Modulus $\tau$ linking leptonic CP violation to baryon asymmetry in $A_4$ modular invariant flavor model

Abstract

We propose an $A_4$ modular invariant flavor model of leptons, in which both CP and modular symmetries are broken spontaneously by the vacuum expectation value of the modulus $\tau$. The value of the modulus $\tau$ is restricted by the observed lepton mixing angles and lepton masses for the normal hierarchy of neutrino masses at $3\sigma$ confidence level. The predictive Dirac CP phase ${\delta }_{CP}$ is in the ranges $[0^{\circ },50^{\circ }]$, $[170^{\circ },175^{\circ }]$ and $[280^{\circ },360^{\circ }]$ for $\mathrm{Re}[\tau ]<0$, and $[0^{\circ },80^{\circ }]$, $[185^{\circ },190^{\circ }]$ and $[310^{\circ },360^{\circ }]$ for $\mathrm{Re}[\tau ]>0$ at $3\sigma$ confidence level. The sum of three neutrino masses is predicted in $[60,84]$ meV, and the effective mass for the $0\nu \beta \beta$ decay is in [0.003, 3] meV. On the other hand, there is no allowed region of the modulus $\tau$ for the inverted hierarchy of neutrino masses at $3\sigma$ confidence level. The modulus $\tau$ links the Dirac CP phase to the cosmological baryon asymmetry (BAU) via the leptogenesis. Due to the strong wash-out effect, the predictive baryon asymmetry $Y_B$ can be at most the same order of the observed value. Then, the lightest right-handed neutrino mass is restricted in the range of $M_1=[1.5,6.5]\times 10^{13}$ GeV. We find the correlation between the predictive $Y_B$ and the Dirac CP phase ${\delta }_{CP}$. Only two predictive ${\delta }_{CP}$ ranges, $[5^{\circ },40^{\circ }]$ ($\mathrm{Re}[\tau ]>0$) and $[320^{\circ },355^{\circ }]$ ($\mathrm{Re}[\tau ]<0$) are consistent with the BAU.

arXiv comment30 pages, 14 figures, 7 tables, minor corrections

References in corpus (106)

• The fate of hints: updated global analysis of three-flavor neutrino oscillations
• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Non-Abelian Discrete Symmetries in Particle Physics
• A lower bound on the right-handed neutrino mass from leptogenesis
• Resonant Leptogenesis
• Towards a complete theory of thermal leptogenesis in the SM and MSSM
• 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
• The importance of flavor in leptogenesis
• Flavour Issues in Leptogenesis
• Unveiling $\nu$ secrets with cosmological data: neutrino masses and mass hierarchy
• Neutrino Mass and Mixing: from Theory to Experiment
• Flavour Matters in Leptogenesis
• Finite Modular Groups and Lepton Mixing
• Lepton mixing and discrete symmetries
• Lepton Masses and Mixing from Modular $S_4$ Symmetry
• Unified Models of Neutrinos, Flavour and CP Violation
• A non-standard CP transformation leading to maximal atmospheric neutrino mixing
• Neutrino mixing from finite modular groups
• Flavor effects on leptogenesis predictions
• Leptonic CP violation
• Running quark and lepton parameters at various scales
• Leptogenesis and Low Energy CP Violation in Neutrino Physics
• Unification of Flavor, CP, and Modular Symmetries
• CP and Discrete Flavour Symmetries
• Atmospheric Neutrino Oscillation and a Phenomenological Lepton Mass Matrix
• Trimaximal Neutrino Mixing from Modular A4 Invariance with Residual Symmetries
• Modular Invariance Faces Precision Neutrino Data
• Modular $A_4$ invariance and neutrino mixing
• Baryon Asymmetry, Neutrino Mixing and Supersymmetric SO(10) Unification
• Connecting Low Energy Leptonic CP-violation to Leptogenesis
• 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
• CP Violation from Finite 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
• Automorphisms in Gauge Theories and the Definition of CP and P
• Discrete Flavour Symmetries, Neutrino Mixing and Leptonic CP Violation
• $SU(5)$ Grand Unified Theory with $A_4$ Modular Symmetry
• Breaking Tri-bimaximal Mixing and Large ${\theta }_{13}$
• 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
• 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
• New $A_4$ lepton flavor model from $S_4$ modular symmetry
• Modular $A_4$ invariance and leptogenesis
• A modular $A_4$ symmetric scotogenic model
• Towards a complete $A_4\times SU(5)$ SUSY GUT
• $A_4$ 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 $S_3$ 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
• On the Impact of Flavour Oscillations in Leptogenesis
• 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
• 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 -- I. Basic results
• 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
• A radiative seesaw model with three Higgs doublets in modular $A_4$ symmetry
• Modular Invariant $A_4$ Models for Quarks and Leptons with Generalized CP Symmetry
• Assessing the Viability of $A_4$, $S_4$ and $A_5$ Flavour Symmetries for Description of Neutrino Mixing
• $SU(5)$ 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
• The eclectic flavor symmetry of the ${\mathbb{Z}}_2$ orbifold
• SUSY Breaking Constraints on Modular flavor $S_3$ Invariant $SU(5)$ GUT Model
• Leptogenesis from Low Energy $CP$ Violation
• Modular symmetry anomaly in magnetic flux compactification
• Siegel modular flavor group and CP from string theory
• Fermion masses and mixing in modular A4 Symmetry
• Symmetries and stabilisers in modular invariant flavour models
• Predictions from warped flavordynamics based on the $T^{\prime }$ family group
• Classification of three generation models by orbifolding magnetized $T^2\times T^2$
• Modular Origin of Mass Hierarchy: Froggatt-Nielsen like Mechanism
• Revisiting $A_4$ model for leptons in light of NuFIT 3.2
• Soft supersymmetry breaking terms and lepton flavor violations in modular flavor models
• Neutrino and dark matter in a gauged $U(1{)}_R$ symmetry
• Resonant leptogenesis at TeV-scale and neutrinoless double beta decay

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• 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
• Minimal seesaw and leptogenesis with the smallest modular finite group
• Subcritical regime of hybrid inflation with modular $A_4$ symmetry
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