SO(14) as a grand unification group and the need for intermediate symmetries

Unification of all the known fermions and antifermions into a single irreducible representation leads to SO(14) as a minimal grand unification group. The number of patterns and steps in the symmetry-breaking schemes is severely limited by the value of the Weinberg angle at the symmetry limit (sin2thetasub(sym) = 3/20). This, plus experimental limits on the Weinberg angle, on αsub(s) (the strong coupling constant) and the proton lifetime, implies the need for an intermediate symmetry which is either SUsub(c)(4) x SUsub(f)(3) or SUsub(c)(4) x SOsub(f)(6). These symmetries must be broken at relatively low energies (values less than 104GeV). There exist some (but not many) possibilities of 'filling the desert' both above and below this intermediate symmetry. The spectrum of fermions is (apart from Majorana neutrinos) the same as that introduced previously. This was based on SU(7), a subgroup of SO(14). Exotic quarks of charge - 4/3 and 5/3 and an exotic lepton of charge - 2 are required. Their existence leads to an increase in the R value in e+e-collisions by 20 units by the time centre-of-mass (CM) energies of the order 200 GeV are reached. (author)