The $\mu$-$\tau$ reflection symmetry of Majorana neutrinos

Abstract

The observed pattern of lepton flavor mixing and CP violation strongly indicates the possible existence of a simple flavor symmetry in the neutrino sector -- the effective Majorana neutrino mass term keeps invariant when the three left-handed neutrino fields transform as ${\nu }_{e\mathrm{L}}^{}\to ({\nu }_{e\mathrm{L}}^{}{)}^c$, ${\nu }_{\mu \mathrm{L}}^{}\to ({\nu }_{\tau \mathrm{L}}^{}{)}^c$ and ${\nu }_{\tau \mathrm{L}}^{}\to ({\nu }_{\mu \mathrm{L}}^{}{)}^c$. A direct application of such a $\mu$-$\tau$ reflection symmetry to the canonical seesaw mechanism can help a lot to constrain the flavor textures of active and sterile Majorana neutrinos. The present article is intended to summarize the latest progress made in exploring the properties of this minimal flavor symmetry, its translational and rotational extensions, its soft breaking effects via radiative corrections from a superhigh energy scale to the electroweak scale, and its various phenomenological implications.

arXiv comment90 pages, 14 figures. Accepted for publication in Rept. Prog. Phys. and dedicated to the memory of Prof. Harald Fritzsch

References in corpus (232)

• Observation of electron-antineutrino disappearance at Daya Bay
• Evidence for High-Energy Extraterrestrial Neutrinos at the IceCube Detector
• Evidence for Neutrino Oscillations from the Observation of Electron Anti-neutrinos in a Muon Anti-Neutrino Beam
• Tri-Bimaximal Mixing and the Neutrino Oscillation Data
• The Reactor Antineutrino Anomaly
• Neutrino Physics with JUNO
• Observation of High-Energy Astrophysical Neutrinos in Three Years of IceCube Data
• Multi-messenger observations of a flaring blazar coincident with high-energy neutrino IceCube-170922A
• Neutrino emission from the direction of the blazar TXS 0506+056 prior to the IceCube-170922A alert
• Leptogenesis
• Improved Predictions of Reactor Antineutrino Spectra
• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Search for Majorana Neutrinos near the Inverted Mass Hierarchy Region with KamLAND-Zen
• Non-Abelian Discrete Symmetries in Particle Physics
• The Swampland: Introduction and Review
• Neutrino Mass and Mixing with Discrete Symmetry
• First observation of PeV-energy neutrinos with IceCube
• Evidence for ${\bar{\nu }}_{\mu }\to {\bar{\nu }}_e$ Oscillations from the LSND Experiment at LAMPF
• Neutrinoless Double-Beta Decay: Status and Prospects
• The Belle II Physics Book
• Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry
• Particle Physics with High Energy Neutrinos
• Nearly Tri-Bimaximal Neutrino Mixing and CP Violation
• Mass and Flavor Mixing Schemes of Quarks and Leptons
• Neutrino-less Double Beta Decay and Particle Physics
• Sterile Neutrino Oscillations: The Global Picture
• A Search for Electron Neutrino Appearance at the Delta m**2 ~ 1 eV**2 Scale
• Significant Excess of ElectronLike Events in the MiniBooNE Short-Baseline Neutrino Experiment
• Detecting Tau Neutrino Oscillations at PeV Energies
• Detecting Nutau Oscillations as PeV Energies
• A portrait of the Higgs boson by the CMS experiment ten years after the discovery
• A detailed map of Higgs boson interactions by the ATLAS experiment ten years after the discovery
• Cosmological Sign of Neutrino CP Violation
• Renormalization of the Neutrino Mass Operator
• Distinguishing seesaw models at LHC with multi-lepton signals
• Cosmic Microwave Background, Matter-Antimatter Asymmetry and Neutrino Masses
