Plato's Fire and the Neutrino Mass Matrix

Abstract

With the accumulation of many years of solar and atmospheric neutrino oscillation data, the approximate form of the 3 X 3 neutrino mixing matrix is now known. The theoretical challenge is to understand where this mixing matrix comes from. Recently, a remarkable fact was discovered that for a specific pattern of the neutrino mass matrix at a high scale, any flavor-changing radiative correction will automatically lead to the desired mixing matrix. It was also discovered that the required specific pattern at the high scale can be maintained by the non-Abelian discrete symmetry A_4 which is also the symmetry group of the regular tetrahedron, one of five perfect geometric solids known to Plato who associated it with the element ``fire''. I discuss this recent development and add to it a new and very simple mechanism for the implementation of the flavor-changing radiative correction.

12 pages, to appear as a Brief Review in MPLA

Cited by in corpus (103)

• The Search for Heavy Majorana Neutrinos
• Flavour physics of leptons and dipole moments
• Flavor structures of charged fermions and massive neutrinos
• A_4 Symmetry and Neutrinos with Very Different Masses
• Neutrino Mixing and Quark-Lepton Complementarity
• A non-standard CP transformation leading to maximal atmospheric neutrino mixing
• The Unique Horizontal Symmetry of Leptons
• A review of mu-tau flavor symmetry in neutrino physics
• Obtaining the Neutrino Mixing Matrix with the Tetrahedral Group
• Tribimaximal Neutrino Mixing from a Supersymmetric Model with A_4 Family Symmetry
• Neutrino Mass Matrix from S_4 Symmetry
• Phenomenological Tests of Supersymmetric A_4 Family Symmetry Model of Neutrino Mass
• Tetrahedral Family Symmetry and the Neutrino Mixing Matrix
• Hybrid Seesaw Neutrino Masses with A_4 Family Symmetry
• Breaking Tri-bimaximal Mixing and Large ${\theta }_{13}$
• Tri-bimaximal mixing, discrete family symmetries, and a conjecture connecting the quark and lepton mixing matrices
• Neutrino Mass Matrix from Delta(27) Symmetry
• Suitability of A_4 as a Family Symmetry in Grand Unification
• Lepton masses, mixings and FCNC in a minimal S_3-invariant extension of the Standard Model
• Dihedral Families of Quarks, Leptons and Higgs Bosons
• Supersymmetric A_4 X Z_3 and A_4 Realizations of Neutrino Tribimaximal Mixing Without and With Corrections
• Running Neutrino Masses, Leptonic Mixing Angles and CP-Violating Phases: From $M_{\mathrm{Z}}$ to ${\Lambda }_{\mathrm{GUT}}$
• μ-τSymmetry and Maximal CP Violation
• Upper Bounds on Lepton-number Violating Processes
• Relatively large theta13 and nearly maximal theta23 from the approximate S3 symmetry of lepton mass matrices
• Resolving the octant of theta23 with T2K and NOvA
• Flavor mixings and textures of the fermion mass matrices
• Neutrino masses and mixing from S4 flavor twisting
• Higgs Potential in Minimal S_3 Invariant Extension of the Standard Model
• mu-tau Interchange symmetry and lepton mixing
• Non-Abelian Discrete Symmetries and Neutrino Masses: Two Examples
• Maximal atmospheric neutrino mixing and the small ratio of muon to tau mass
• Scotogenic $A_4$ Neutrino Model for Nonzero ${\theta }_{13}$ and Large ${\delta }_{CP}$
• Phased Breaking of mu-tau symmetry and Leptogenesis
• Radiative Origin of All Quark and Lepton Masses through Dark Matter with Flavor Symmetry
• Dark Scalar Doublets and Neutrino Tribimaximal Mixing from A_4 Symmetry
• Neutrino Mass and New Physics
• Exact $S_3$ symmetry solving the supersymmetric flavor problem
• Discrete Flavor Symmetry, Dynamical Mass Textures, and Grand Unification
• Trimaximal $\mu$-$\tau$ reflection symmetry
• Origin of Constrained Maximal CP Violation in Flavor Symmetry
• Texture 4 zero Fritzsch-like lepton mass matrices
• New Simple A_4 Neutrino Model for Nonzero θ_{13} and Large δ_{CP}
• Neutrino Mixing and Geometric CP Violation with Delta(27) Symmetry
