Gauge boson families in grand unified theories of fermion masses: E_6^4 x S_4

Abstract

In third quantization the origin of fermion families is easy to understand: the electron field, the muon field and the tau field are identical fields in precisely the same sense as three electrons are identical and undistinguishable particles of a theory of second quantization. In both cases, the permutation of these fields or particles leaves the lagrangian invariant. One can also extend the concept of family to gauge bosons. This can be obtained through the semidirect product of the gauge group with the group of permutations of n objects. In this paper we have studied the group E_6^4 x S_4. We explain why we have chosen E_6 as fundamental gauge group factor and why we start with a model with four gauge boson/fermion families to accommodate and to fit the standard model with only three fermion families. We suggest a possible symmetry breaking pattern of E_6^4 x S_4 that could explain quark, lepton and neutrino masses and mixings.

arXiv comment21 pages, no figure

References in corpus (65)

• Evidence for oscillation of atmospheric neutrinos
• Direct Evidence for Neutrino Flavor Transformation from Neutral-Current Interactions in the Sudbury Neutrino Observatory
• First Results from KamLAND: Evidence for Reactor Anti-Neutrino Disappearance
• Limits on Neutrino Oscillations from the CHOOZ Experiment
• Search for neutrino oscillations on a long base-line at the CHOOZ nuclear power station
• Determination of Solar Neutrino Oscillation Parameters using 1496 Days of Super-Kamiokande-I Data
• Status of global fits to neutrino oscillations
• Tau Neutrinos Favored over Sterile Neutrinos in Atmospheric Muon Neutrino Oscillations
• Underlying A_4 Symmetry for the Neutrino Mass Matrix and the Quark Mixing Matrix
• Softly Broken A_4 Symmetry for Nearly Degenerate Neutrino Masses
• Tri-Bimaximal Neutrino Mixing from Discrete Symmetry in Extra Dimensions
• Mass and Flavor Mixing Schemes of Quarks and Leptons
• Mu-Tau Reflection Symmetry in Lepton Mixing and Neutrino Oscillations
• Global analysis of three-flavor neutrino masses and mixings
• Not Even Decoupling Can Save Minimal Supersymmetric SU(5)
• Permutation Symmetry, Tri-Bimaximal Neutrino Mixing and the S3 Group Characters
• A 2-3 Symmetry in Neutrino Oscillations
• Bimaximal Neutrino Mixing and Neutrino Mass Matrix
• Tri-bimaximal Neutrino Mixing from Orbifolding
• Large Leptonic Flavor Mixing and the Mass Spectrum of Leptons
• A4 family symmetry and quark-lepton unification
• $S_3$ Symmetry and Tri-bimaximal Mixing
• Tribimaximal Neutrino Mixing from a Supersymmetric Model with A_4 Family Symmetry
• Proton Decay in Minimal Supersymmetric SU(5)
• Broken mu-tau Symmetry and Leptonic CP Violation
• Exceptional Supersymmetric Standard Model
• The solar LMA neutrino oscillation solution in the Zee model
• Neutrino Mass Matrix from S_4 Symmetry
• Phenomenological Tests of Supersymmetric A_4 Family Symmetry Model of Neutrino Mass
• Precision Corrections to Supersymmetric Unification
• Large neutrino mixing and normal mass hierarchy: a discrete understanding
• Deviations from Tribimaximal Neutrino Mixing
• The strong coupling, unification, and recent data
• Maximal Neutrino Mixing and Maximal CP Violation
• The All-Purpose Neutrino Mass Matrix
• Quark Masses and Mixing with A4 Family Symmetry
• An SO(10)XS-4 Scenario for Naturally Degenerate Neutrinos
• An SO(10) GUT Model with $S4$ Flavor Symmetry
• Higgs Potential in Minimal S_3 Invariant Extension of the Standard Model
• Non-Abelian Discrete Symmetries and Neutrino Masses: Two Examples
• Grand unification of $\mu -\tau$ Symmetry
• Discrete Flavor Symmetry, Dynamical Mass Textures, and Grand Unification
• Large Mixing Angle MSW Solution in S_3 Flavor Symmetry
• E_6 Unification, Doublet-Triplet Splitting and Anomalous U(1)_A Symmetry
• E_6 Unification with Bi-Large Neutrino Mixing
• Scaling in the Neutrino Mass Matrix
• Neutrino 2-3 Symmetry and Inverted Hierarchy
• Permutation Symmetry S_3 and VEV Structure of Flavor-Triplet Higgs Scalars
• Universal Seesaw Mass Matrix Model with an S_3 Symmetry
• Flavor Mass and Mixing and S_3 Symmetry -- An S_3 Invariant Model Reasonable to All --
• Democratic Neutrino Mixing Reexamined
• Majorana Phase in Minimal S_3 Invariant Extension of the Standard Model
• An approach to permutation symmetry for the electroweak theory
• Fermion Masses and Coupling Unification in E6. Life in the Desert
• Neutrino masses and mixings with an S3 family permutation symmetry
• Democratic Neutrino Mixing and Radiative Corrections
• Neutrino Masses in the Effective Rank-5 Subgroups of E_6 I: Non-supersymmetric Case
• Two predictive supersymmetric S3 x Z2 models for the quark mass matrices
• Neutrino Masses in the Effective Rank-5 Subgroups of E_6 II: Supersymmetric Case
• Fermion masses in E_6 grand unification with family permutation symmetries
• Precision Test of Quark Mass Textures: A Model Independent Approach
• Higgs Doublets as Pseudo Nambu-Goldstone Bosons in Supersymmetric E_6 Unification
• Quark masses and mixings in E6 x S3 : a montecarlo approach
• E_6 unification model building III. Clebsch-Gordan coefficients in E_6 tensor products of the 27 with higher dimensional representations
• The problem of hierarchies and family replications in an extension of quantum field theory

