Generalized $\mu$-$\tau$ symmetry and discrete subgroups of O(3)

Abstract

The generalized $\mu$-$\tau$ interchange symmetry in the leptonic mixing matrix $U$ corresponds to the relations: $|U_{\mu i}|=|U_{\tau i}|$ with $i=1,2,3$. It predicts maximal atmospheric mixing and maximal Dirac CP violation given ${\theta }_{13}\ne 0$. We show that the generalized $\mu$-$\tau$ symmetry can arise if the charged lepton and neutrino mass matrices are invariant under specific residual symmetries contained in the finite discrete subgroups of $O(3)$. The groups $A_4$, $S_4$ and $A_5$ are the only such groups which can entirely fix $U$ at the leading order. The neutrinos can be (a) non-degenerate or (b) partially degenerate depending on the choice of their residual symmetries. One obtains either vanishing or very large ${\theta }_{13}$ in case of (a) while only $A_5$ can provide ${\theta }_{13}$ close to its experimental value in the case (b). We provide an explicit model based on $A_5$ and discuss a class of perturbations which can generate fully realistic neutrino masses and mixing maintaining the generalized $\mu$-$\tau$ symmetry in $U$. Our approach provides generalization of some of the ideas proposed earlier in order to obtain the predictions, ${\theta }_{23}=\pi /4$ and ${\delta }_{\mathrm{CP}}=\pm \pi /2$.

18 pages

References in corpus (15)

• Updated fit to three neutrino mixing: status of leptonic CP violation
• Neutrino oscillations refitted
• The Unique Horizontal Symmetry of Leptons
• The Horizontal Symmetry for Neutrino Mixing
• Symmetry of Lepton Mixing
• The golden ratio prediction for the solar neutrino mixing
• S_4 Flavored CP Symmetry for Neutrinos
• Lepton Mixing Patterns from a Scan of Finite Discrete Groups
• Discrete symmetries and model-independent patterns of lepton mixing
• Tribimaximal Mixing From Small Groups
• A Bottom-Up Approach to Lepton Flavor and CP Symmetries
• Group Theory and Dynamics of Neutrino Mixing
• [Re]constructing Finite Flavour Groups: Horizontal Symmetry Scans from the Bottom-Up
• Neutrino Mixing and CP Phase Correlations
• Discrete flavour symmetries for degenerate solar neutrino pair and their predictions

Cited by in corpus (52)

• Flavor structures of charged fermions and massive neutrinos
• A review of mu-tau flavor symmetry in neutrino physics
• Generalized $\mu -\tau$ reflection symmetry and leptonic CP violation
• Neutrino Mixing: $A_4$ Variations
• Trimaximal $\mu$-$\tau$ reflection symmetry
• Predictions for Leptonic Mixing Angle Correlations and Non-trivial Dirac CP Violation from $A_5$ with Generalised CP Symmetry
• Origin of Constrained Maximal CP Violation in Flavor Symmetry
• A variant of 3-3-1 model for the generation of the SM fermion mass and mixing pattern
• Soft $A_4\to Z_3$ Symmetry Breaking and Cobimaximal Neutrino Mixing
• $A_4$ and CP symmetry and a model with maximal CP violation
• Breakings of the neutrino mu-tau reflection symmetry
• Mu-tau symmetry and the Littlest Seesaw
• A 3-3-1 model with low scale seesaw mechanisms
• Neutrino mu-tau reflection symmetry and its breaking in the minimal seesaw
• Cobimaximal Neutrino Mixing from $S_3\times Z_2$
• Mu-tau reflection symmetry with a texture-zero
• Littlest Inverse Seesaw Model
• Mu-tau reflection symmetry with a high scale texture-zero
• Cobimaximal lepton mixing from soft symmetry breaking
• Consequences of $\mu -\tau$ Reflection Symmetry at DUNE
• A new and trivial CP symmetry for extended $A_4$ flavor
• Flavored Non-Minimal Left-Right Symmetric Model Fermion Masses and Mixings
• Cobimaximal Neutrino Mixing from $A_4$ and its Possible Deviation
• Interplay between $\mu$-$\tau$ reflection symmetry, four-zero texture and universal texture
• Neutrino masses and mixing in $A_5$ with flavour antisymmetry
• Exploring Partial $\mu$-$\tau$ Reflection Symmetry at DUNE and Hyper-Kamiokande
• Modifications to the neutrino mixing from the mu-tau reflection symmetry
• Maximal CP Violation in Flavor Neutrino Masses
• $\Delta \left(27\right)$ flavor singlet-triplet Higgs model for fermion masses and mixings
• Generalised $\mu$-$\tau$ symmetries and calculable gauge kinetic and mass mixing in $U(1{)}_{L_{\mu }-L_{\tau }}$ models
• Scotogenic model for co-bimaximal mixing
• Phase broken $\mu -\tau$ symmetry and the neutrino mass hierarchy
• Low scale type I seesaw model for lepton masses and mixings
• Muon anomalies and the $SU(5)$ Yukawa relations
• CP transformed mixed $\mu \tau$ antisymmetry for neutrinos and its consequences
• $\mu -\tau$ Reflection Symmetry and Its Explicit Breaking for Leptogenesis in a Minimal Seesaw Model
• A modified Friedberg-Lee symmetry for the TM1 neutrino mixing
• Consequences of $\mu$-$\tau$ reflection symmetry for $3+1$ neutrino mixing
• Almost exact diagonal reflection symmetries and three-zero texture
• Fully constrained mass matrix: Can symmetries alone determine the flavon vacuum alignments?
• On the textures of neutrino mass matrix for maximal atmospheric mixing angle and Dirac CP phase
• Theory Review of Neutrino Models and CP Violation
• Neutrino Parameters from Reactor and Accelerator Neutrino Experiments
• Pseudo-Dirac neutrinos from flavour dependent CP symmetry
• Diagonal reflection symmetries and universal four-zero texture
• Lepton and quark mixing patterns with generalized CP transformations
• An extended 3-3-1 model with two scalar triplets and linear seesaw mechanism
• Dirac neutrino mixings from hidden $\mu -\tau$ symmetry
• A lepton model with nearly Cobimaximal mixing
• Lepton mixing patterns from $PS{L}_2(7)$ with a generalised CP symmetry
• Leptogenesis in the $\mu \tau$ basis
• Fermion masses and mixings and charged lepton flavor violation in a 3-3-1 model with inverse seesaw