The special Two zeros texture based on $A_4$ symmetry and perturbation method

Abstract

The current study aimed to investigate the special case of two zeros in a Majorana neutrino mass matrix based on $A_4$ symmetry, where charged lepton mass matrix is diagonal. The texture $M_{\nu }^{S_7}$ with $(\mu ,\mu )$ and $(\tau ,\tau )$ vanishing element of mass matrix has magic and $\mu -\tau$ symmetry, with a tribimaximal form of the mixing matrix which leads to ${\theta }_{13}=0$ that it is not consistent with experimental data and does not seem to be allowed. Since ${\theta }_{13}$ is small compared to other neutrino mixing angles, we show that ${\theta }_{13}$, and $\delta$ could be obtained by using a complex symmetrical perturbation in the mass basis and also could be shown that $\delta m^2\equiv m_2^2-m_1^2\ne 0$ affecting the atmospheric mixing angle. We find that for the complex perturbation mass matrix, only the results of the case I, $\Delta <0$ and $\text{Re}(\alpha )<0$, are consistent with experimental data. Furthermore, the allowed range of our parameter space and complex element of perturbation are found which led to finding the deviation of ${\theta }_{23}$ from $45^{\circ }$ where this deviation is in line with the experimental data which indicate the accuracy of our model and its results. Our prediction is inverted mass ordering in the Case I. The results of the case II, $\Delta >0$ and $\text{Re}(\alpha )>0$, are ruled out.

References in corpus (76)

• The Cosmological Parameters 2006
• Big-Bang nucleosynthesis (Particle Data Group mini-review)
• Observation of Reactor Electron Antineutrino Disappearance in the RENO Experiment
• Tri-Bimaximal Mixing and the Neutrino Oscillation Data
• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Softly Broken A_4 Symmetry for Nearly Degenerate Neutrino Masses
• Tri-Bimaximal Neutrino Mixing, A4 and the Modular Symmetry
• 2020 Global reassessment of the neutrino oscillation picture
• Mass and Flavor Mixing Schemes of Quarks and Leptons
• Status of three-neutrino oscillation parameters, circa 2013
• Reactor electron antineutrino disappearance in the Double Chooz experiment
• Zeroes of the Neutrino Mass Matrix
• Spectral measurement of electron antineutrino oscillation amplitude and frequency at Daya Bay
• Texture Zeros and Majorana Phases of the Neutrino Mass Matrix
• Possible Alternatives to Tri-bimaximal Mixing
• Residual Symmetries for Neutrino Mixing with a Large theta_13 and Nearly Maximal delta_D
• A review of mu-tau flavor symmetry in neutrino physics
• Two-zero Textures of the Majorana Neutrino Mass Matrix and Current Experimental Tests
• The Elements of the Neutrino Mass Matrix: Allowed Ranges and Implications of Texture Zeros
• A Simplest A4 Model for Tri-Bimaximal Neutrino Mixing
• Flavor Mixing and CP Violation of Massive Neutrinos
• Parametrizing the lepton mixing matrix in terms of deviations from tri-bimaximal mixing
• Aspects of the Tetrahedral Neutrino Mass Matrix
• A_4 symmetry and prediction of U_{e3} in a modified Altarelli-Feruglio model
• Near Tribimaximal Neutrino Mixing with Delta(27) Symmetry
• Nonzero theta(13) for neutrino mixing in the context of A(4) symmetry
• Phenomenology of Two-Texture Zero Neutrino Mass Matrices
• Discrete Flavour Groups, θ_13 and Lepton Flavour Violation
• Predictive flavour symmetries of the neutrino mass matrix
• Sizeable θ_13 from the Charged Lepton Sector in SU(5), (Tri-)Bimaximal Neutrino Mixing and Dirac CP Violation
• Minimal extension of tri-bimaximal mixing and generalized Z_2 X Z_2 symmetries
• The reactor mixing angle and CP violation with two texture zeros in the light of T2K
• Embedding A4 into left-right flavor symmetry: Tribimaximal neutrino mixing and fermion hierarchy
• Three-Neutrino Mass Matrices with Two Texture Zeros
• A4 models of tri-bimaximal-reactor mixing
• TriMinimal Parametrization of the Neutrino Mixing Matrix
• Tri-Bimaximal Neutrino Mixing and Discrete Flavour Symmetries
• Simplified Renormalizable $T^{{}^{\prime }}$ Model for Tribimaximal Mixing and Cabibbo Angle
• Fine-tuning and naturalness issues in the two-zero neutrino mass textures
• Flavor mixings and textures of the fermion mass matrices
• Phenomenological Implications of a Class of Neutrino Mass Matrices
• How to Describe Neutrino Mixing and CP Violation
• The One-zero Textures of Majorana Neutrino Mass Matrix and Current Experimental Tests
• Tribimaximal Mixing From Small Groups
• Implications of a class of neutrino mass matrices with texture zeros for non-zero ${\theta }_{13}$
• Scotogenic $A_4$ Neutrino Model for Nonzero ${\theta }_{13}$ and Large ${\delta }_{CP}$
• Large mixing, family structure, and dominant block in the neutrino mass matrix
• Deviations from Tri-bimaximal Mixing: Charged Lepton Corrections and Renormalization Group Running
• Deviations from tribimaximal mixing due to the vacuum expectation value misalignment in A_4 models
• Q_6 flavor symmetry model for the extension of the minimal standard model by three right-handed sterile neutrinos
• Non-zero ${\theta }_{13}$ and CP violation in a model with $A_4$ flavor symmetry
• Texture 4 zero Fritzsch-like lepton mass matrices
• Large U_{e3} and Tri-bimaximal Mixing
• New Simple A_4 Neutrino Model for Nonzero θ_{13} and Large δ_{CP}
• Minimal Mass Matrices for Dirac Neutrinos
• Magic Neutrino Mass Matrix and the Bjorken-Harrison-Scott Parameterization
• Two-parameter neutrino mass matrices with two texture zeros
• Large θ_13 in a SUSY SU(5)xT' Model
• Group space scan of flavor symmetries for nearly tribimaximal lepton mixing
• Implications of Fritzsch-like lepton mass matrices
• Zeros in the magic neutrino mass matrix
• Discrete Symmetries and Neutrino Mass Perturbations for θ_{13}
• The $\mu$-$\tau$ mixed symmetry and neutrino mass matrix
• Tri-bimaximal Mixing from Cascades
• Large and Almost Maximal Neutrino Mixing within the Type II See-Saw Mechanism
• Small entries of neutrino mass matrices
• An eigenvector based approach to neutrino mixing
• A new A4 model for lepton mixing
• Texture Zeros for Dirac Neutrinos and Current Experimental Tests
• Perturbing exactly tri-bimaximal neutrino mixings with charged lepton mass matrices
• Minimal modifications to the Tri-Bimaximal neutrino mixing
• Consistency of perturbed Tribimaximal, Bimaximal and Democratic mixing with Neutrino mixing data
• Generalized perturbations in neutrino mixing
• Is θ_{13}^{PMNS} correlated with θ_{23}^{PMNS} or not?
• Two-zero textures based on $A_4$ symmetry and unimodular mixing matrix
• Generating CP violation from a modified Fridberg-Lee model