Semisimple unified gauge theories of strong, weak, and electromagnetic interactions

Abstract

Unified theories of strong, weak, and electromagnetic interactions, which are based on simple groups, require large unification energies on the order of 10/sup 9/ to 10/sup 1/7 GeV. This paper describes a new type of semisimple model in which the unification occurs at energies as low as 10/sup 3/ GeV. Most gauge models for a group C x F have two coupling constants which cannot be related without destroying renormalizability. In this work a computer is used to look at millions of different models for various C x F and fermion representations. The machine picks out those models which are compatible with the existence of any renormalizable coupling-constant relation at the two-loop level. A small number of such theories is found. In every case the coupling-constant relation is linear and fixes the strengths of the C and F interactions so that they are inversely proportional to the size of the respective groups. Therefore, a semisimple model, which is constructed from a small C group and a large F group, will have a natural hierarchy of interaction strengths. If we embed color SU(3) in C and SU(2) x U(1) in F, this group-theoretical effect can account for much of the observedmore » difference between strong and weak interactions. Because the remaining difference can be explained by a relatively small renormalization effect, the unification energy can be small. We exhibit an SU(3) x O(11) model of this sort, in which the unification energy is 10/sup 3/ or 10/sup 4/ GeV. The theory is in agreement with the usual low-energy phenomenology and particle spectra. As the energy approaches the unification energy from below, many new leptons and O(11) gauge bosons will be produced suddenly. In this model the great strength of the strong interactions can be attributed to the fact that color SU(3) is one of the smallest Lie groups.« less