Unity of All Elementary-Particle Forces

We present a series of hypotheses and speculations leading inescapably to the conclusion that SU(5) is the gauge group of the world~hat all elementary particle forces (strong, weak, and electromagnetic) are different manifestations of the same fundamental interaction involving a single coupling strength, the fine-structure constant. Our hypotheses may be wrong and our speculations idle, but the uniqueness and simplicity of our scheme are reasons enough that it be taken seriously. Our starting point is the assumption that ueaA and electromagnetic forces are mediated by the vector bosons of a gauge-invariant theory with spontaneous symmetry breaAinI, . A model describing the interactions of leptons using the gauge group SU(2) Cg U(1) was first proposed by Glashow, and was improved by Weinberg and Salam who incorporated spontaneous symmetry breaking. ' This scheme can also describe hadrons, and is just one example of an infinite class of models compatible with observed weak-interaction phenomenology. If we assume that there are as few fermion fields as Possible and, in particular, that there are no unobserved leptons, the Weinberg model becomes unique up to extensions of the gauge group: The observed leptons may be described by six left-handed Weyl fields v,., vL', e, ', p, , ') and their charge conjugates. If the gauge couplings do not mix leptons with quarks, these six fields must transform as a representation of the gauge group: one of the 23 subgroups of U(6) containing an SU(2) ISU(1) subgroup in which the leptons behave as they do in the Weinberg model. To include hadrons in the theory, we must use the Glashow-Iliopoulos-Maiani (GIM) mechanism and introduce a fourth quark p' carrying charm. ' Still, decisions must be made: Should the quarks have fractional or integer charges? Should there be one quartet of quarks or several'P Bouchiat, Iliopoulos, and Meyer suggested what seems the most attractive alternative: three quartets of fractionally charged quarhs 'This com. bination of the GIM mechanism with the notion of colored quarks' keeps the successes of the quark model and gives an important bonus: Lepton and hadron anomalies cancel so that the theory of weak and electromagnetic interactions is renormalizable. ' The next step is to include strong interactions. We assume that strong interactions are nied~ate~ by an octet of neHtral vector gauge gluons associated with local color SU(3) symmetry, and that there are no fundamental strongly interacting scalar-meson fields. " This insures that parity and hypercharge are conserved to order z, ' and does not lead to any new anomalies, so that the theory remains renormalizable. The strongest binding forces are in color singlet states which may explain why observed hadrons lie in qqq and qq configurations. And, it gives another important bonus: Since the strong interactions are associated with a non-Abelian theory, they may be asymptotically free. Thus, we see how attractive it is for strong, weak, and electromagnetic interactions to spring from a gauge theory based on the group P = SU(3)