• Final Results of GERDA on the Search for Neutrinoless Double-$\beta$ Decay
• Mu-Tau Reflection Symmetry in Lepton Mixing and Neutrino Oscillations
• Updated Values of Running Quark and Lepton Masses
• Constraint on the Matter-Antimatter Symmetry-Violating Phase in Neutrino Oscillations
• Running Neutrino Masses, Mixings and CP Phases: Analytical Results and Phenomenological Consequences
• Updated global analysis of neutrino oscillations in the presence of eV-scale sterile neutrinos
• Status of non-standard neutrino interactions
• Running Neutrino Mass Parameters in See-Saw Scenarios
• Neutrino Masses and the LHC: Testing Type II Seesaw
• Unitarity of the Leptonic Mixing Matrix
• Some Simple Mixing and Mass Matrices for Neutrinos
• Renormalization Group Equations for Seesaw Neutrino Masses
• Flavor structures of charged fermions and massive neutrinos
• Global constraints on heavy neutrino mixing
• Analytic Approximations for Three Neutrino Oscillation Parameters and Probabilities in Matter
• The Neutrino Mass Window for Baryogenesis
• Neutrino Mass Models
• Non-unitarity of the leptonic mixing matrix: Present bounds and future sensitivities
• A possible symmetry of the $\nu$MSM
• Neutrino Mass Operator Renormalization Revisited
• Search for Neutrinoless Double-Beta Decay with the Complete EXO-200 Dataset
• Lepton Mass Hierarchy and Neutrino Oscillations
• Physics Potential of a Long Baseline Neutrino Oscillation Experiment Using J-PARC Neutrino Beam and Hyper-Kamiokande
• The Unique Horizontal Symmetry of Leptons
• Possible Alternatives to Tri-bimaximal Mixing
• Updated Global 3+1 Analysis of Short-BaseLine Neutrino Oscillations
• Non-Unitarity, sterile neutrinos, and Non-Standard neutrino Interactions
• General RG Equations for Physical Neutrino Parameters and their Phenomenological Implications
• Leptonic CP violation
• Can Neutrinos be Degenerate in Mass?
• Large Leptonic Flavor Mixing and the Mass Spectrum of Leptons
• Neutrinoless Double-Beta Decay: a Probe of Physics Beyond the Standard Model
• Current unknowns in the three neutrino framework
• Charged Lepton Flavor Violation: An Experimenter's Guide
• Light Sterile Neutrinos: Models and Phenomenology
• CP and Discrete Flavour Symmetries
• Residual Symmetries for Neutrino Mixing with a Large theta_13 and Nearly Maximal delta_D
• Small Neutrino Masses from Supersymmetry Breaking
• A review of mu-tau flavor symmetry in neutrino physics
• Detection of a particle shower at the Glashow resonance with IceCube
• Flavor Mixing and CP Violation of Massive Neutrinos
• Z_2 Symmetry Prediction for the Leptonic Dirac CP Phase
• Primordial Lepton Family Asymmtries in Seesaw Model
• Automorphisms in Gauge Theories and the Definition of CP and P
• Light sterile neutrinos
• Manifest CP Violation from Majorana Phases
• Neutrino Mass Matrix Running for Non-Degenerate See-Saw Scales
• Impacts of the Higgs mass on vacuum stability, running fermion masses and two-body Higgs decays
• Nearly Tri-bimaximal Neutrino Mixing and CP Violation from mu-tau Symmetry Breaking
• Non-Standard Interactions in Radiative Neutrino Mass Models
• Pathways to Naturally Small Dirac Neutrino Masses
• Neutrino mass hierarchy and Majorana CP phases within the Higgs triplet model at the LHC
• Tri-bimaximal Neutrino Mixing and Flavor-dependent Resonant Leptogenesis
• Neutrino Masses, Lepton Flavor Mixing and Leptogenesis in the Minimal Seesaw Model
• Correlation between the Charged Current Interactions of Light and Heavy Majorana Neutrinos