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• Fermion Masses and Mixings in a S4 Based Model
• Phenomenological Consequences of See-Saw in S4 Based Models
• Is S4 the horizontal symmetry of tri-bimaximal lepton mixing?
• Tri-bimaximal Neutrino Mixing from A(4) and θ_{13} \sim θ_C
• The 3-3-1 model with S_4 flavor symmetry
• The Interplay Between GUT and Flavour Symmetries in a Pati-Salam x S4 Model
• Tri-Bimaximal Lepton Mixing and Leptogenesis
• An A4 model for lepton masses and mixings
• On the finite subgroups of U(3) of order smaller than 512
• Generation Symmetry and E_6 Unification
• Natural Vacuum Alignment from Group Theory: The Minimal Case
• Flavored Orbifold GUT - an SO(10) x S4 model
• A direct link between neutrinoless double beta decay and leptogenesis in a seesaw model with $S_4$ symmetry
• An S4 model for quarks and leptons with maximal atmospheric angle
• Predictive Model of Inverted Neutrino Mass Hierarchy and Resonant Leptogenesis
• Mapping the geometry of the E6 group
• Tri-bimaximal Mixing and Cabibbo Angle in S4 Flavor Model with SUSY
• Exceptional Lie Algebras, SU(3) and Jordan Pairs Part 2: Zorn-type Representations
• Towards Minimal S4 Lepton Flavor Model
• Towards the minimal renormalizable supersymmetric $E_6$ model
• Predictive $S_4$ flavon model with ${\text{TM}}_1$ mixing and baryogenesis through leptogenesis
• Like-sign dimuon asymmetry of B0 meson and LFV in SU(5) SUSY GUT with S4 flavor symmetry
• ${\text{TM}}_1$ neutrino mixing with $\sin {\theta }_{13}=\frac{1}{\sqrt{3}}\sin \frac{\pi }{12}$