SO(14) as a grand unified theory

We consider a unification of the strong, weak and electromagnetic theories into a single gauge theory based on the group SO(14). In this theory, the fermions and antifermions are all placed in a single irreducible representation of SO(14). Experimental constraints on the known quarks and leptons necessarily imply the existence of exotically charged fermions (quarks with charges -4/3, +5/3 and a lepton of charge -2). Since the low energy symmetry group is not observed to be SO(14), it must be spontaneously broken. The number of symmetry breaking patterns and their possible steps are severely limited by the value of the Weinberg angle at the symmetry limit. This, plus experimental limits on the Weinberg angle (measured from the weak interactions), strong coupling constant (α/sub s/) and the proton lifetime, implies the need for intermediate symmetries. Fermion masses in the SO(14) theory are then considered. Mass relations amongst fermions are derived and used to construct the fermion mass matrices. A new mass relation is found which explains the inversion of the charge Q= +2/3 quark and charge Q= -1/3 quark masses between the first and second generations. Mass relations between exotic fermions are also found. Constraints due to parameters describing the decay of the b quark are found to impose conditions on mixing parameters of the Q= -1/3 mass matrix and on the patterns of symmetry breaking. Predictions of the model include: violation of e-μ universality in b decays and an increase of 20 units in the ratio of the e+e- → anything cross section to the e+e-→μ+μ- cross section. Our theory is also found to have no problem with the grand unified magnetic monopoles which afflict the standard models