• Search for a Light Sterile Neutrino at Daya Bay
• A full parametrization of the 6 X 6 flavor mixing matrix in the presence of three light or heavy sterile neutrinos
• Common Origin of mu-tau and CP Breaking in Neutrino Seesaw, Baryon Asymmetry, and Hidden Flavor Symmetry
• Flavor Ratios of Astrophysical Neutrinos: Implications for Precision Measurements
• Light Sterile Neutrino in the Minimal Extended Seesaw
• Mass Independent Textures and Symmetry
• Running Neutrino Masses, Leptonic Mixing Angles and CP-Violating Phases: From $M_{\mathrm{Z}}$ to ${\Lambda }_{\mathrm{GUT}}$
• Improved Search for a Light Sterile Neutrino with the Full Configuration of the Daya Bay Experiment
• Common Origin of Soft mu-tau and CP Breaking in Neutrino Seesaw and the Origin of Matter
• Upper Bound of Neutrino Masses from Combined Cosmological Observations and Particle Physics Experiments
• Relatively large theta13 and nearly maximal theta23 from the approximate S3 symmetry of lepton mass matrices
• Soft L_e-L_mu-L_tau flavour symmetry breaking and sterile neutrino keV Dark Matter
• Dirac neutrinos from flavor symmetry
• Naturalness and Testability of TeV Seesaw Mechanisms
• Flavor Symmetry L_e - L_mu - L_tau, Atmospheric Neutrino Mixing and CP Violation in the Lepton Sector
• Flavor mixings and textures of the fermion mass matrices
• Nonstandard neutrino interactions at DUNE, T2HK and T2HKK
• Renormalization group running of neutrino parameters
• A See-Saw Model for Atmospheric and Solar Neutrino Oscillations
• A(4) Flavor Symmetry Model for Dirac-Neutrinos and Sizable U(e3)
• Precise Values of Running Quark and Lepton Masses in the Standard Model
• mu-tau Interchange symmetry and lepton mixing
• Improved Constraints on Sterile Neutrino Mixing from Disappearance Searches in the MINOS, MINOS+, Daya Bay, and Bugey-3 Experiments
• Naturally Small Dirac Neutrino Mass with Intermediate $SU(2{)}_L$ Multiplet Fields
• Grand unification of $\mu -\tau$ Symmetry
• Radiative Corrections to Neutrino Mixing and CP Violation in the Minimal Seesaw Model with Leptogenesis
• Littlest Seesaw
• Broken S_3 Flavor Symmetry of Leptons and Quarks: Mass Spectra and Flavor Mixing Patterns
• Trimaximal $\mu$-$\tau$ reflection symmetry
• Large Mixing Angle MSW Solution in S_3 Flavor Symmetry
• Implications of $\mu -\tau$ Flavored CP Symmetry of Leptons
• Minimal Mass Matrices for Dirac Neutrinos
• Neutrino Telescopes as a Probe of Broken $\mu$-$\tau$ Symmetry
• Dirac Neutrinos with $S_4$ Flavor Symmetry in Warped Extra Dimensions
• The minimal seesaw and leptogenesis models
• The smallest neutrino mass
• Naturally Light Dirac Neutrino in Left-Right Symmetric Model
• Fermion Masses and Mixings in a $\mu$-$\tau$ symmetric SO(10)
• Models of Lepton and Quark Masses
• Complete One-loop Matching of the Type-I Seesaw Model onto the Standard Model Effective Field Theory
• Radiative corrections and explicit perturbations to the tetra-maximal neutrino mixing with large theta_13
• Democratic Neutrino Mixing Reexamined
• An approach to permutation symmetry for the electroweak theory
• Lepton Mass Matrices with Four Texture Zeros
• A Generic Diagonalization of the 3X3 Neutrino Mass Matrix and Its Implications on the mu-tau Flavor Symmetry and Maximal CP Violation
• Can four-zero-texture mass matrix model reproduce the observed quark and lepton mixing angles and CP violating phases?
• Perturbed S3 neutrinos
• Vanishing Effective Mass of the Neutrinoless Double Beta Decay?
