Fundamental Fermion Interactions via Vector Bosons of Unified SU(2)⊗SU(4) Gauge Fields
Employing the fermion uniﬁcation model based on the intrinsic SU(8) symmetry of a generalized Dirac equation, we discuss the fundamental interactions under the SU(8) = SU(2) ⊗ SU(4) symmetry group. The physics involved can describe all fermions, the leptons (electron and neutrino), and the colored up and down quarks of the ﬁrst generation in the standard model (SM) by a complex SU(8) octet of Dirac spinor ﬁelds. The fermion interactions are found to be mediated by the uniﬁed SU(4) and SU(2) vector gauge boson ﬁelds, which include the photon, the gluons, and the bosons Z and W as well known from the SM, but also comprise new ones, namely three colored X bosons carrying a fractional hypercharge of ± 4/3 and transmuting leptons into quarks and vice versa. The full covariant derivative of the model is derived and discussed. The Higgs mechanism gives mass to the Z and W bosons, but also permits one to derive the mass of the colored X boson, for which depending on the choice of the values of the coupling constant, the estimates are 35 or 156 GeV, values that are well within reach of the LHC. The scalar Higgs ﬁeld can also lend masses to the fermions and ﬁx their physical values for given appropriate coupling constants to that ﬁeld.