Modular $A_4$ invariance and neutrino mixing

Abstract

We study the phenomenological implications of the modular symmetry $\Gamma (3)\simeq A_4$ of lepton flavors facing recent experimental data of neutrino oscillations. The mass matrices of neutrinos and charged leptons are essentially given by fixing the expectation value of modulus $\tau$, which is the only source of modular invariance breaking. We introduce no flavons in contrast with the conventional flavor models with $A_4$ symmetry. We classify our neutrino models along with the type I seesaw model, the Weinberg operator model and the Dirac neutrino model. In the normal hierarchy of neutrino masses, the seesaw model is available by taking account of recent experimental data of neutrino oscillations and the cosmological bound of sum of neutrino masses. The predicted ${\sin }^2{\theta }_{23}$ is restricted to be larger than $0.54$ and $δ_{CP}=\pm (50^{\circ}\mbox{--}180^{\circ})$. Since the correlation of ${\sin }^2{\theta }_{23}$ and ${\delta }_{CP}$ is sharp, the prediction is testable in the future. It is remarkable that the effective mass $m_{ee}$ of the neutrinoless double beta decay is around $22$\,meV while the sum of neutrino masses is predicted to be $145$\,meV. On the other hand, for the inverted hierarchy of neutrino masses, only the Dirac neutrino model is consistent with the experimental data.

arXiv comment17 pages, 6 figures, 5 tables, major modifications

References in corpus (31)

• 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
• Unveiling $\nu$ secrets with cosmological data: neutrino masses and mass hierarchy
• Neutrino Mass and Mixing: from Theory to Experiment
• Finite Modular Groups and Lepton Mixing
• Searching for realistic 4d string models with a Pati-Salam symmetry -- Orbifold grand unified theories from heterotic string compactification on a Z6 orbifold
• Computing Yukawa Couplings from Magnetized Extra Dimensions
• Stringy origin of non-Abelian discrete flavor symmetries
• Lepton Masses and Mixing from Modular $S_4$ Symmetry
• Neutrino mixing from finite modular groups
• Majorana Neutrinos, Neutrino Mass Spectrum, CP-Violation and Neutrinoless Double Beta-Decay: I. The Three-Neutrino Mixing Case
• Modular Invariance Faces Precision Neutrino Data
• On the improvement of cosmological neutrino mass bounds
• Non-Abelian Discrete Flavor Symmetries from Magnetized/Intersecting Brane Models
• Measurement of neutrino and antineutrino oscillations by the T2K experiment including a new additional sample of ${\nu }_e$ interactions at the far detector
• Breaking Tri-bimaximal Mixing and Large ${\theta }_{13}$
• Modular symmetry and non-Abelian discrete flavor symmetries in string compactification
• Non-Abelian discrete gauge symmetries in 4d string models
• String-derived D4 flavor symmetry and phenomenological implications
• Unitarity triangles and geometrical description of CP violation with Majorana neutrinos
• Majorana Neutrinos, Neutrino Mass Spectrum, CP-Violation and Neutrinoless Double Beta-Decay: II. Mixing of Four Neutrinos
• Assessing the Viability of $A_4$, $S_4$ and $A_5$ Flavour Symmetries for Description of Neutrino Mixing
• Zero-modes on orbifolds : magnetized orbifold models by modular transformation
• Rephasing-invariant CP violating parameters with Majorana neutrinos
• Predictions for the Majorana CP Violation Phases in the Neutrino Mixing Matrix and Neutrinoless Double Beta Decay
• Revisiting $A_4$ model for leptons in light of NuFIT 3.2

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