• Sterile Neutrinos for Warm Dark Matter and the Reactor Anomaly in Flavor Symmetry Models
• Properties of CP Violation in Neutrino-Antineutrino Oscillations
• Majorana CP-violating phases in neutrino-antineutrino oscillations and other lepton-number-violating processes
• Neutrino Anti-neutrino Transitions
• On the four-zero texture of quark mass matrices and its stability
• Naturally small Dirac neutrino masses in supergravity
• A partial $\mu$-$\tau$ symmetry and its prediction for leptonic CP violation
• Towards the meV limit of the effective neutrino mass in neutrinoless double-beta decays
• Neutrino mixing with broken $S_3$ symmetry
• Breakings of the neutrino mu-tau reflection symmetry
• Relic Right-handed Dirac Neutrinos and Implications for Detection of Cosmic Neutrino Background
• Tetra-maximal Neutrino Mixing and Its Implications on Neutrino Oscillations and Collider Signatures
• Mu-tau symmetry and the Littlest Seesaw
• The Symmetry behind Extended Flavour Democracy and Large Leptonic Mixing
• On the origin of matter in the Universe
• Lepton Number And Neutrino Masses
• Neutrino mu-tau reflection symmetry and its breaking in the minimal seesaw
• Hidden Symmetry of the CKM and Neutrino Mapping Matrices
• Mu-tau reflection symmetry with a texture-zero
• Renormalization Group Evolution of Dirac Neutrino Masses
• The $\mu$-$\tau$ mixed symmetry and neutrino mass matrix
• One-loop Matching of the Type-II Seesaw Model onto the Standard Model Effective Field Theory
• Flavour-dependent radiative correction to neutrino-neutrino refraction
• Global oscillation data analysis on the $3\nu$ mixing without unitarity
• How to interpret a discovery or null result of the $0\nu 2\beta$ decay
• Mu-tau reflection symmetry with a high scale texture-zero
• Generating ${\theta }_{13}$ from sterile neutrinos in $\mu -\tau$ symmetric models
• Texture Zeros for Dirac Neutrinos and Current Experimental Tests
• Non-unitary Leptonic Flavor Mixing and CP Violation in Neutrino-antineutrino Oscillations
• Neutrino mass ordering and μ-τreflection symmetry breaking
• The $\mu -\tau$ reflection symmetry of Dirac neutrinos and its breaking effect via quantum corrections
• Radiative Decays of Charged Leptons in the Seesaw Effective Field Theory with One-loop Matching
• Resolving the octant of theta_{23} via radiative mu-tau symmetry breaking
• The effective neutrino mass of neutrinoless double-beta decays: how possible to fall into a well
• Lepton masses and mixing angles from heterotic orbifold models
• Neutrino Sector with Majorana Mass Terms and Friedberg-Lee Symmetry
• A combination of the neutrino trimaximal mixings and mu-tau reflection symmetry in the type-I seesaw model
• Littlest Seesaw model from S4 x U(1)
• Generalization of Friedberg-Lee Symmetry
• Littlest Modular Seesaw
• Renormalization-Group Equations of Neutrino Masses and Flavor Mixing Parameters in Matter
• Interplay between $\mu$-$\tau$ reflection symmetry, four-zero texture and universal texture
• Jarlskog Invariant of the Neutrino Mapping Matrix
• Common origin of reactor and sterile neutrino mixing
• Modifications to the neutrino mixing from the mu-tau reflection symmetry
• Compatibility of $A_4$ Flavour Symmetric Minimal Extended Seesaw with $(3+1)$ Neutrino Data
• Neutrino mixing in matter
• Correlation of normal neutrino mass ordering with upper octant of ${\theta }_{23}^{}$ and third quadrant of $\delta$ via RGE-induced $\mu$-$\tau$ symmetry breaking
• Radiative decays of charged leptons as constraints of unitarity polygons for active-sterile neutrino mixing and CP violation
• Tri-Bimaximal Mixing from Twisted Friedberg-Lee Symmetry
• Non-zero ${\theta }_{13}$ with Unbroken $\mu -\tau$ Symmetry of the Active Neutrino Mass Matrix in the Presence of a Light Sterile Neutrino
• Correlations between quark mass and flavor mixing hierarchies
• Neutrino mass determination from a four-zero texture mass matrix
