Mass Scales in Grand Unified Theories.

Grand unified theories of the strong, weak, and electromagnetic interactions based on the gauge groups SU(5), SO(10), and E(,6) are investigated. The structure of these theories is examined and all spontaneous symmetry breakdown patterns leading to acceptable low-energy theories are tabulated. The renormalization group equations governing the energy dependence of the gauge coupling constants are used to derive limits on the mass scales corresponding to the various breakdowns; explicit expressions for the mass bounds are obtained using a one-loop approximation to the renormalization equations for all cases while limits on the masses are calculated numerically using a two-loop approximation for selected cases. The gauge theoretic interaction forms and the values for mass scales derived from renormalization are used to estimate the rates for new physical processes allowed in these theories, especially nucleon decay. A relation between the coupling constants of the grand unification subgroups and the electromagnetic charge necessary for the renormalization program is proved along with related properties of the electromagnetic field in unified theories. An appendix considers the electroweak interactions in one SO(10) breakdown scheme as an example of the richer weak interaction structure possible in grand unified theories based on groups larger than SU(5).