• Nonabelian Discrete Family Symmetry to Soften the SUSY Flavor Problem and to Suppress Proton Decay
• Neutrino mixing matrix in the 3-3-1 model with heavy leptons and $A_4$ symmetry
• Scotogenic $Z_2$ or $U(1{)}_D$ Model of Neutrino Mass with $\Delta (27)$ Symmetry
• Octant of ${\theta }_{23}$ in danger with a light sterile neutrino
• Deviation of Atmospheric Mixing from Maximal and Structure in the Leptonic Flavor Sector
• Form Invariance of the Neutrino Mass Matrix
• Resolving theta_{23} Degeneracy by Accelerator and Reactor Neutrino Oscillation Experiments
• Lepton Flavor Model from Delta(54) Symmetry
• Can four-zero-texture mass matrix model reproduce the observed quark and lepton mixing angles and CP violating phases?
• A Generic Diagonalization of the 3X3 Neutrino Mass Matrix and Its Implications on the mu-tau Flavor Symmetry and Maximal CP Violation
• Generating extremal neutrino mixing angles with Higgs family symmetries
• S_3-flavour symmetry as realized in lepton flavour violating processes
• Determination of theta_{23} in Long-Baseline Neutrino Oscillation Experiments with Three-Flavor Mixing Effects
• A New Type of Complex Neutrino Mass Texture and mu-tau Symmetry
• New Lepton Family Symmetry and Neutrino Tribimaximal Mixing
• Deviation from tri-bimaximal mixing and flavor symmetry breaking in a seesaw type A4 model
• Texture specific mass matrices with Dirac neutrinos and their implications
• Transformative A_4 Mixing of Neutrinos with CP Violation
• Possible textures of the fermion mass matrices
• Discrete symmetries and models of flavor mixing
• Determination of Neutrino Mass Texture for Maximal CP Violation
• $\mu -\tau$ Symmetry and Radiatively Generated Leptogenesis
• Delta(54) Flavor Model for Leptons and Sleptons
• Radiative corrections to neutrino mass matrix in the Standard Model and beyond
• Soft supersymmetry breaking terms from A4 lepton flavor symmetry
• Broken Flavor 2 <-> 3 Symmetry and phenomenological approach for universal quark and lepton mass matrices
• Correlation between Leptonic CP Violation and mu-tau Symmetry Breaking
• Tri-bimaximal Mixing and Cabibbo Angle in S4 Flavor Model with SUSY
• Exploring the parameter space of texture 4 zero quark mass matrices
• Triplicity of Quarks and Leptons
• Non-Abelian Discrete Flavor Symmetries
• General Property of Neutrino Mass Matrix and CP Violation
• Neutrino Mass Textures with Maximal CP Violation
• New "Square Root" Model of Lepton Family Cyclic Symmetry
• Maximal CP Violation in Flavor Neutrino Masses
• Semidirect Product Groups, Vacuum Alignment and Tribimaximal Neutrino Mixing
• Investigating non-Fritzsch like texture specific quark mass matrices
• Self-Organizing Neutrino Mixing Matrix
• Double Suppression of FCNCs in Supersymmetric Models
• Dihedral Flavor Symmetry from Dimensional Deconstruction
• Non-Abelian Discrete Flavor Symmetries on Orbifolds
• Towards Minimal S4 Lepton Flavor Model
• Maximal CP Violation in Minimal Seesaw Model
• Radiative Scaling Neutrino Mass with $A_4$ Symmetry
• The Kobayashi-Maskawa Parametrization of Lepton Flavor Mixing and Its Application to Neutrino Oscillations in Matter
• Heptagonic Symmetry for Quarks and Leptons
• A potential scenario for the Majorana neutrino detection at future lepton colliders
• Like-sign dimuon asymmetry of B0 meson and LFV in SU(5) SUSY GUT with S4 flavor symmetry
• Neutrino mass matrix in triplet Higgs models with $A_4$ symmetry
• A(4) Symmetry and Neutrinos
• A close look on 2-3 mixing angle with DUNE in light of current neutrino oscillation data
• Neutrino Parameters from Reactor and Accelerator Neutrino Experiments
• Dynamical $\mu$ and MSSM
• Identifying a minimal flavor symmetry of the seesaw mechanism behind neutrino oscillations
• Quark Mixing from Mass Matrix Model with Flavor 2 (\leftrightarrow) 3 Symmetry
• Investigating texture six zero lepton mass matrices
• Tribimaximal Neutrino Mixing from A_4 Replication
• String Field Theory from Quantum Gravity
• The Higgs Connection -- Flavor and Dark Matter