from a direct kinematic method by KATRIN
• Finite Modular Groups and Lepton Mixing
• Current Status and Future Prospects of the SNO+ Experiment
• Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE) Conceptual Design Report Volume 2: The Physics Program for DUNE at LBNF
• Lepton Masses and Mixing from Modular $S_4$ Symmetry
• Neutrino mixing from finite modular groups
• The Large Enriched Germanium Experiment for Neutrinoless Double Beta Decay (LEGEND)
• Running quark and lepton parameters at various scales
• Unification of Flavor, CP, and Modular Symmetries
• Trimaximal Neutrino Mixing from Modular A4 Invariance with Residual Symmetries
• Modular Invariance Faces Precision Neutrino Data
• Modular $A_4$ invariance and neutrino mixing
• Sensitivity and discovery potential of the proposed nEXO experiment to neutrinoless double beta decay
• Modular $A_5$ Symmetry for Flavour Model Building
• CP violation of quarks in $A_4$ modular invariance
• Modular $S_4$ Models of Lepton Masses and Mixing
• 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
• Spontaneous CP violation from vacuum alignment in $S_4$ models of leptons
• Unification and Fermion Mass Structure
• 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
• A note on the predictions of models with modular flavor symmetries
• 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
• Flavour-Dependent Leptogenesis with Sequential Dominance
• A modular $A_4$ symmetric model of dark matter and neutrino
• 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 modular $A_4$ symmetric scotogenic model
• Physics Potentials with the Second Hyper-Kamiokande Detector in Korea
• $A_4$ 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
• Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE) Conceptual Design Report Volume 1: The LBNF and DUNE Projects
• 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
• Modular Invariant Models of Lepton Masses at Levels 4 and 5
• Lepton Flavor Mixing and CP Violation in the Minimal Type-(I+II) Seesaw Model with a Modular $A_4$ Symmetry
• Fermion Mass Hierarchies, Large Lepton Mixing and Residual Modular Symmetries
• 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
• The Minimal Seesaw Model with a Modular $S_4$ Symmetry
• Metaplectic Flavor Symmetries from Magnetized Tori
• 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
• CP violation and modular symmetries
• Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE) Conceptual Design Report, Volume 4 The DUNE Detectors at LBNF
• $SU(5)$ GUTs with $A_4$ modular symmetry
• Twin Modular $S_4$ with $SU(5)$ GUT
• Testing Moduli and Flavon Dynamics with Neutrino Oscillations
• CP Symmetry and Symplectic Modular Invariance
• SUSY Breaking Constraints on Modular flavor $S_3$ Invariant $SU(5)$ GUT Model
• Spontaneous breaking of CP symmetry by orbifold moduli
• Dirac neutrino mass models with a modular $S_4^{}$ symmetry
• Adjoint SU(5) GUT model with Modular $S_4$ Symmetry
• Alternative Schemes of Predicting Lepton Mixing Parameters from Discrete Flavor and CP Symmetry
• CP Violation and Moduli Stabilization in Heterotic Models
• Quark and Lepton Mixing Patterns from a Common Discrete Flavor Symmetry with Generalized CP
• A radiative seesaw model in modular $A_4$ symmetry
• Modulus $\tau$ linking leptonic CP violation to baryon asymmetry in $A_4$ modular invariant flavor model
• Quark and lepton flavors with common modulus $\tau$ in $A_4$ modular symmetry
• Toward a unified interpretation of quark and lepton mixing from flavor and CP symmetries
• A linear seesaw model with $A_4$-modular flavor and local $U(1{)}_{B-L}$ symmetries
• Leptogenesis in a $\Delta (27)\times SO(10)$ SUSY GUT
• Project 8: Determining neutrino mass from tritium beta decay using a frequency-based method
• Implications of $A_4$ modular symmetry on Neutrino mass, Mixing and Leptogenesis with Linear Seesaw

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