• The Friedberg-Lee Symmetry and Minimal Seesaw Model
• Discrete symmetries and mixing of Dirac neutrinos
• On the two-loop radiative origin of the smallest neutrino mass and the associated Majorana CP phase
• Phase broken $\mu -\tau$ symmetry and the neutrino mass hierarchy
• Neutrino Oscillation in Dense Matter
• Littlest mu-tau seesaw
• A full parametrization of the $9\times 9$ active-sterile flavor mixing matrix in the inverse or linear seesaw scenario of massive neutrinos
• Flavoured leptogenesis and ${\mathrm{CP}}^{\mu \tau }$ symmetry
• Generic Friedberg-Lee Symmetry of Dirac Neutrinos
• Integral solutions to the one-loop renormalization-group equations for lepton flavor mixing parameters and the Jarlskog invariant
• Leptogenesis in a model with Friedberg-Lee symmetry
• A Comprehensive Renormalisation Group Analysis of the Littlest Seesaw Model
• Renormalisation Group Corrections to the Littlest Seesaw Model and Maximal Atmospheric Mixing
• The Kobayashi-Maskawa Parametrization of Lepton Flavor Mixing and Its Application to Neutrino Oscillations in Matter
• Nonstandard neutrino interactions and mu-tau reflection symmetry
• Impact of RGE-induced $\mu -\tau$ Reflection Symmetry Breaking on the Effective Majorana Neutrino Mass in $0\nu \beta \beta$ Decay
• A further study of μ-τsymmetry breaking at neutrino telescopes after the Daya Bay and RENO measurements of θ_{13}
• Importance of generalized $\mu \tau$ symmetry and its CP extension on neutrino mixing and leptogenesis
• A modified Friedberg-Lee symmetry for the TM1 neutrino mixing
• Seesaw mirroring between light and heavy Majorana neutrinos with the help of the $S_3^{}$ reflection symmetry
• Leptonic unitarity triangles: RGE running effects and $\mu$-$\tau$ reflection symmetry breaking
• Renormalization group evolution induced leptogenesis in the minimal seesaw model with the trimaximal mixing and mu-tau reflection symmetry
• Generalized Friedberg-Lee model for CP violation in neutrino physics
• Consequences of $\mu$-$\tau$ reflection symmetry for $3+1$ neutrino mixing
• Complete One-loop Structure of the Type-(I+II) Seesaw Effective Field Theory
• A Timeon Model of Quark and Lepton Mass Matrices
• Diagonal reflection symmetries, four-zero texture, and trimaximal mixing with predicted ${\theta }_{13}$ in an $A_4$ symmeric model
• Phenomenological implications of the Friedberg-Lee transformation in a neutrino mass model with $\mu \tau$-flavored CP symmetry
• Further study on the textures of neutrino mass matrix for maximal atmospherical mixing angle and Dirac CP phase
• On the textures of neutrino mass matrix for maximal atmospheric mixing angle and Dirac CP phase
• The Smallest Neutrino Mass Revisited
• 3D mapping of the effective Majorana neutrino masses with neutrino oscillation data
• Deviations of the Lepton Mapping Matrix from the Harrison-Perkins-Scott Form
• Identifying a minimal flavor symmetry of the seesaw mechanism behind neutrino oscillations
• A translational flavor symmetry in the mass terms of Dirac and Majorana fermions
• The translational $\mu$-$\tau$ reflection symmetry of Majorana neutrinos
• Particular textures of the minimal seesaw model
• A split seesaw model with hidden neutrinoless double beta decay but successful leptogenesis
• Leptogenesis in the $\mu \tau$ basis
• Breaking of the tetra-maximal neutrino mixing pattern

Cited by in corpus (8)

• A Realistic Neutrino mixing scheme arising from $A_4$ symmetry
• Unveiling Neutrino Mysteries with $\Delta (27)$ Symmetry
• Low scale leptogenesis under neutrino $\mu$-$\tau$ reflection symmetry
• A Nearest-neighbor Expansion of Lepton Flavor Mixing in Powers of the $\mu$-$\tau$ Permutation Symmetry Breaking Effect
• A lepton model with nearly Cobimaximal mixing
• Experimental Constraints on Seesaw Parameters in the Wigner-like Parametrization
• Approximate magic symmetry in a cobimaximal scenario of Majorana neutrinos
• Minimal structure for neutrino mass matrix