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.

21 pages, no figure

References in corpus (6)

• An SO(10) GUT Model with $S4$ Flavor Symmetry
• Grand unification of $\mu -\tau$ Symmetry
• Scaling in the Neutrino Mass Matrix
• An approach to permutation symmetry for the electroweak theory
• Neutrino masses and mixings with an S3 family permutation symmetry
• The problem of hierarchies and family replications in an extension of quantum field theory

Cited by in corpus (10)

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• Generation Symmetry and E_6 Unification
• A direct link between neutrinoless double beta decay and leptogenesis in a seesaw model with $S_4$ symmetry
• Mapping the geometry of the E6 group
• Predictive Model of Inverted Neutrino Mass Hierarchy and Resonant Leptogenesis
• 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