Running Coupling Constants and Grand Unification Models

The evolution of the gauge coupling constants in the SU (N) and SO (N) grand unification models is examined. It is shown that the three coupling constants α s , α 2 , α 1 in the minimal SU(5) model do not merge into one at 99% confidence level when they are extrapolated from the values at the mass scale M Z , whereas in its supersymmetric version, the coupling constants do merge into one within one standard deviation. In the SU (N) (with N > 5) models with a two-step symmetry breaking the coupling constants can merge into one, but these models are ruled out by the constraint imposed on the unification mass scale from the absence of proton decay. The SO (N) models with N ≥ 10 are shown to be consistent with the proton decay constraint. In particular, the unification scale for the SO(10) model is shown to be 10 15 ~10 16 GeV and the intermediate energy scale is 10 13 ~10 14 GeV .