A Generic Diagonalization of the 3X3 Neutrino Mass Matrix and Its Implications on the mu-tau Flavor Symmetry and Maximal CP Violation

Abstract

In the flavor basis where the mass eigenstates of three charged leptons are identified with their flavor eigenstates, one may diagonalize a 3 X 3 Majorana neutrino mass matrix M_nu by means of the standard parametrization of the 3 X 3 neutrino mixing matrix V. In this treatment the unphysical phases of M_nu have to be carefully factored out, unless a special phase convention for neutrino fields is chosen so as to simplify M_nu to M'_nu without any unphysical phases. We choose this special flavor basis and establish some exact analytical relations between the matrix elements of M'_nu M'_nu^dag and seven physical parameters --- three neutrino masses (m_1, m_2, m_3), three flavor mixing angles (theta_12, theta_13, theta_23) and the Dirac CP-violating phase (delta). Such results allow us to derive the conditions for the mu-tau flavor symmetry with theta_23 = pi/4 and maximal CP violation with delta = +/- pi/2, which should be useful for discussing specific neutrino mass models. In particular, we show that theta_23 = pi/4 and delta = +/- pi/2 keep unchanged when constant matter effects are taken into account for a long-baseline neutrino oscillation experiment.

11 pages. More discussions and references added. To appear in PLB

References in corpus (33)

• Underlying A_4 Symmetry for the Neutrino Mass Matrix and the Quark Mixing Matrix
• Mass and Flavor Mixing Schemes of Quarks and Leptons
• Low energy effects of neutrino masses
• Unitarity of the Leptonic Mixing Matrix
• Updated global fit to three neutrino mixing: status of the hints of theta13 > 0
• A non-standard CP transformation leading to maximal atmospheric neutrino mixing
• CP-violation from non-unitary leptonic mixing
• Models of Neutrino Masses and Mixings
• Flavor Mixing and CP Violation of Massive Neutrinos
• The Simplest Neutrino Mass Matrix
• Nearly Tri-bimaximal Neutrino Mixing and CP Violation from mu-tau Symmetry Breaking
• Plato's Fire and the Neutrino Mass Matrix
• Correlation between the Charged Current Interactions of Light and Heavy Majorana Neutrinos
• Probing non-unitary mixing and CP-violation at a Neutrino Factory
• μ-τSymmetry and Maximal CP Violation
• Naturalness and Testability of TeV Seesaw Mechanisms
• How to Describe Neutrino Mixing and CP Violation
• New Formulation of Matter Effects on Neutrino Mixing and CP Violation
• Implications of Leptonic Unitarity Violation at Neutrino Telescopes
• Multiple seesaw mechanisms of neutrino masses at the TeV scale
• 'Mu-Tau' symmetry, tribimaximal mixing and four zero neutrino Yukawa textures
• Non-standard interactions versus non-unitary lepton flavor mixing at a neutrino factory
• Tetra-maximal Neutrino Mixing and Its Implications on Neutrino Oscillations and Collider Signatures
• Right Unitarity Triangles, Stable CP-violating Phases and Approximate Quark-Lepton Complementarity
• Determination of Neutrino Mass Texture for Maximal CP Violation
• Theoretical Overview of Neutrino Properties
• Correlation between Leptonic CP Violation and mu-tau Symmetry Breaking
• General Property of Neutrino Mass Matrix and CP Violation
• Neutrino Mass Textures with Maximal CP Violation
• Leptonic CP Violation Induced by Approximately mu-tau Symmetric Seesaw Mechanism
• Majorana CP Violation in Approximately μ-τSymmetric Models with det(M_ν)=0
• Friedberg-Lee symmetry and tri-bimaximal neutrino mixing in the inverse seesaw mechanism
• Flavor Neutrino Masses giving sinθ_{13}=0

Cited by in corpus (32)

• Flavor structures of charged fermions and massive neutrinos
• A review of mu-tau flavor symmetry in neutrino physics
• Neutrino Mass, Dark Matter and Anomalous Magnetic Moment of Muon in a $U(1{)}_{L_{\mu }-L_{\tau }}$ Model
• Radiative neutrino masses, lepton flavor mixing and muon $g-2$ in a leptoquark model
• The $\mu$-$\tau$ reflection symmetry of Majorana neutrinos
• On Neutrino Mixing in Matter and CP and T Violation Effects in Neutrino Oscillations
• The $\mu -\tau$ reflection symmetry of Dirac neutrinos and its breaking effect via quantum corrections
• CP violation in neutrino mixing with $\delta =-\pi /2$ in $A_4$ Type-II seesaw model
• Interplay between $\mu$-$\tau$ reflection symmetry, four-zero texture and universal texture
• Flavored Non-Minimal Left-Right Symmetric Model Fermion Masses and Mixings
• Maximal CP Violation in Flavor Neutrino Masses
• Charged Lepton Corrections to Scaling Neutrino Mixing
• Correlation of normal neutrino mass ordering with upper octant of ${\theta }_{23}^{}$ and third quadrant of $\delta$ via RGE-induced $\mu$-$\tau$ symmetry breaking
• On ${\mathbf{Q}}_6$ flavor symmetry and the breaking of $\mu \leftrightarrow \tau$ symmetry
• Phase broken $\mu -\tau$ symmetry and the neutrino mass hierarchy
• The Kobayashi-Maskawa Parametrization of Lepton Flavor Mixing and Its Application to Neutrino Oscillations in Matter
• Neutrino Mass Textures and Partial $\mu$-$\tau$ Symmetry
• Bi-pair Neutrino Mixing
• Discriminating the HTM and MLRSM models in collider studies via doubly charged Higgs boson pair production and the subsequent leptonic decays
• Baryon asymmetry from leptogenesis with four zero neutrino Yukawa textures
• A minimal inverse seesaw model with $S_4$ flavour symmetry
• Almost exact diagonal reflection symmetries and three-zero texture
• Further study on the textures of neutrino mass matrix for maximal atmospherical mixing angle and Dirac CP phase
• Fermion Masses and Mixing in General Warped Extra Dimensional Models
• Leptonic CP Violation Phases, Quark-Lepton Similarity and Seesaw Mechanism
• Diagonal reflection symmetries and universal four-zero texture
• CP violation in bipair neutrino mixing
• Partial $\mu -\tau$ Textures and Leptogenesis
• Neutrino Mixing and Leptogenesis in $\mu -\tau$ Symmetry
• Phases of Flavor Neutrino Masses and CP Violation
• Exploring the Null Results in the Direct Detection Experiments, $(g-2{)}_{\ell }$ and Neutrino Mass in an Extended $U(1{)}_{L_{\mu }-L_{\tau }}$ Model Constrained through the $Z\to {\ell }^{+}{\ell }^{-}$ Decays
• Rotated $\mu$\,--\,$\tau$ Symmetry for One Generic Neutrino Mixing Angle: An analytical Study